tag:theconversation.com,2011:/nz/topics/r-number-88473/articlesR number – The Conversation2021-01-27T01:55:43Ztag:theconversation.com,2011:article/1539632021-01-27T01:55:43Z2021-01-27T01:55:43ZCOVID-19: Northland case is a reminder NZ’s ‘dumb good luck’ may run out<p>When a COVID-19 case was <a href="https://covid19.govt.nz/updates-and-resources/latest-updates/probable-community-case-of-covid-19-in-northland/">found in Northland</a> last Sunday, Aotearoa’s second-longest period with no detected community case came to an end. </p>
<p><a href="https://www.esr.cri.nz/">ESR</a> scientists worked late into Sunday night to obtain a whole genome sequence and reported Monday morning it was one of the “variants of concern” we have heard so much about since mid-December.</p>
<p>So far, close contacts of the infected woman have <a href="https://www.stuff.co.nz/national/300214166/live-dr-ashley-bloomfield-and-chris-hipkins-give-covid19-update">tested negative</a>. But this is the <a href="https://blogs.otago.ac.nz/pubhealthexpert/time-to-stop-dodging-bullets-nzs-eight-recent-border-control-failures/">ninth community incursion</a> detected since August. With a makeshift managed isolation and quarantine (MIQ) system using hotels in the country’s biggest city, rather than purpose-built facilities, further community cases have been expected. </p>
<p>And the increasing prevalence of the new variants worldwide meant it was inevitable we’d eventually see one in the community. Unless there are major improvements at the border, we can expect more cases. </p>
<h2>How concerned should we be?</h2>
<p>Briefly, there are three variants that all share a common mutation known as 501Y in the region of the genome that codes for the spike protein — the part of the virus that binds to our cells and establishes infection. </p>
<p>The three variants are most simply known as 501Y-V1 (or B.1.1.7, first detected in the UK), 501Y-V2 (B.1.351, detected in South Africa) and 501Y-V3 (P1 or B.1.1.28.1, first detected in Brazil). </p>
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<p>While the 501Y mutation has been seen multiple times in several countries, what makes these three variants of particular interest is that they are all accompanied by <a href="https://www.nytimes.com/interactive/2021/health/coronavirus-mutations-B117-variant.html">multiple other mutations</a> that are not seen together elsewhere.</p>
<p>It is thought the combined effect of these mutations helps the virus spread more quickly and potentially helps it evade parts of our immune response. Very early and incomplete evidence suggests they may pose a <a href="https://www.sciencemediacentre.org/expert-reaction-to-suggestion-made-in-downing-street-press-conference-that-the-new-uk-variant-may-be-linked-to-higher-mortality-than-the-old-variant-nervtag-paper-also-now-published/">slightly greater risk of death</a> than the original virus.</p>
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<h2>Risk of increased transmission</h2>
<p>Trying to establish whether one variant spreads faster than any other is very difficult. A huge range of factors influence viral spread and there is a lot of random chance involved. </p>
<p>Before December, there was only evidence that one variant — with spike protein mutation 614G — might have a higher rate of transmission. This is now the dominant strain worldwide. </p>
<p>But it might have achieved its current dominance by simple luck as it spread to new and fertile grounds for transmission. Scientists spent much of the last year batting down suggestions that new mutations were changing the dynamics of the pandemic.</p>
<p>Reports from the UK of 501Y-V1, the first variant of concern, changed that. Here was a variant competing with many others in the same location — and it seemed to be growing much more quickly. </p>
<h2>Winter plays a role</h2>
<p>We can think of viral transmission as a tree, new infections being branches budding off and current cases the tips of those branches. If we see 100 branches, 50 of one variant and 50 of another, grow into 200 branches, we’d expect to end up with roughly 100 of each variant. </p>
<p>Whole genome sequences of viral cases sampled across the UK let researchers construct the family tree of the virus and watch it grow. What they observed was 501Y-V1 outgrowing other variants: the split was more like 115 501Y-V1 branches and 85 of the other type. </p>
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<p>Of course, chance may also be involved here. The big factors that influence transmission are how we respond as a society through preventive measures. <a href="https://qz.com/1961313/the-coronavirus-in-winter-may-be-worse-than-scientists-thought/">Seasonal influences</a> are increasingly being recognised, too. </p>
<p>As the UK variant spread, cases rose as winter set in and students returned to education. Growth in case numbers was no surprise.</p>
<p>But the higher growth rate for 501Y-V1 has now been observed repeatedly. Estimates typically put it around 30-70% more transmissible. </p>
<p>Rapid growth has also been observed in 501Y-V2 in South Africa, and genetic similarities suggest 501Y-V3 may also share this trait. </p>
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<h2>The known unknowns</h2>
<p>We should be cautious about transferring these numbers to other environments. The UK was at a fairly high alert level, which reduced the reproduction number (or R number — the average number of people each infected person is expected to infect) to about 0.9 for the standard strain. </p>
<p>The R number for 501Y-V1 was above 1, at around 1.2 to 1.5, hence the claim it was up to 70% worse. It is not yet clear, though, whether the effect is multiplicative (meaning we multiply the observed R number by 170%), or additive (we simply add the difference between the higher and lower R numbers to make the adjustment, so up to 0.6 based on the UK data). </p>
<p>If there was an undetected outbreak in New Zealand right now, given we have very few restrictions and it is summer, R for the standard virus might be around 2. A multiplicative effect of 70% would increase R to 3.4, while an additive effect would just add the same amount — 0.6 — seen in the restricted UK environment, putting R at 2.6. </p>
<p>The difference between 2, 2.6 and 3.4 may seem small. But after four weeks of spread starting from one case it could be the difference between 30, 120 and 450 new cases. </p>
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<h2>What can NZ do now?</h2>
<p>As New Zealand moves into the cooler weather of autumn and winter, the background R number will creep up. </p>
<p>So far we have been somewhat lucky with the community cases detected since the first wave. With the notable exception of the <a href="https://www.tepunahamatatini.ac.nz/2020/10/15/aucklands-august-2020-covid-19-outbreak-cabinet-advice/">Auckland outbreak</a> in August, the index case has always been quickly identified, linked to the border, and has not been a super-spreader. </p>
<p>While many of the individual cases involved have done everything right in getting tested early, at some point our “<a href="https://www.rnz.co.nz/national/programmes/checkpoint/audio/2018781065/dumb-good-luck-no-outbreak-after-covid-19-community-case-health-expert">dumb good luck</a>” may run out, with a case triggering a super-spreading event. </p>
<p>It has been estimated that around 15-20% of cases are <a href="https://www.pnas.org/content/117/47/29416">super-spreaders</a> and these cause 70-90% of infections. Seeing one major outbreak from nine border incursions tallies with these estimates.</p>
<p>The most obvious and cheapest way to reduce the risk of a rapid outbreak would be to reduce the number of people returning from high-risk countries (though not necessarily the number of people overall). </p>
<p>We can also reduce the chance of super-spreading events by adding extra post-quarantine testing requirements and having those leaving quarantine severely limit their contacts for the first week in the community.</p><img src="https://counter.theconversation.com/content/153963/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>David Welch receives funding from MBIE and HRC related to COVID work.</span></em></p>Without improvements to New Zealand’s ‘makeshift’ border quarantine system the risk of further community cases of COVID-19 variants remains high.David Welch, Senior Lecturer, University of Auckland, Waipapa Taumata RauLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1535352021-01-22T00:09:52Z2021-01-22T00:09:52ZWhy the COVID-19 variants are so dangerous and how to stop them spreading<figure><img src="https://images.theconversation.com/files/380092/original/file-20210121-13-1s85zfk.jpg?ixlib=rb-1.1.0&rect=198%2C162%2C5808%2C3701&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Shutterstock/Lakeview Images</span></span></figcaption></figure><p>With new, more infectious <a href="https://theconversation.com/what-you-need-to-know-about-the-new-covid-19-variants-153366">variants of COVID-19</a> detected around the world, and at New Zealand’s border, the risk of further level 3 or 4 lockdowns is increased if those viruses get into the community.</p>
<p>These include a variant called <a href="https://www.nytimes.com/interactive/2021/health/coronavirus-mutations-B117-variant.html">B.1.1.7</a> that has spread very quickly within the UK, with other new variants now observed in <a href="https://www.bbc.com/news/health-55534727">South Africa</a> and <a href="https://www.reuters.com/article/us-health-coronavirus-japan-variant/new-coronavirus-variant-found-in-travellers-from-brazil-japan-government-idUSKBN29F08R">Brazil</a>. </p>
<p>Changes in the genetic code of viruses like COVID-19 occur all the time but most of these mutations don’t have any effect on how the disease spreads or its severity.</p>
<p>These changes can be useful because they leave a signature in the virus’s genetic code that allows us to <a href="https://www.stuff.co.nz/national/health/coronavirus/123388632/covid19-new-community-case-directly-genomically-linked-to-defence-force-worker">trace how the virus has spread</a> from one person to another.</p>
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<p>But the new variant detected in the UK is <a href="https://www.theguardian.com/uk-news/2021/jan/11/the-new-uk-covid-variant-your-questions-answered">more transmissible</a> than the original virus that was dominant in 2020. That means it spreads more easily from one person to another.</p>
<p>The good news is it <a href="https://www.cdc.gov/coronavirus/2019-ncov/more/science-and-research/scientific-brief-emerging-variants.html">does not cause more severe illness</a> or have a higher fatality rate than the original variant. Evidence so far suggests <a href="https://www.biorxiv.org/content/10.1101/2021.01.18.426984v1" title="Neutralization of SARS-CoV-2 lineage B.1.1.7 pseudovirus by BNT162b2 vaccine-elicited human sera">vaccines will still be effective</a> against it. </p>
<p>But the bad news is because it spreads more easily, it has the potential to infect many more people, causing more hospitalisations and deaths as a result. </p>
<h2>Why variants that spread more easily are so dangerous</h2>
<p>The average number of people an infected person with COVID-19 passes the virus on to — the so-called R number — is 40%-70% higher with B.1.1.7 than the original variant.</p>
<p>As the graph below shows, the mathematics of exponential growth means that even a small increase in the transmission rate gets compounded over time, quickly generating enormous growth in the number of cases.</p>
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<p>A variant like B.1.1.7 with a higher transmission rate is actually more dangerous than one with a higher fatality rate.</p>
<p>Sure, a 50% increase in the fatality rate would cause 50% more deaths. But because of exponential growth, shown in the graph, a 50% increase in transmissibility causes 25 times more cases in just a couple of months if left unchecked.</p>
<p>That would lead to 25 times more deaths at the original mortality rate.</p>
<h2>How do we know the new variant is more transmissible?</h2>
<p>The number of <a href="https://www.statnews.com/2021/01/14/more-infectious-variants-could-make-things-much-worse/">cases of the B.1.1.7</a> variant has risen rapidly relative to the original variant.</p>
<p>This can happen for a number of reasons. The new variant might simply happen to be present in a part of the country or group of people who are spreading the virus more rapidly for some other reason.</p>
<p>It could have become resistant to immunity, meaning it could more easily re-infect people who have already had COVID-19. Or it might cause people to become infectious more quickly. </p>
<p>Researchers in the UK used <a href="https://cmmid.github.io/topics/covid19/uk-novel-variant.html">mathematical models</a> to test these hypotheses. </p>
<p>They found the explanation that fitted best with the data was that the new variant really is more transmissible. And they estimated a person with the new variant infects 56% more people on average than a person with the original variant. </p>
<p><a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/950823/Variant_of_Concern_VOC_202012_01_Technical_Briefing_3_-_England.pdf">Contact tracing data</a> from the UK also showed more of the close contacts of someone with the new variant go on to be infected.</p>
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<a href="https://images.theconversation.com/files/379903/original/file-20210121-19-16smdsy.jpg?ixlib=rb-1.1.0&rect=215%2C130%2C3515%2C2055&q=45&auto=format&w=1000&fit=clip"><img alt="A sign at an airport saying flights from UK cancelled after new COVID-19 variant discovered," src="https://images.theconversation.com/files/379903/original/file-20210121-19-16smdsy.jpg?ixlib=rb-1.1.0&rect=215%2C130%2C3515%2C2055&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/379903/original/file-20210121-19-16smdsy.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=365&fit=crop&dpr=1 600w, https://images.theconversation.com/files/379903/original/file-20210121-19-16smdsy.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=365&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/379903/original/file-20210121-19-16smdsy.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=365&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/379903/original/file-20210121-19-16smdsy.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=459&fit=crop&dpr=1 754w, https://images.theconversation.com/files/379903/original/file-20210121-19-16smdsy.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=459&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/379903/original/file-20210121-19-16smdsy.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=459&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
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<span class="caption">Some countries cancelled flights from the UK over fears of the new COVID strain.</span>
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<p>Patients with the new variant have also been found to carry <a href="https://www.medrxiv.org/content/10.1101/2020.12.24.20248834v1" title="S-variant SARS-CoV-2 is associated with significantly higher viral loads in samples tested by ThermoFisher TaqPath RT-QPCR">more of the virus</a>. Together, this provides strong evidence the B.1.1.7 variant is between 40% and 70% more transmissible than the original variant. </p>
<p>The variants found in South Africa and Brazil <a href="https://www.cdc.gov/coronavirus/2019-ncov/more/science-and-research/scientific-brief-emerging-variants.html">share some of the same mutations</a> as the B.1.1.7 variant. There is some evidence they <a href="https://cmmid.github.io/topics/covid19/sa-novel-variant.html">may also be more transmissible</a> or better able to <a href="https://www.sciencemag.org/news/2021/01/new-coronavirus-variants-could-cause-more-reinfections-require-updated-vaccines">evade immunity</a>.</p>
<p>But there is more uncertainty about these variants, partly because the data quality isn’t as high as in the UK, which is <a href="https://www.cogconsortium.uk/">very good at doing genome sequencing</a>.</p>
<h2>What does this mean for New Zealand’s border controls?</h2>
<p>The new variants have been detected in <a href="https://www.theguardian.com/world/ng-interactive/2021/jan/08/which-countries-have-reported-new-uk-covid-variant">many countries</a>, including in people in <a href="https://www.stuff.co.nz/national/health/coronavirus/300201729/covid19-health-officials-confirm-31-new-cases-of-coronavirus-first-case-of-south-african-variant-found">New Zealand’s managed isolation facilities</a>. </p>
<p>There have previously been several cases of <a href="https://www.nzherald.co.nz/nz/covid-19-coronavirus-25-in-isolation-after-auckland-quarantine-worker-case/PSHJFO2VSNNI56FDPVUWULM4RY/">people working in these facilities picking up infections</a> from recent arrivals.</p>
<p>The more transmissible variants arriving at the New Zealand border increase the risks to these workers, who in turn have a higher chance of passing the virus onto others in the community, amplifying the risk of a community outbreak.</p>
<p>In response, the government says <a href="https://www.stuff.co.nz/travel/news/123988930/covid19-predeparture-test-extended-to-all-passengers-from-next-week">international arrivals will require a negative test</a> in the 72 hours prior to departure. They will also be required to take an arrival day test when they get to New Zealand. </p>
<p>These measures provide an <a href="https://thespinoff.co.nz/science/22-10-2020/siouxsie-wiles-toby-morris-covid-19-and-the-swiss-cheese-system/">extra layer</a> in our defences against COVID-19.</p>
<h2>How can we manage the risk?</h2>
<p>The new variants spread in the same way as the original one: through close contacts between people, especially in <a href="https://www.japantimes.co.jp/news/2020/06/27/national/japanese-cluster-study-3cs-warning-coronavirus/">crowded or poorly ventilated environments</a>.</p>
<p>This means all the tools we have developed to fight the virus will still work. These include testing, contact tracing, masks and physical distancing.</p>
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<figcaption><span class="caption">How face masks make a difference.</span></figcaption>
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<p>But any variant that is more transmissible has a higher R number. To control an outbreak, we need to bring the R number under 1 and so we may need to use more of these tools to achieve this.</p>
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<a href="https://theconversation.com/with-covid-19-mutating-and-surging-nz-urgently-needs-to-tighten-border-controls-153078">With COVID-19 mutating and surging, NZ urgently needs to tighten border controls</a>
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<p>For example, in the <a href="https://theconversation.com/aucklands-rapid-lockdown-has-given-new-zealand-a-better-chance-of-eliminating-coronavirus-again-145011">Auckland outbreak</a> in August 2020, alert level 3 was enough to contain and eventually eliminate the outbreak. <a href="https://www.tepunahamatatini.ac.nz/2020/10/15/aucklands-august-2020-covid-19-outbreak-cabinet-advice/">Our analysis</a> showed alert level 3 reduced R to about 0.7.</p>
<p>If we had a similar outbreak with the new variant, R could be 50% higher which would mean it is above 1. In other words, we would likely need to use alert level 4 to contain an outbreak, and it might take longer to eliminate the virus than it has previously.</p>
<p>To give our contact tracers the best possible chance of containing a new outbreak without needing alert level 3 or 4, we all need do our bit. This means looking for QR codes when out about and using the app to scan them, as well as <a href="https://covid19.govt.nz/health-and-wellbeing/protect-yourself-and-others/keep-track-of-where-youve-been/nz-covid-tracer-app/">turning on Bluetooth</a>. And it means staying at home and getting tested if you feel sick.</p><img src="https://counter.theconversation.com/content/153535/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Michael Plank is affiliated with the University of Canterbury and receives funding from the Ministry of Business, Innovation and Employment (MBIE) and Te Pūnaha Matatini, New Zealand's Centre of Research Excellence in complex systems. </span></em></p><p class="fine-print"><em><span>Shaun Hendy is affiliated with the University of Auckland and receives funding from the Ministry of Business, Innovation and Employment (MBIE) and Te Pūnaha Matatini, New Zealand's Centre of Research Excellence in complex systems.</span></em></p>A variant with a higher transmission rate is much more dangerous than one with just a higher fatality rate.Michael Plank, Professor in Applied Mathematics, University of CanterburyShaun Hendy, Professor of Physics, University of Auckland, Waipapa Taumata RauLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1528632021-01-21T13:21:19Z2021-01-21T13:21:19ZCoronavirus variants: why being more transmissible rather than more deadly isn’t good news<figure><img src="https://images.theconversation.com/files/379946/original/file-20210121-21-ba0h1m.jpg?ixlib=rb-1.1.0&rect=5%2C0%2C3484%2C1791&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-vector/vector-coronavirus-2019ncov-virus-background-disease-1660181482">Fotomay/Shutterstock</a></span></figcaption></figure><p>Every time the coronavirus replicates, it has a chance to mutate. And given that it is currently rampaging around the world, it has plenty of opportunities to do just that. </p>
<p>Many mutations will make little or no difference to the virus’s ability to spread or cause more severe disease. Others will make it less likely to spread – those mutations are more likely to die out. But some will make the virus more deadly or more transmissible. These are the mutations we need to worry about. </p>
<p>On the afternoon of Friday 18, December, the UK government was alerted to the possibility that a new variant of the coronavirus circulating in the UK was <a href="https://khub.net/documents/135939561/338928724/SARS-CoV-2+variant+under+investigation%2C+meeting+minutes.pdf/962e866b-161f-2fd5-1030-32b6ab467896?t=1608470511452">70% more transmissible</a> than previously dominant variants.</p>
<p>Without any control measures (such as social distancing or wearing a mask), in a wholly susceptible population each person newly infected with the previously dominant variant of the virus would pass it on to three others (<a href="https://theconversation.com/how-to-model-a-pandemic-134187">known as the basic reproduction number or R0</a>). With a 70% increase in transmissibility, the number of people each person might infect, in the absence of control measures, increases to around five. </p>
<p>Fortunately, we have taken preventative measures to reduce the reproduction number (R) and slow the spread of the virus. However, even if these control measures were enough to reduce the previous variant’s R to 1 (the critical value below which infections start to fall), they would only reduce the new variant’s R to 1.7. Every ten people infected would infect 17 others and infections would spread <a href="https://theconversation.com/coronavirus-is-growing-exponentially-heres-what-that-really-means-134591">exponentially</a>.</p>
<p>In short, this increased transmissibility looked like really bad news. The hard lockdown the UK undertook last spring was thought to be enough to reduce R for the old variant to around 0.6. A 70% increase in transmissibility would mean that it was questionable whether even restrictions as tight as the ones the UK implemented in the spring of 2020 would be enough to suppress the spread of the new variant.</p>
<p>As more has become known, this estimate of increased transmissibility has begun to be revised down. A <a href="https://www.lshtm.ac.uk/newsevents/news/2021/new-modelling-estimates-potential-impact-new-covid-19-strain">follow-up study</a> from researchers at the London School of Hygiene and Tropical Medicine – which is yet to be published in a scientific journal – suggested that the variant might be between 50-70% more transmissible. A more recent investigation from <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/950823/Variant_of_Concern_VOC_202012_01_Technical_Briefing_3_-_England.pdf?utm_source=newsletter&utm_medium=email&utm_campaign=newsletter_axiosvitals&stream=topp;stream=top">Public Health England</a> suggested that the variant may only be between 30-50% more transmissible. This might explain why the UK’s current lockdown, which is less stringent than the first lockdown, has been enough to bring cases of this more transmissible variant down. Whatever the exact figure, there is little doubt that the new variant is significantly more transmissible.</p>
<h2>Variants of concern</h2>
<p>As new variants (particularly B117) take hold in <a href="https://www.bmj.com/content/372/bmj.n158">countries around the world</a>, there are three things we should be worried about: first, whether the new variants are more transmissible; second, whether they are more deadly, and third, whether they are able to evade the COVID vaccines that are currently being rolled out.</p>
<p>There is no evidence to suggest that the UK variant makes any of the approved vaccines less effective, (although there is reason to believe the new South African variant may render existing immunity <a href="https://gizmodo.com/south-african-coronavirus-variant-may-dodge-existing-im-1846085738">less effective</a>). </p>
<p>Indeed, news of the increased transmissibility of the new variant is often accompanied by a seemingly reassuring mention that the variant is <a href="https://www.reuters.com/article/us-health-coronavirus-britain-strain/uk-says-new-coronavirus-strain-is-more-infectious-but-vaccines-should-still-work-idUSKBN28T0TU">not more deadly</a>. Many news outlets have cited the <a href="https://www.telegraph.co.uk/global-health/science-and-disease/could-sars-cov-2-evolving-become-transmissible-less-lethal">“law of declining virulence”</a>, which suggests that a more transmissible variant will be associated with milder illness. The idea behind the theory is that viruses that evolve to be more deadly will wipe out their host before being passed on, limiting chains of transmission and causing the variant to die out. </p>
<p>Unfortunately, given the long infectious period of COVID-19, the potential for asymptomatic transmission, and the length of time between infection and death, there is no reason why this rule of thumb should hold. But given that we have a more transmissible variant that does not appear to be more deadly, should we be happier about this than if it were the other way around?</p>
<p>In fact, even a 30% more transmissible variant can be way worse than a variant that is 30% more deadly. At the heart of this counter-intuitive assertion lies an old foe that has plagued us right from the start of this pandemic: <a href="https://theconversation.com/coronavirus-is-growing-exponentially-heres-what-that-really-means-134591">exponential growth</a>. Here’s a simple thought experiment that helps to explain why.</p>
<p>Imagine the old variant spreading under measures that have reduced R to 1. Starting with 10,000 infected people, every generation interval (time becoming infected and infecting someone else) they will infect 10,000 more. Of everyone that gets infected, let’s assume that 1% of them will die. After ten generations, 100,000 new infections will have occurred leading to 1,000 deaths. </p>
<p>With a variant that is 30% more deadly, the same number of infections will occur, but they will lead to 1,300 deaths. Yet with a variant that is 30% more transmissible but not more deadly, because cases will grow exponentially, the eventual death toll over the same period stretches to over 4,200. The longer this goes on for, the bigger the death toll discrepancy between the more transmissible and the more deadly strain becomes.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/379639/original/file-20210119-13-1i4fn6n.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/379639/original/file-20210119-13-1i4fn6n.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/379639/original/file-20210119-13-1i4fn6n.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=361&fit=crop&dpr=1 600w, https://images.theconversation.com/files/379639/original/file-20210119-13-1i4fn6n.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=361&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/379639/original/file-20210119-13-1i4fn6n.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=361&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/379639/original/file-20210119-13-1i4fn6n.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=453&fit=crop&dpr=1 754w, https://images.theconversation.com/files/379639/original/file-20210119-13-1i4fn6n.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=453&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/379639/original/file-20210119-13-1i4fn6n.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=453&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A hypothetical scenario demonstrates that the total number of deaths from a 30% transmissible variant significantly outweighs the number of deaths from a variant that is 30% more deadly.</span>
</figcaption>
</figure>
<p>While the above scenario is not intended to be completely realistic, it illustrates that a change in the rate at which the disease spreads exponentially can have a far more significant impact than the rate at which it kills. We shouldn’t take comfort when we hear of the emergence of new variants that are <a href="https://www.reuters.com/article/us-health-coronavirus-britain-strain/uk-says-new-coronavirus-strain-is-more-infectious-but-vaccines-should-still-work-idUSKBN28T0TU">“more transmissible, but no more deadly”</a>.</p><img src="https://counter.theconversation.com/content/152863/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Christian Yates does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>A virus that is 30% more transmissible is more deadly than a virus that is 30% more deadly. Counter-intuitive but true.Christian Yates, Senior Lecturer in Mathematical Biology, University of BathLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1530252021-01-15T16:02:05Z2021-01-15T16:02:05ZMutating coronavirus: reaching herd immunity just got harder, but there is still hope<figure><img src="https://images.theconversation.com/files/378616/original/file-20210113-19-1srkvf7.jpg?ixlib=rb-1.1.0&rect=0%2C7%2C4720%2C2710&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-illustration/coronavirus-covid19-under-microscope-3d-illustration-1643947495">Andrii Vodolazhskyi/Shutterstock</a></span></figcaption></figure><p>A year after the <a href="https://theconversation.com/one-year-since-we-first-reported-on-this-coronavirus-what-weve-learned-and-still-need-to-know-152762">first cases</a> of COVID-19 were found in China, <a href="https://www.theatlantic.com/health/archive/2020/11/vaccines-end-covid-19-pandemic-sight/617141/?utm_source=pocket-newtab-global-en-GB">mass vaccination programmes</a> are now offering a chance to end the pandemic. At the same time, <a href="https://www.vox.com/22213033/covid-19-mutation-variant-vaccine-uk-south-africa">new strains</a>, some of which appear to be more infectious than the original one, are threatening to <a href="https://www.bbc.co.uk/news/live/world-55673006">derail progress</a> in fighting the disease. </p>
<p>One way to capture the effectiveness of our effort to fight the virus is to consider the concept of <a href="https://theconversation.com/herd-immunity-why-the-figure-is-always-a-bit-vague-141839">“herd immunity”</a>. During an epidemic, people become infected and those who survive usually become immune. Resistance to the disease can also be reached by vaccination, which complements the levels of natural immunity. Infected people increasingly come into contact with immune people rather than those who are still susceptible. Like a forest fire that runs out of dry wood, at the point of reaching herd immunity, the epidemic stops growing and starts to decline.</p>
<p><a href="https://www.theguardian.com/commentisfree/2021/jan/04/covid-model-epidemic-collaboration-experiment">Mathematical models</a> help us relate herd immunity levels to how fast the disease spreads. The percentage of immune people needed to create herd immunity <a href="https://ccdd.hsph.harvard.edu/2020/12/17/covid-19-vaccines-and-herd-immunity/">depends</a> on the <a href="https://www.bbc.co.uk/news/health-52473523">reproductive number</a>, R, which is a measure of how many people each infected person will infect on average. We can reach herd immunity either by waiting long enough so that large parts of the society pass through infection, by reducing the value of R using social distancing forever, or by vaccinating enough people.</p>
<p>Letting the epidemic <a href="https://science.sciencemag.org/content/371/6526/230">run unchecked</a> threatens to overload the health system and will result in many deaths. Conversely, lockdowns are causing economic, social and mental health issues. So we hope <a href="https://theconversation.com/how-will-vaccines-affect-the-length-of-englands-lockdown-152714">vaccines</a> will stop the epidemic more effectively. </p>
<p>But how many people will <a href="https://ccdd.hsph.harvard.edu/2020/12/17/covid-19-vaccines-and-herd-immunity/">need to be vaccinated</a> to stop the disease spreading? This depends on how infectious the viral strain is, how effective the vaccine is, and how much we are prepared to continue with lockdown measures. The model predictions for the success of the vaccination programmes depend on the vaccine being able to limit the transmission of the virus – not just stop people getting ill. But we still <a href="https://news.sky.com/story/covid-19-do-the-vaccines-stop-transmission-how-can-i-volunteer-to-help-your-questions-answered-12183087">don’t know</a> if the current batch of approved COVID vaccines stops transmission. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/378411/original/file-20210112-15-94zai7.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Scenarios for vaccine coverage" src="https://images.theconversation.com/files/378411/original/file-20210112-15-94zai7.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/378411/original/file-20210112-15-94zai7.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=519&fit=crop&dpr=1 600w, https://images.theconversation.com/files/378411/original/file-20210112-15-94zai7.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=519&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/378411/original/file-20210112-15-94zai7.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=519&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/378411/original/file-20210112-15-94zai7.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=652&fit=crop&dpr=1 754w, https://images.theconversation.com/files/378411/original/file-20210112-15-94zai7.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=652&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/378411/original/file-20210112-15-94zai7.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=652&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Critical vaccination levels depend on the estimated effective reproductive number, with the vaccine efficiency of 90%.</span>
<span class="attribution"><span class="source">Adam Kleczkowski</span></span>
</figcaption>
</figure>
<p>We could continue with very strict social distancing indefinitely, bringing R below 1 so that the number of new infections decreases. In this case, we would not need any vaccination (point marked A on the graph). But the moment control measures were relaxed, R would jump back above 1 and the epidemic would start to spread again. </p>
<p>Or we could <a href="https://theconversation.com/back-to-normal-by-spring-are-we-expecting-too-much-from-the-first-covid-19-vaccines-149342">combine some level of lockdown</a> with the roll out of vaccines. In this scenario (point marked B on the graph) we would see a decline in cases once 40% of the population were immune to the virus. However, this strategy relies on keeping R just above 1. The disease would probably come back as soon as further relaxation occurred.</p>
<p>As we want to return to our activities and freedoms without social distancing, the vaccination levels need to be much higher, taking into account how fast the virus can spread with no additional control. </p>
<p>A reliable estimate of the rate of spread of the first variant of SARS-CoV-2, during the first stages of the epidemic, is R=3. In other words, every person infected with the coronavirus passes it on to three other people, on average. The corresponding herd immunity level for this value of R is 67%, so assuming a vaccine efficacy of 90%, we need to vaccinate <a href="https://ccdd.hsph.harvard.edu/2020/12/17/covid-19-vaccines-and-herd-immunity/">74% of the population</a> (point marked C) to stop the virus from advancing further. </p>
<p>How does the emergence of the new variants change this value? We do not know for sure how fast the new strains would have spread if allowed to do so without any mitigation measures. The evidence suggests that the UK strain is <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/950823/Variant_of_Concern_VOC_202012_01_Technical_Briefing_3_-_England.pdf">30-50%</a>, and maybe <a href="https://www.bmj.com/content/371/bmj.m4944">as much as 70%</a>, more infectious than the original one. Choosing the <a href="https://www.forbes.com/sites/carlieporterfield/2020/12/24/new-coronavirus-strain-is-56-more-infectious-scientists-estimate/">value of 50%</a>, the needed vaccination levels are pushed up to 86% (point marked D). </p>
<p>An even higher proportion will need to be immunised if we want to push the virus towards eradication or to guard against a potential underestimation of the rate of spread.</p>
<p>Can such high levels of protection <a href="https://www.ft.com/content/8def3a81-9b80-46a1-9742-f64b80bfc74f">be attained at all</a>? If a vaccine is only 50-70% effective, as the Oxford and Sinovac vaccines appear to be, this is the highest herd immunity level that can be achieved, if everybody gets the vaccine. Even with the higher efficacy of the Pfizer and Moderna vaccines, vaccinating nearly 90% of the population will be very difficult, as not everybody can or will want to be treated. </p>
<p>On the positive side, a previous COVID infection still provides <a href="https://www.gov.uk/government/news/past-covid-19-infection-provides-some-immunity-but-people-may-still-carry-and-transmit-virus">good protection</a> against reinfections and so we can probably count on nearly 20% of the population having natural immunity. </p>
<p>The herd immunity levels depend on R values and we can, to some extent, manipulate them by lockdowns. If countries can keep R reduced to just above 1, eradication can be achieved even with smaller vaccination levels. But what is really needed is a coherent <a href="https://theconversation.com/vaccines-alone-arent-enough-to-eradicate-a-virus-lessons-from-history-152734">long-term plan</a>: one that includes both quick vaccination roll out and continuing social distancing and testing.</p><img src="https://counter.theconversation.com/content/153025/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Adam Kleczkowski has received funding from BBSRC, NSF, Academy of Medical Sciences, and the Scottish Government.</span></em></p>New variants will push the number needed to reach herd immunity up.Adam Kleczkowski, Professor of Mathematics and Statistics, University of Strathclyde Licensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1464352020-10-12T14:24:17Z2020-10-12T14:24:17ZCOVID-19 will probably become endemic – here’s what that means<p>We can’t say with any certainty what the future of COVID-19 is. But based on our experience with other infections, there is little reason to believe that the coronavirus SARS-CoV-2 will go away any time soon, even when vaccines become available. A more realistic scenario is that it will be added to the (large and growing) family of infectious diseases that are what is known as “endemic” in the human population. </p>
<p>With the worldwide spread of the disease increasing again, it seems unlikely that the currently available measures can do more than bring that spread under control – except in countries that can effectively isolate themselves from the outside world. The fact that the vast majority of people are still susceptible to some degree means that there is sufficient fuel for the fire to keep burning for quite some time.</p>
<p>This will be the case even if specific locations reach what is known as population (or herd) immunity (and <a href="https://theconversation.com/coronavirus-what-will-happen-if-we-cant-produce-a-vaccine-144307">it’s not clear</a> how likely this is to happen). When a sufficient number of people become immune to a disease, either through vaccination or natural infection, its spread starts to slow down and the number of cases gradually decreases. But that doesn’t mean it will disappear instantly or completely.</p>
<p>Outside any areas with population immunity, there are likely to be plenty of locations that still have enough susceptible individuals to keep transmission going. No measure of isolation is so strong that it will completely stop human interaction between regions, within and between countries, or globally.</p>
<p>It’s also possible that the spread of an infection will eventually stabilise at a constant level so that it becomes present in communities at all times, possibly at a relatively low, sometimes predictable rate. This is what we mean when we say <a href="https://www.verywellhealth.com/what-is-an-endemic-disease-3132825">a disease is endemic</a>. </p>
<p>Some infections are present and actively spreading almost everywhere (such as many sexually transmitted infections and childhood infections). But most infections are endemic in specific parts of the world. </p>
<p>This can occur when effective control has eliminated the infection elsewhere, or because the conditions needed for effective transmission can only be found in specific locations. This is the case for malaria and many other infections transmitted by mosquitoes.</p>
<figure class="align-center ">
<img alt="Silhouette of mosquito on human skin." src="https://images.theconversation.com/files/362954/original/file-20201012-21-odsih9.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/362954/original/file-20201012-21-odsih9.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/362954/original/file-20201012-21-odsih9.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/362954/original/file-20201012-21-odsih9.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/362954/original/file-20201012-21-odsih9.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/362954/original/file-20201012-21-odsih9.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/362954/original/file-20201012-21-odsih9.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Malaria is endemic in many countries.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/mosquito-on-human-skin-sunset-200494427">Mycteria/Shutterstock</a></span>
</figcaption>
</figure>
<p>Theoretically speaking, an infection becomes endemic if on average each infected individual transmits it to one other person. In other words, when the <a href="https://theconversation.com/how-to-model-a-pandemic-134187">reproduction number</a> (R) = 1. In comparison, during an epidemic when the spread of the disease is increasing, R is more than 1, and when the spread is decreasing through control measures or population immunity, R is less than 1.</p>
<p>In practice, there are a number of patterns that can be observed in endemic diseases. Some can exist at low levels throughout the year, while others might show periods of higher transmission interspersed with periods of low transmission. This might happen if seasonal factors influence how much contact people have with one another, how susceptible they are to the disease, or other organisms that spread it such as insects.</p>
<p>As long as there is a sufficient supply of people still susceptible to the disease for each infected person to pass it on to, it will continue to spread. This supply can be replenished in various ways, depending on the characteristics of the disease. </p>
<h2>Waning immunity</h2>
<p>In diseases that give permanent immunity after infection, each new child born is susceptible after the immunity obtained from the mother wears off. This is why childhood infections such as measles are endemic in many parts of the world where the birth rate is high enough.</p>
<p>In diseases that only give temporary immunity through natural infection, people lose that immune protection to become susceptible again. A virus or bacteria can also evade the immune memory by mutation so that people with immunity to an older strain will become susceptible to the new version of the disease. Influenza is a <a href="https://www.cdc.gov/flu/about/viruses/change.htm">prime example</a>.</p>
<p>We don’t yet know how long immunity from infection from COVID-19 will last, or how good vaccines will be at protecting people. But other coronaviruses that are endemic in the human population, such as those that cause colds, only confer temporary immunity of <a href="https://www.nature.com/articles/s41591-020-1083-1">about one year</a>.</p>
<p>Another important point is that people with immunity, whether from infection or vaccination, are rarely evenly distributed throughout a community or country, let alone the world. Certainly in the case of COVID-19, there are areas where the infection has spread more intensively and areas that have been relatively spared. Without even distribution, there is no population immunity even if enough people have been vaccinated to meet the predicted necessary threshold.</p>
<p>In these cases, the average R can be low enough that the infection is under control, but in the unprotected pockets it will be well above 1. This leads to localised outbreaks and allows the disease to remain endemic. It continues to spread from place to place, seeded by a few locations where population density and interaction are high enough, and protection low enough, to sustain transmission.</p>
<h2>How we respond</h2>
<p>How we deal with COVID-19 once it becomes endemic will depend on how good our vaccines and treatments are. If they can protect people from the most severe outcomes, the infection will become manageable. COVID-19 will then be like several other diseases that we have learned to live with and many people will experience during their lives. </p>
<p>Depending on whether immunity – either from natural infection or from vaccination – is permanent or temporary, we may need yearly <a href="https://theconversation.com/a-coronavirus-vaccine-may-require-boosters-heres-what-that-means-143370">vaccine updates</a> to protect us (like influenza). Or it could be controlled by vaccination at some optimal age (like many childhood infections). </p>
<p>If vaccines not only prevent clinical disease but also strongly reduce transmission and confer long-lasting immunity, we can envisage other scenarios, such as the potential eradication of the disease. But realistically this is unlikely. Eradication is notoriously difficult, even for diseases for which we have almost perfect vaccines and permanent immunity. Endemic disease is therefore the most likely outcome.</p><img src="https://counter.theconversation.com/content/146435/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Hans Heesterbeek currently receives funding from the Netherlands Organization for Medical Research (ZonMw) and the Netherlands Organisation for Scientific Research (NWO). His main funding is from his employer Utrecht University.</span></em></p>Even if some places reach herd immunity, the virus is unlikely to disappear.Hans Heesterbeek, Professor of Theoretical Epidemiology, Utrecht UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1472882020-10-12T14:23:42Z2020-10-12T14:23:42ZCoronavirus: R number does not measure risk – financial disaster modelling offers a better alternative<p>The most important measure on the state of the pandemic is the R number. Also known as the reproduction rate, this is the average number of people an infected person will pass the virus on to. The R number guides government decisions, and there is no doubt it is a very intuitive way to measure the state of the pandemic. </p>
<p>However, the R number has come in for <a href="https://theconversation.com/is-the-k-number-the-new-r-number-what-you-need-to-know-140286">much criticism</a> because it is an average, meaning it ignores useful information about individuals and therefore does not account for uncertainty. This includes the fact that there is a sizeable variation in the incubation time of the virus and a large number of infected but asymptomatic people who are hard to detect, plus superspreaders who infect many more people than the average. </p>
<p>To better estimate the threat to our populations from the virus, governments should look to the statistical models used for financial markets. I say this because the public health shares an important characteristic with financial markets: they are both made up of many interacting parts that can be exposed to rare, pervasive shocks, with potentially critical consequences that can spread across borders. </p>
<h2>Tail events and downside risk</h2>
<p>The global financial crisis of 2007-09 was in many ways the financial equivalent of a pandemic. It started when a housing bubble burst in the US and quickly spread internationally through the complex system that existed for trading mortgage debt between financial institutions. This led to everything from banking collapses to national debt defaults to the great recession. </p>
<p>To try to prevent such a catastrophe happening again, the global financial system developed a regulatory system for stress testing banks and the investment portfolios of major firms. These tests assess the fragility of banks and investment portfolios and improve their immunity to shocks by asking questions such as, “how much could they lose from a rare event?” and “how severe must that shock be before the bank would collapse?” </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/361082/original/file-20201001-21-1s32nac.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Piggy bank with knife sawing under it" src="https://images.theconversation.com/files/361082/original/file-20201001-21-1s32nac.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/361082/original/file-20201001-21-1s32nac.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=515&fit=crop&dpr=1 600w, https://images.theconversation.com/files/361082/original/file-20201001-21-1s32nac.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=515&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/361082/original/file-20201001-21-1s32nac.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=515&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/361082/original/file-20201001-21-1s32nac.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=648&fit=crop&dpr=1 754w, https://images.theconversation.com/files/361082/original/file-20201001-21-1s32nac.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=648&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/361082/original/file-20201001-21-1s32nac.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=648&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Pig in a poke.</span>
<span class="attribution"><a class="source" href="https://www.bankofengland.co.uk/-/media/boe/files/monetary-policy-report/2020/august/monetary-policy-report-august-2020">Mopic</a></span>
</figcaption>
</figure>
<p>These tests rely on financial predictive risk modelling. This technique doesn’t focus on what is expected to happen next, but rather on the probability of rare events like the ones that precipitated the 2007-09 crisis. Such outcomes are referred to as tail events because, unlike the average outcome (the “central value”), they arise from the “tail” of the distribution of probabilities. Such tests focus on tail events associated with losses, whose probability is known as the “downside risk”.</p>
<p>This modelling is also used to look at the downside risk of what might happen to the macroeconomy, which is another highly uncertain environment. For instance, how much GDP will be lost if a rare negative shock hits the financial markets. Similar techniques could be used to improve our predictions about COVID-19.</p>
<h2>Financial modelling and COVID-19</h2>
<p>To get around the problems with the R number being an average, an <a href="https://www.theatlantic.com/health/archive/2020/09/k-overlooked-variable-driving-pandemic/616548/">alternative indicator</a> known as the <a href="https://theconversation.com/is-the-k-number-the-new-r-number-what-you-need-to-know-140286">K number</a> is used alongside it when the R is very low. The K number measures the dispersion of probability around the average to show how many people are passing on infections. A higher K number means that more individuals are responsible for the observed infections, while a lower number means the virus is being spread by fewer people – in other words, superspreaders. </p>
<p>Measuring uncertainty with dispersion is also very common in economics. For example, economists produce charts that show what they estimate is the most likely to happen (the central value) and then illustrate the uncertainty as different shaded areas of other possible outcomes that fan out from the main area. The Bank of England has used these fan charts to predict inflation since the 1990s, for instance (see below). </p>
<p><strong>Bank of England inflation projections, August 2020</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/361080/original/file-20201001-13-9krsid.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Bank of England inflation fan chart" src="https://images.theconversation.com/files/361080/original/file-20201001-13-9krsid.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/361080/original/file-20201001-13-9krsid.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=384&fit=crop&dpr=1 600w, https://images.theconversation.com/files/361080/original/file-20201001-13-9krsid.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=384&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/361080/original/file-20201001-13-9krsid.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=384&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/361080/original/file-20201001-13-9krsid.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=483&fit=crop&dpr=1 754w, https://images.theconversation.com/files/361080/original/file-20201001-13-9krsid.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=483&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/361080/original/file-20201001-13-9krsid.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=483&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><a class="source" href="https://www.bankofengland.co.uk/-/media/boe/files/monetary-policy-report/2020/august/monetary-policy-report-august-2020">Bank of England, August 2020</a></span>
</figcaption>
</figure>
<p>Superspreaders are certainly a major issue with coronavirus. For example, the current R number in the UK <a href="https://www.gov.uk/guidance/the-r-number-in-the-uk#history">is estimated</a> to be within a range of 1.2 to 1.5 – meaning the average infected person will infect between 1.2 and 1.5 people. Yet a superspreader has been linked to <a href="https://www.bbc.co.uk/news/uk-wales-54359674">32 secondary infections</a>, and even more extreme cases have <a href="https://www.theguardian.com/us-news/2020/sep/17/maine-wedding-superspreader-event">been reported</a>.</p>
<p>But the K number’s ability to alert us to this phenomenon has two important limitations. First, it is less accurate when the R number is higher. This is because K is not able to distinguish between variation above and below the average.</p>
<p>When R is low, there can’t be much dispersion below average since zero is the minimum number of infections that anyone can transmit. This means that when K is showing a wide variation from the average, it must be due to superspreaders. On the other hand, when R is higher, there is more scope for below-average spreaders to explain a wide variation from the average, so K is less useful. </p>
<p>Second, even if the R is low enough, in statistics it is well known that when extreme events like superspreading are sufficiently probable, dispersion becomes a rather poor indicator of the risk associated with such tail events.</p>
<p>To get a more accurate picture of COVID-19 risk that could be used alongside the information from the R and K numbers, I would therefore argue that governments should use stress testing for adverse tail events. This would make it possible to estimate the likelihood of a particular rise in cases in a given span of time – say a twofold increase in a week. </p>
<p>And given that most cases are mild or asymptomatic, it is arguably not contagion that is the ultimate concern for society but the burden on the health system. As several countries have seen, the pandemic can overwhelm hospitals with large numbers of incoming patients – way too high for the resources available. </p>
<p>Stress testing can help measure the vulnerability of the health system by providing answers to questions such as, “how likely is it today that the available intensive-care beds, personal protective equipment and ventilators reach a critical level, say 90% of capacity?”; and “how much can contagion rise before that level is reached?”</p>
<p>After the 2007-09 financial crisis, regulators introduced stress testing to restore confidence in the banking system. With <a href="https://www.theguardian.com/world/2020/sep/24/10000-more-deaths-than-usual-occurred-in-uk-homes-since-june">fading trust</a> in the health system and people avoiding hospitals due to COVID-19 fears, a more transparent and detailed way of measuring the risks using the same kind of predictive modelling might produce similar benefits.</p><img src="https://counter.theconversation.com/content/147288/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Stefano Soccorsi does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>How the lessons learned from the global financial crisis can transform our view of COVID risk.Stefano Soccorsi, Lecturer in Financial Economics, Lancaster UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1472802020-10-02T08:43:11Z2020-10-02T08:43:11ZCoronavirus: are cases in England really slowing?<p>The latest <a href="https://www.imperial.ac.uk/media/imperial-college/institute-of-global-health-innovation/REACT1_12345_Interim-(1).pdf">REACT report</a>, the biggest regular study of COVID-19 infection rates in England, seems to provide some much-needed good news. The authors of the report suggest that a combination of national measures and local lockdowns may have played a role in slowing down the spread of the virus. </p>
<p>Daily case numbers in England are still increasing, but at a slower rate. The all-important R number may have fallen from a high of 1.7 in late August to a current value of 1.1, although there is significant uncertainty around both numbers.</p>
<p>Between September 18 and 26, the REACT researchers at Imperial College London randomly selected more than 84,000 people across the country to test. Of those swab tests, 363 came back positive, suggesting more than 400,000 infections in England. This represents roughly one in 140 people, which is a significant increase from the roughly one in 800 people found to be infectious in the previous edition of the study a month earlier. Although the deceleration of the spread is a positive step, the numbers still reflect a worryingly high prevalence of coronavirus in the community. </p>
<p>The report also highlights that virus prevalence has increased across all regions and all age groups in recent weeks. This will inevitably lead to more hospitalisations and eventually to deaths over the weeks to come.</p>
<p>It might seem counter-intuitive that R can be falling, which appears to be good news, yet the number of daily cases is still increasing, which is definitely bad news. </p>
<p>R is the number of new infections that a single infected person will pass the disease to, on average, during their infectious period. If R is above 1, then each new infection spawns at least one other and the epidemic continues to grow. R gives us a measure of how quickly the disease can spread through the population. The REACT report suggests that R has fallen from 1.7 to 1.1, which is good news, but as long as the value of R remains above one, the number of infected people will continue to increase.</p>
<p>This fall in the rate of spread is consistent with other data sources from which we can estimate the rate of growth of the epidemic. <a href="https://coronavirus.data.gov.uk/healthcare?areaType=nation&areaName=England">Hospital admissions</a>, for example, have shown a fall in the rate of growth in recent days, suggesting a reduction in the rate of transmission compared with a week or so earlier. The increases in the number of calls to NHS and emergency services have also been <a href="https://www.imperial.ac.uk/media/imperial-college/institute-of-global-health-innovation/REACT1_12345_Interim-(1).pdf">slowing in recent days</a>.</p>
<p>Much was made, at the time, of the stark projection illustrated by Sir Patrick Vallance, the government’s chief scientific adviser, at a briefing earlier in September. The apocalyptic graphic suggested that, if the current growth in cases continued, the UK could be facing <a href="https://www.bbc.co.uk/news/uk-54234084">50,000 new cases a day by mid-October</a>. However, the rise in case numbers, although significant, does not appear to support this projection – showing a slower rate of growth in line with the REACT study. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/361234/original/file-20201001-20-e4ywbv.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/361234/original/file-20201001-20-e4ywbv.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/361234/original/file-20201001-20-e4ywbv.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=338&fit=crop&dpr=1 600w, https://images.theconversation.com/files/361234/original/file-20201001-20-e4ywbv.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=338&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/361234/original/file-20201001-20-e4ywbv.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=338&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/361234/original/file-20201001-20-e4ywbv.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=424&fit=crop&dpr=1 754w, https://images.theconversation.com/files/361234/original/file-20201001-20-e4ywbv.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=424&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/361234/original/file-20201001-20-e4ywbv.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=424&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Patrick Vallance’s seven-day doubling time projection (red) doesn’t agree with what is actually happening (blue) as the rate of increase of daily cases has decreased.</span>
<span class="attribution"><span class="source">https://twitter.com/RP131</span></span>
</figcaption>
</figure>
<p>Ironically, it may have been precisely this reinforced message that contributed to the public’s renewed compliance with social distancing, hand-washing and the wearing of face coverings and had an effect on slowing the spread - a happily self-defeating prophecy.</p>
<h2>Which data?</h2>
<p>Of course, there are caveats about all data sources from which we can estimate rates of growth of the epidemic. Cases give us the most up-to-date picture of what’s happening, but with delays in processing and difficulties in getting tests, case data is perhaps not the most reliable source. Hospitalisations seem a more trustworthy indicator – we don’t miss too many of the people who really need to go to hospital – but there is a lag, typically over a week, between contracting the virus and needing hospitalisation.</p>
<p>There are also arguments about whether people have been admitted because of COVID or simply tested positive after finding themselves in hospital with some other illness. Deaths seem to be the most reliable indicator - it should be quite clear whether someone has died or not - but even with this metric, there has been <a href="https://www.cebm.net/covid-19/why-no-one-can-ever-recover-from-covid-19-in-england-a-statistical-anomaly/">controversy</a> over how long after testing positive someone can be said to have died from COVID. </p>
<p>Restricting these figures to deaths <a href="https://www.cebm.net/covid-19/public-health-england-death-data-revised/">within 28 days of a positive test</a> has removed much of the potential for overcounting (potentially tipping the balance towards undercounting), but there is still a big lag between cases and deaths, which means death data doesn’t paint an up-to-date picture.</p>
<p>REACT is often viewed as an authoritative measure because of the sheer number of people it samples, but the study has its own issues. Data is sampled for short periods of time (known as rounds) rather than continuously, which means we don’t have a good picture of what’s happening in the intervening periods between rounds. </p>
<p>Fitting independent rates of growth to the individual rounds of data shows a drop in R from the start of September to the end of the month. However, assuming the rate of growth is constant between the testing periods gives a similarly good fit and suggests that R could have been steady at around 1.5 throughout September. The data is variable, and it’s inadvisable to draw too firm a conclusion based on one study in isolation.</p>
<p>The fall off in the rate of increase of cases, hospitalisations and triage data in recent days in combination with the REACT study seems to suggest this steep upward trend is not continuing. However, as further tightening in the restrictions affecting the <a href="https://www.bbc.co.uk/news/uk-england-54371073">north of England attest</a>, we are not on top of this wave of the epidemic yet.</p><img src="https://counter.theconversation.com/content/147280/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Christian Yates does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>The latest REACT study provides some reassurance, but there is significant uncertainty in the numbers.Christian Yates, Senior Lecturer in Mathematical Biology, University of BathLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1418392020-07-17T13:30:20Z2020-07-17T13:30:20ZHerd immunity: why the figure is always a bit vague<figure><img src="https://images.theconversation.com/files/347322/original/file-20200714-26-uui1l0.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C3173%2C1661&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-vector/large-group-people-crowd-seamless-background-1166104225">hobbit/Shutterstock</a></span></figcaption></figure><p>Nearly 100 years ago, two British researchers, William Topley and Graham Wilson, were experimenting with <a href="https://www.cambridge.org/core/journals/epidemiology-and-infection/article/spread-of-bacterial-infection-the-problem-of-herdimmunity/FAFA36F92CEA92AC1FA6C942B37568D9">bacterial infections in mice</a>. They noticed that individual survival depended on how many of the mice were vaccinated. So the role of the immunity of an individual needed to be distinguished from the immunity of the entire herd. </p>
<p>Fast forward a century and the concept of <a href="https://academic.oup.com/cid/article/52/7/911/299077">“herd immunity”</a> is now widely discussed in <a href="https://ftalphaville.ft.com/2020/06/01/1591001732000/Making-sense-of-nonsensical-Covid-19-strategy/">government dispatches</a> and newspaper articles. But what does it actually mean?</p>
<p>When a disease such as COVID-19 spreads through the population, it <a href="https://www.nature.com/articles/s41586-020-2456-9">leaves some people immune</a>, at least in the short term. The people who become infected later will increasingly have contact with these immune people and not with the susceptible ones. As a result, the risk of infection is reduced and eventually the disease stops spreading. This might happen even if some people in the population are still susceptible. </p>
<p><a href="https://journals.lww.com/co-infectiousdiseases/Abstract/2012/06000/Vaccination_and_herd_immunity___what_more_do_we.3.aspx">Vaccination can be used</a> to protect susceptible people and thereby hasten the decline of <a href="https://science.sciencemag.org/content/368/6493/860">the epidemic</a>. It can also be used to stop the virus from spreading in the first place.</p>
<h2>How does it work?</h2>
<p>Imagine a population in which everybody is susceptible. An infected person (the red dot in the chart below) arrives and the virus spreads with the ever-increasing number of new cases. The epidemic continues until most individuals catch the virus and become immune to it or die.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/347067/original/file-20200713-22-1nqj9ej.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/347067/original/file-20200713-22-1nqj9ej.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=428&fit=crop&dpr=1 600w, https://images.theconversation.com/files/347067/original/file-20200713-22-1nqj9ej.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=428&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/347067/original/file-20200713-22-1nqj9ej.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=428&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/347067/original/file-20200713-22-1nqj9ej.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=538&fit=crop&dpr=1 754w, https://images.theconversation.com/files/347067/original/file-20200713-22-1nqj9ej.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=538&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/347067/original/file-20200713-22-1nqj9ej.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=538&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Epidemic spread with a random number of secondary cases and average R=2; four generations are shown from the first person marked in red, through yellow, green and blue. Empty circles represent individuals who are still healthy.</span>
<span class="attribution"><span class="source">Adam Kleczkowski</span></span>
</figcaption>
</figure>
<p>If some people are protected – for example, in the initial stages of a mass vaccination programme – the disease will spread more slowly.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/347071/original/file-20200713-58-6x1qch.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/347071/original/file-20200713-58-6x1qch.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/347071/original/file-20200713-58-6x1qch.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=448&fit=crop&dpr=1 600w, https://images.theconversation.com/files/347071/original/file-20200713-58-6x1qch.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=448&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/347071/original/file-20200713-58-6x1qch.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=448&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/347071/original/file-20200713-58-6x1qch.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=563&fit=crop&dpr=1 754w, https://images.theconversation.com/files/347071/original/file-20200713-58-6x1qch.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=563&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/347071/original/file-20200713-58-6x1qch.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=563&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Protecting a few people (grey circles) does not stop the epidemic.</span>
<span class="attribution"><span class="source">Adam Kleczkowski</span></span>
</figcaption>
</figure>
<p>An even more substantial proportion needs to be protected to completely stop the virus, but amazingly it does not need to be the whole population.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/347072/original/file-20200713-58-1fazr1x.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/347072/original/file-20200713-58-1fazr1x.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=439&fit=crop&dpr=1 600w, https://images.theconversation.com/files/347072/original/file-20200713-58-1fazr1x.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=439&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/347072/original/file-20200713-58-1fazr1x.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=439&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/347072/original/file-20200713-58-1fazr1x.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=552&fit=crop&dpr=1 754w, https://images.theconversation.com/files/347072/original/file-20200713-58-1fazr1x.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=552&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/347072/original/file-20200713-58-1fazr1x.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=552&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Successful protection stops the epidemic from further spread.</span>
<span class="attribution"><span class="source">Adam Kleczkowski</span></span>
</figcaption>
</figure>
<p>In the 1970s, mathematical epidemiologists found out that this proportion depends on <a href="https://theconversation.com/what-is-herd-immunity-and-how-many-people-need-to-be-vaccinated-to-protect-a-community-116355">how infectious the disease is</a>, with a simple formula relating it to the <a href="https://www.bbc.co.uk/news/health-52473523">reproductive number</a>, R. For measles this critical percentage is 95%, but for influenza, it could be as low as 35%. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/347182/original/file-20200713-26-100em92.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/347182/original/file-20200713-26-100em92.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/347182/original/file-20200713-26-100em92.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=378&fit=crop&dpr=1 600w, https://images.theconversation.com/files/347182/original/file-20200713-26-100em92.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=378&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/347182/original/file-20200713-26-100em92.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=378&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/347182/original/file-20200713-26-100em92.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=475&fit=crop&dpr=1 754w, https://images.theconversation.com/files/347182/original/file-20200713-26-100em92.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=475&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/347182/original/file-20200713-26-100em92.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=475&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Vaccination coverage and measles cases in the USA.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/w/index.php?curid=89526713">Julius Senegal</a>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>Once the population reaches herd immunity, either through vaccination or naturally by recovering from the disease, any new infection chain will quickly die out. In this way, the population is protected from future outbreaks, but only as long as the <a href="https://theconversation.com/explainer-what-is-herd-immunity-52377">immunity levels are maintained</a>. </p>
<p>If the immunity level <a href="https://theconversation.com/why-are-vaccination-rates-in-england-falling-64931">falls below the critical value</a>, the disease can reemerge. Newborn individuals who are susceptible will need to be vaccinated, and those whose resistance to the disease falls over time might need boosters.</p>
<h2>Coronavirus herd immunity</h2>
<p>The current <a href="https://www.worldometers.info/coronavirus/">estimate of R</a> for COVID-19 is <a href="https://www.ft.com/content/033745f3-2d78-4869-9690-ea46fcc9cb3d?shareType=nongift">around 3</a>, but is perhaps as low as 1.4 and as high as 4. The <a href="https://spiral.imperial.ac.uk/handle/10044/1/77731">corresponding herd immunity level</a> is 60% (50% to 75%). </p>
<p>This value is in the absence of any non-pharmaceutical control measures, such as <a href="https://www.cmaj.ca/content/192/21/E566">lockdown</a>. Maintaining some levels of social distancing in the long term allows the desired immunity to be lower while keeping the population safe. </p>
<p>A <a href="https://science.sciencemag.org/content/368/6493/860">long time might be needed</a> to eventually eradicate the disease, even after the herd immunity level is reached. So the final size of the epidemic, the number of people who have been through infection when the virus is finally eradicated, can be much higher. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/347365/original/file-20200714-54-11oq7c4.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/347365/original/file-20200714-54-11oq7c4.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/347365/original/file-20200714-54-11oq7c4.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=361&fit=crop&dpr=1 600w, https://images.theconversation.com/files/347365/original/file-20200714-54-11oq7c4.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=361&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/347365/original/file-20200714-54-11oq7c4.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=361&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/347365/original/file-20200714-54-11oq7c4.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=453&fit=crop&dpr=1 754w, https://images.theconversation.com/files/347365/original/file-20200714-54-11oq7c4.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=453&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/347365/original/file-20200714-54-11oq7c4.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=453&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">The range of population proportion to achieve herd immunity and the final epidemic size depend on the reproductive number, R.</span>
<span class="attribution"><a class="source" href="https://statisticallyinsignificant.blog/herd-immunity/">Adam Kleczkowski</a>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<h2>Are we there yet?</h2>
<p>It is not easy to determine how close we are to the <a href="https://theconversation.com/herd-immunity-in-europe-are-we-close-139253">herd immunity level</a> or whether we will ever reach this stage. </p>
<p>First, the critical assumption is that the coronavirus infection results in a <a href="https://www.biorxiv.org/content/10.1101/2020.06.29.174888v1">lasting and uniform resistance</a> to future outbreaks. This is far from certain, and if people can catch the SARS-CoV-2 virus <a href="https://doi.org/10.1093/infdis/jiaa392">more than once</a>, as is the case for the common cold, <a href="https://www.vox.com/2020/7/12/21321653/getting-covid-19-twice-reinfection-antibody-herd-immunity">it will make herd immunity disappear</a>. From large studies to <a href="https://edition.cnn.com/2020/07/06/health/spain-coronavirus-antibody-study-lancet-intl/index.html">estimate the population immunity</a>, we know that the numbers are currently <a href="https://www.bloomberg.com/opinion/articles/2020-04-24/is-coronavirus-worse-than-the-flu-blood-studies-say-yes-by-far">between 5% and 25%</a>. </p>
<p>Second, the reproductive number, R, <a href="https://www.ft.com/content/301c847c-a317-4950-a75b-8e66933d423a">varies with location</a>, and so does the herd immunity level <a href="https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)31483-5/fulltext">needed to stop the disease</a>.</p>
<p>Third, studies suggest that some people have a much higher resistance to COVID-19, perhaps because they suffered from <a href="https://www.bbc.co.uk/news/health-53248660">another similar disease</a> in the past or <a href="https://www.pnas.org/content/early/2020/07/07/2008410117">were vaccinated against other diseases</a>. </p>
<p>Finally, there is a <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2610468/">large variability</a> in people’s response to the virus and in the length of time for which someone preserves the levels of antibodies they use to fight the infection. The immunity <a href="https://www.vox.com/science-and-health/2020/4/28/21237922/antibody-test-covid-19-immunity">might not be equally distributed</a> among those who <a href="https://www.vox.com/science-and-health/2020/5/15/21256282/immunity-duration-covid-19-how-lon">have been ill with COVID-19</a>. </p>
<p>People who suffer most might come from the areas that are also most at risk. Such diversity <a href="https://www.dailymail.co.uk/news/article-8518493/Covid-19-herd-immunity-develop-20-study-claims.html">might significantly lower</a> <a href="https://theconversation.com/coronavirus-could-it-be-burning-out-after-20-of-a-population-is-infected-141584">the herd immunity levels</a> needed to stop the disease by targeting only these parts of the society where it is needed most. <a href="https://www.medrxiv.org/content/medrxiv/early/2020/05/21/2020.04.27.20081893.full.pdf">This phenomenon</a> resembles the <a href="https://www.cdc.gov/smallpox/bioterrorism-response-planning/public-health/ring-vaccination.html">ring vaccination strategy</a> that was successfully used to combat such diseases as <a href="https://www.who.int/features/2010/smallpox/en/">smallpox</a>.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/347353/original/file-20200714-30-9mbj8h.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/347353/original/file-20200714-30-9mbj8h.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=431&fit=crop&dpr=1 600w, https://images.theconversation.com/files/347353/original/file-20200714-30-9mbj8h.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=431&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/347353/original/file-20200714-30-9mbj8h.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=431&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/347353/original/file-20200714-30-9mbj8h.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=541&fit=crop&dpr=1 754w, https://images.theconversation.com/files/347353/original/file-20200714-30-9mbj8h.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=541&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/347353/original/file-20200714-30-9mbj8h.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=541&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Localising immunity where it is needed most will lower the herd immunity threshold even more.</span>
<span class="attribution"><span class="source">Adam Kleczkowski</span></span>
</figcaption>
</figure>
<h2>Individuals or the herd</h2>
<p>The concept of herd immunity, although useful for planning a response to the pandemic, is <a href="https://theconversation.com/the-herd-immunity-route-to-fighting-coronavirus-is-unethical-and-potentially-dangerous-133765">not without controversy</a>. In a <a href="https://www.dailymail.co.uk/news/article-8489039/Oxford-professor-Sunetra-Gupta-says-Australia-embrace-herd-immunity.html">campaign to achieve it</a>, many people are exposed to an <a href="https://www.nytimes.com/2020/05/01/opinion/sunday/coronavirus-herd-immunity.html">increased individual risk</a> to protect the rest of the population. </p>
<p>Not imposing <a href="https://www.vox.com/future-perfect/2020/7/8/21311347/arizona-coronavirus-pandemic-covid-outbreak">strict lockdown measures</a> or relaxing too early might lead to people becoming immune to COVID-19 sooner, <a href="https://theconversation.com/herd-immunity-wont-solve-our-covid-19-problem-139724">reaching herd immunity earlier</a>. But this also leads to <a href="https://www.huffingtonpost.co.uk/entry/how-sweden-and-portugal-went-from-pandemic-role-models-to-record-infections_uk_5f0836aec5b63a72c3401141?guccounter=1">excess deaths of vulnerable people</a> who would have survived otherwise. </p>
<p>Herd immunity needs to be maintained. The level required to stop the disease depends on disease transmission, which in turn <a href="https://www.pnas.org/content/101/36/13391">depends on human behaviour</a>. When faced with potentially grim consequences, our behaviour is naturally to prevent the transmission, which lowers the herd immunity requirement. </p>
<p>Once this is reached, other factors (social, economic, risk of vaccine complications) become more important, transmission increases as a result of behaviour change, and herd immunity is lost. In devising successful strategies, <a href="https://www.ft.com/content/7ecd5ded-9b90-4052-b849-0e153f701e1f">governments must take into account</a> both the population and individual risks and benefits.</p><img src="https://counter.theconversation.com/content/141839/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Adam Kleczkowski has received funding from BBSRC, NSF, Academy of Medical Sciences, and the Scottish Government.</span></em></p>We’ll achieve herd immunity when 60% of the population is immune to COVID. No, wait, make it 70%. Or is it 80%?Adam Kleczkowski, Professor of Mathematics and Statistics, University of Strathclyde Licensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1425802020-07-15T09:47:56Z2020-07-15T09:47:56ZCoronavirus: England’s R number is creeping up – does that mean a second wave is on the way?<p>Since the UK government began lifting pandemic lockdown restrictions, there <a href="https://www.ft.com/content/26eaa9cd-021c-48e2-95ae-342e2f2cad37">have been warnings</a> that going too fast would allow the coronavirus to start spreading again. And ever since, there <a href="https://www.theguardian.com/world/2020/jun/05/calls-for-local-lockdowns-as-study-finds-r-value-above-1-in-north-west-england">have been reports</a> about <a href="https://www.thesun.co.uk/news/12023747/coronavirus-r-rate-up-england-rises-above-one-london/">parts of the country</a> that have seen the R number – a key measure of the spread of the disease – rise above the crucial threshold of 1, which would mean case numbers start rising again.</p>
<p>Recent <a href="https://news.sky.com/story/coronavirus-r-number-rises-slightly-in-england-following-lockdown-easing-12025709">data has suggested</a> that the R number in south-west England may be as high as 1.1, with the overall number for England rising to between 0.8 and 1, compared to being between 0.8 and 0.9 the week before. Is this increase in R a sign that the country could be heading towards <a href="https://theconversation.com/coronavirus-what-a-second-wave-might-look-like-138980">a second wave</a> of COVID-19? The reality is more complex than that.</p>
<p>You may have heard a lot about R – the basic reproduction number – as a metric for tracking the COVID-19 epidemic spread in the UK. It represents the average number of people each infectious person will pass the virus on to, and reflects the rate at which the virus spreads across the population. When R rises above 1, unless action is taken the number of new cases will start to grow exponentially and so, in a population with no immunity, the virus can spread fast. This is what happened in the early days of the pandemic. When R is below 1, each person will infect on average less than one person, implying that gradually fewer people will be affected and the outbreak will eventually die out.</p>
<p>At the onset of the epidemic in the UK, different studies estimated R in the UK to be <a href="https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf">2.4</a>, <a href="https://cmmid.github.io/topics/covid19/reports/LSHTM-CMMID-20200401-CoMix-social-contacts.pdf">2.6</a>, around <a href="https://www.medrxiv.org/content/10.1101/2020.06.01.20100461v1">3</a>, or between <a href="https://www.nature.com/articles/s41586-020-2405-7_reference.pdf">3 and 4</a>. An R value of 3 implies that every infectious person will infect 3 more people, so if there are 100 people infected with the virus they will likely infect 300 more and these will produce another 900 infections. </p>
<p>But when you are comparing locations, the R number alone doesn’t give you the whole picture of what is happening. For example, if R is smaller in one location than another, but had more people infected to begin with, the numbers of new infections can be higher. An R value of 2.5 in a population with 150 infected persons will induce 375 secondary infections, which in turn will produce 938 more infections – more than in the previous example where R was 3.</p>
<p>As a result of the lockdown and the reduced social contact that spreads airborne diseases, the number of new cases of COVID-19 in the UK was reduced and R pushed below 1. But as an epidemic progresses and the number of cases starts to decrease, R can be subject to large fluctuations and uncertainty. </p>
<p>Specifically, when the number of cases falls to low levels or if transmission across the country varies significantly, R estimates can fluctuate a lot and so it becomes a less robust way of representing what’s happening.</p>
<p>This means news that R may have increased above 1 again, particularly in specific regions, may not necessarily mean that current public health measures aren’t working or that the disease is about to come roaring back. It may simply mean that we have fluctuations in the reported R value or a slightly increased number of infections in a local area.</p>
<p>Importantly, since R represents an average across settings or populations, it can also miss regional clusters of infection. Another measure, referred to as <a href="https://theconversation.com/is-the-k-number-the-new-r-number-what-you-need-to-know-140286">the K number</a>, can describe how much of the spread of a disease is occurring in these kind of localised clusters. </p>
<p>A lower K number can indicate that more transmission is coming from a small number of people, potentially from <a href="https://theconversation.com/what-is-a-super-spreader-an-infectious-disease-expert-explains-130756">superspreading events</a> where many people are infected from one or just a few starting cases. These events can increase the R number locally but may not indicate that transmission of the disease is increasing in general. And we should also remember that values reported today, are often an indication of what has happened at least a week ago.</p>
<h2>More data needed</h2>
<p><a href="https://wellcomeopenresearch.org/articles/5-67">Initial analysis</a> suggests the COVID-19 pandemic may have a low K number and that the disease may have particular superspreading potential. While further work is required to explore how this might apply to the UK, these results reminds us how important it is to consider other measures of the virus’s spread alongside R, particularly as more localised outbreaks emerge. These include number of cases, hospitalisations and deaths on a national and local level, and the K number.</p>
<p>Crucially, while we should keep track of R in different locations and from one week to the next, we also need to be wary of the fact it becomes less reliable as the epidemic slows down. A slightly higher R number may not necessarily mean a second wave is coming right now or that recent easing of the lockdown must be reversed.</p>
<p>But equally, we mustn’t forget that there are still around <a href="https://coronavirus.data.gov.uk">400 people catching the virus each day</a> in the UK. So even when R is below one, there is still an ongoing risk of transmission. This could be reduced by slowing the lockdown easing and doing more to encourage people to adhere to the existing rules. <a href="https://www.medrxiv.org/content/10.1101/2020.06.01.20100461v1">Models are</a> predicting that a second wave may occur and returning to pre-COVID-19 behaviour is still far away.</p><img src="https://counter.theconversation.com/content/142580/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Jasmina Panovska-Griffiths does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article. While her models are used to inform government scientific bodies, she discloses no other affiliations beyond her academic appointment.</span></em></p>The R number fluctuates more as case numbers fall.Jasmina Panovska-Griffiths, Senior Research Fellow and Lecturer in Mathematical Modelling, UCLLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1413342020-06-26T09:01:12Z2020-06-26T09:01:12ZCoronavirus: Germany’s new local lockdown is a warning not a disaster<p>German authorities have had to take the difficult decision of <a href="https://www.bbc.co.uk/news/world-europe-53149762">reimposing a pandemic lockdown</a> in the state of North Rhine-Westphalia after a resurgence of the coronavirus. This comes after the country’s R number, a measure of how quickly new cases of the disease are emerging, <a href="https://news.sky.com/story/coronavirus-germanys-r-number-rockets-again-from-1-79-to-2-88-12012143">almost tripled</a> over the course of few days.</p>
<p>Germany has been <a href="https://www.economist.com/europe/2020/04/25/germany-excels-among-its-european-peers">widely praised</a> for <a href="https://www.theguardian.com/world/2020/apr/05/germanys-devolved-logic-is-helping-it-win-the-coronavirus-race">its response</a> <a href="https://www.ft.com/content/cc1f650a-91c0-4e1f-b990-ee8ceb5339ea">to the pandemic</a>. It has had <a href="https://ourworldindata.org/coronavirus-data-explorer?zoomToSelection=true&deathsMetric=true&totalFreq=true&aligned=true&smoothing=0&country=GBR%7EFRA%7EITA%7EDEU%7ECAN%7EUSA%7EESP&pickerMetric=location&pickerSort=asc">far fewer deaths</a> than most similar sized western countries, its national lockdown <a href="https://www.bbc.com/news/world-europe-52557718">was relaxed</a> after just six weeks, and new cases recently reached a low of <a href="https://www.spiegel.de/wissenschaft/medizin/faq-zu-corona-daten-woher-kommen-sie-wie-zuverlaessig-sind-sie-a-f6b77af7-aa7c-4197-a87e-def2d360ee8d">about 500 a day</a> in a country of more than 80 million.</p>
<p><strong>Daily new cases of COVID-19 (seven-day average)</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/344236/original/file-20200626-104484-z0pox0.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/344236/original/file-20200626-104484-z0pox0.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/344236/original/file-20200626-104484-z0pox0.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=382&fit=crop&dpr=1 600w, https://images.theconversation.com/files/344236/original/file-20200626-104484-z0pox0.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=382&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/344236/original/file-20200626-104484-z0pox0.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=382&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/344236/original/file-20200626-104484-z0pox0.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=480&fit=crop&dpr=1 754w, https://images.theconversation.com/files/344236/original/file-20200626-104484-z0pox0.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=480&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/344236/original/file-20200626-104484-z0pox0.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=480&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Data downloaded on June 26th, 2020.</span>
<span class="attribution"><a class="source" href="https://github.com/CSSEGISandData/COVID-19">Adam Kleczkowski (data from Johns Hopkins University)</a>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>So does the big increase in the R number and the reintroduction of lockdown at a local level suggest something has gone wrong in the country’s strategy? In reality it may be related to how R is calculated and <a href="https://theconversation.com/coronavirus-is-the-r-number-still-useful-138542">its limits</a> as a measure of the spread of disease. But it also signals the risks that remain even as many other countries end their lockdowns.</p>
<p>Alarm bells first sounded in mid-June, when more than 1,500 workers at a meat-processing factory in Gütersloh in North Rhine-Westphalia <a href="https://www.reuters.com/article/us-health-coronavirus-meat-toennies/german-coronavirus-outbreak-at-abattoir-infects-more-than-1000-idUSKBN23R0Q5">tested positive</a>. More cases were found in the broader area, including in neighbouring counties.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/344237/original/file-20200626-104504-1u3nv8q.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/344237/original/file-20200626-104504-1u3nv8q.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/344237/original/file-20200626-104504-1u3nv8q.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=382&fit=crop&dpr=1 600w, https://images.theconversation.com/files/344237/original/file-20200626-104504-1u3nv8q.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=382&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/344237/original/file-20200626-104504-1u3nv8q.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=382&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/344237/original/file-20200626-104504-1u3nv8q.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=480&fit=crop&dpr=1 754w, https://images.theconversation.com/files/344237/original/file-20200626-104504-1u3nv8q.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=480&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/344237/original/file-20200626-104504-1u3nv8q.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=480&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Data downloaded on June 26th, 2020.</span>
<span class="attribution"><a class="source" href="https://github.com/CSSEGISandData/COVID-19">Adam Kleczkowski (data from Johns Hopkins University)</a>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>This localised outbreak has had a disproportionate effect on the country’s overall R (reproductive) number. <a href="https://www.bbc.co.uk/news/health-52473523">R represents</a> the average number of people who catch the virus from an infected person. When R is bigger than 1 it means the number of cases are increasing. </p>
<p>During the mid-June Gütersloh outbreak, R <a href="https://www.rki.de/DE/Content/Infekt/EpidBull/Archiv/2020/Ausgaben/17_20.pdf?__blob=publicationFile">jumped from the value of about 1 to almost 3</a> before <a href="https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Situationsberichte/2020-06-25-de.pdf">falling back to below 1</a>. But, such values of R need to be carefully interpreted.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/343822/original/file-20200624-132972-19y0t5m.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/343822/original/file-20200624-132972-19y0t5m.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/343822/original/file-20200624-132972-19y0t5m.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=383&fit=crop&dpr=1 600w, https://images.theconversation.com/files/343822/original/file-20200624-132972-19y0t5m.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=383&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/343822/original/file-20200624-132972-19y0t5m.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=383&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/343822/original/file-20200624-132972-19y0t5m.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=481&fit=crop&dpr=1 754w, https://images.theconversation.com/files/343822/original/file-20200624-132972-19y0t5m.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=481&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/343822/original/file-20200624-132972-19y0t5m.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=481&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Data downloaded on June 26th, 2020.</span>
<span class="attribution"><a class="source" href="https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Projekte_RKI/Nowcasting.html">Adam Kleczkowski (data from from Robert Koch Institute)</a>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>There are different methods that can be used to calculate R. The one <a href="https://doi.org/10.1111/biom.12194">used in Germany</a> is based on the total number of known infected individuals in the whole country. It essentially compares the number of new cases on a given day with those four-to-seven days earlier. </p>
<p>If 500 new cases were noted seven days before the Gütersloh outbreak of 1,500 new cases, R will be equal to 3. This means each person with the virus has infected, on avereage, three others. </p>
<p>But, this number hides substantial <a href="https://www.theguardian.com/world/2020/may/15/regional-differences-in-covid-19-transmission-rate-emerge-in-england">potential variation in different locations</a>. While in most of the country, the numbers of new cases may have continued to fall, one or only a few people in Gütersloh could have triggered an outbreak on a scale of around 1,500. Such large and localised outbreaks are called <a href="https://theconversation.com/is-the-k-number-the-new-r-number-what-you-need-to-know-140286">super-spreading events</a>.</p>
<p>It’s too early to speculate on exactly what caused the June outbreak and whether it started with one or more people. But with a continuous supply of both infected and susceptible individuals in a population which is still far away from herd immunity, the disease is likely to spread when the conditions are right. </p>
<p>The nature of <a href="https://www.spiegel.de/wissenschaft/medizin/covid-19-risikofaktor-fleischbetrieb-a-4ba2d1ed-60d1-407c-b9e8-c76b2154c220">meat processing factories</a> may have been a factor. Cold temperatures can combine with busy workplace conditions, intensive labour, and a noisy environment encouraging <a href="https://www.nature.com/articles/s41598-019-38808-z">shouting</a>, which can spread the virus. Other localised outbreaks have also been linked to meat factories in a variety of <a href="https://www.ft.com/content/1045bfc5-fd8c-4240-b944-3ccef0b00b1e">countries</a>.</p>
<h2>Lessons for the future</h2>
<p>In many countries, COVID-19 cases are generally falling to low numbers. This means any substantial but localised outbreak will cause the R number to <a href="https://theconversation.com/coronavirus-what-a-second-wave-might-look-like-138980">increase temporarily</a>. </p>
<p>But this does signal an increased risk of a more sustained spread. In the “first wave” of COVID-19, a single person caused an outbreak in a ski resort of Ischgl that arguably led to a rapid increase in cases across Europe <a href="https://cepr.org/sites/default/files/news/CovidEconomics22.pdf">including in Germany</a>. </p>
<p>The risk of a new superspreading event contributing to a <a href="https://theconversation.com/coronavirus-what-a-second-wave-might-look-like-138980">“second wave”</a> requires <a href="https://www.politico.eu/article/germany-coronavirus-second-wave-risk-gutersloh/">quick and decisive action</a>. So it’s essential that such events are <a href="https://www.theguardian.com/commentisfree/2020/may/19/second-coronavirus-wave-r-number-uk-test-and-trace-mass-gatherings-travel">managed by appropriate control measures</a>, including <a href="https://www.spiegel.de/politik/deutschland/laschet-verkuendet-lockdown-massnahmen-fuer-ganzen-kreis-guetersloh-a-ebee31df-b50c-4558-bd77-2a36574533fd">renewed lockdowns</a>. Since lockdown decisions imply huge economic costs, they need to be supported by predictions based on epidemiological models.</p>
<p>While the role of socio-economic versus medical factors in the Gütersloh outbreak needs to be discussed, we still need to consider <a href="https://www.bmas.de/DE/Presse/Pressemitteilungen/2020/mehr-arbeitsschutz-und-hygiene-in-der-fleischwirtschaft.html">pro-active measures</a> to prevent such outbreaks. Until a vaccine is successfully deployed, government and the public need to get used to living with the virus and continuing to act to <a href="https://theconversation.com/four-graphs-that-show-how-the-coronavirus-pandemic-could-now-unfold-133979">stop it spreading again</a>.</p><img src="https://counter.theconversation.com/content/141334/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Adam Kleczkowski has received funding from BBSRC, NSF, Academy of Medical Sciences, and the Scottish Government.</span></em></p>Germany’s resurgent R number is largely down to a localised outbreak.Adam Kleczkowski, Professor of Mathematics and Statistics, University of Strathclyde Licensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1402862020-06-16T09:57:09Z2020-06-16T09:57:09ZIs the K number the new R number? What you need to know<p>Just a few months ago, no one, aside from epidemiologists and their ilk, had heard of the R number. Now, thanks to the coronavirus, everyone has heard of it and most people can tell you that it’s the reproduction number, an indicator of whether the number of infected people is increasing or decreasing.</p>
<p>The R number is regularly referred to by governments around the world and by news anchors and their guests when discussing the pandemic. Yet no sooner had the public wrapped their head around one mathematical symbol than another cropped up. This time, the <a href="https://www.theguardian.com/world/2020/jun/01/k-number-what-is-coronavirus-metric-crucial-lockdown-eases">letter K</a>. So what do we need to know about K and why has it suddenly become <a href="https://news.sky.com/story/coronavirus-what-is-the-k-number-and-how-could-it-help-end-lockdown-11999741">the focus of interest</a>?</p>
<p>The <a href="https://www.bbc.co.uk/news/health-52473523">R number</a> represents the average number of people an infected person goes on to infect. If R is <a href="https://theconversation.com/coronavirus-what-a-second-wave-might-look-like-138980">larger than one</a>, the number of people with the disease is increasing. The target for control strategies, including lockdown, self-isolation and masks wearing, is to bring R below one and thereby reduce the number of people with the disease. </p>
<p>At the start of the coronavirus outbreak, R in the UK was <a href="https://www.ft.com/content/033745f3-2d78-4869-9690-ea46fcc9cb3d?shareType=nongift">around three</a>. If every infected person infected exactly three people, the epidemic would have spread as in the figure below.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/341536/original/file-20200612-153849-1ko8h3x.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/341536/original/file-20200612-153849-1ko8h3x.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=316&fit=crop&dpr=1 600w, https://images.theconversation.com/files/341536/original/file-20200612-153849-1ko8h3x.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=316&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/341536/original/file-20200612-153849-1ko8h3x.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=316&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/341536/original/file-20200612-153849-1ko8h3x.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=397&fit=crop&dpr=1 754w, https://images.theconversation.com/files/341536/original/file-20200612-153849-1ko8h3x.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=397&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/341536/original/file-20200612-153849-1ko8h3x.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=397&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Epidemic spread with R=3; four generations are shown from the first person marked in red, through yellow, green and blue. Numbers indicate how many new infections originate from each case.</span>
<span class="attribution"><span class="source">Adam Kleczkowski</span></span>
</figcaption>
</figure>
<h2>The average is not enough</h2>
<p>The R mentioned in the daily press briefings represents an average of the whole country or region, involving millions of people. But its single value hides <a href="https://www.sciencemag.org/news/2020/05/why-do-some-covid-19-patients-infect-many-others-whereas-most-don-t-spread-virus-all">many differences</a> between individuals and their impact on virus transmission. </p>
<p>Rather than assuming that every infected person and every contact they make follows the same pattern (as with the R number), scientists working on epidemic models allow for the number of new cases caused by each infected person to <a href="https://www.nature.com/articles/nature04153#MOESM1">vary randomly</a>. </p>
<p>Some people might have <a href="https://wwwnc.cdc.gov/eid/article/21/11/15-0764_article">high viral loads</a> or might simply <a href="https://www.nature.com/articles/s41598-019-38808-z">cough more</a> and hence spread the virus more effectively. </p>
<p>Many people, although ill and highly infectious, <a href="https://www.acpjournals.org/doi/10.7326/M20-3012">don’t show any symptoms</a>. They <a href="https://doi.org/10.1093/cid/ciaa424">might make many contacts</a> without realising they pose a danger to others. An example from history is the infamous <a href="https://en.wikipedia.org/wiki/Mary_Mallon">Mary Mallon</a> (“Typhoid Mary”), a cook in New York City in the early 1900s. Although she carried typhoid bacteria, she didn’t show any symptoms and is believed to have infected more than 50 people over seven years. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/341662/original/file-20200614-153808-8cdo8c.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/341662/original/file-20200614-153808-8cdo8c.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=445&fit=crop&dpr=1 600w, https://images.theconversation.com/files/341662/original/file-20200614-153808-8cdo8c.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=445&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/341662/original/file-20200614-153808-8cdo8c.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=445&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/341662/original/file-20200614-153808-8cdo8c.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=559&fit=crop&dpr=1 754w, https://images.theconversation.com/files/341662/original/file-20200614-153808-8cdo8c.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=559&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/341662/original/file-20200614-153808-8cdo8c.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=559&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Mary Mallon in hospital (foreground).</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/w/index.php?curid=689801">Wikimedia Commons</a></span>
</figcaption>
</figure>
<h2>Super-spreaders</h2>
<p>People also differ in the way they interact with others. For some, contacts might involve just the immediate family or a small group of colleagues at work or friends. The disease will then only have a chance to be transmitted to a few people. But if an infected person goes to <a href="https://www.cdc.gov/mmwr/volumes/69/wr/mm6919e6.htm">choir practice</a>, a <a href="https://www.independent.co.uk/news/world/coronavirus-italy-champions-league-atlanta-valencia-milan-bergamo-a9426616.html">football match</a> or visits <a href="https://www.cbsnews.com/news/south-korea-coronavirus-cluster-linked-to-seoul-nightclubs-fueling-homophobia-fears-gay-men/">several pubs or nightclubs</a>, the number of people who might catch the disease becomes large. Scientists call such <a href="https://arxiv.org/abs/2005.13689">massive and rapid outbreaks</a> caused by one or a few infected individuals, <a href="https://www.nature.com/articles/nature04153#MOESM1">super-spreading events</a>, and their initiators are known as <a href="https://www.journalofhospitalinfection.com/article/S0195-6701(20)30177-8/fulltext#secsectitle0015">super-spreaders</a>. In many cases, 80% of the new disease cases are caused by only 20% of such super-spreading individuals.</p>
<h2>Dispersion parameter, K</h2>
<p>Different pathogens will have different ways in which they spread and statisticians use K, the so-called <a href="https://www.huffingtonpost.co.uk/entry/what-is-the-r-number-and-how-is-it-different-to-the-k-number_uk_5ed8ae41c5b6f3c22ef014e9">dispersion parameter</a>, to describe how variable the infection can be. For some diseases, the variation will not be large, as shown below.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/341549/original/file-20200612-153817-nh8d82.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/341549/original/file-20200612-153817-nh8d82.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=329&fit=crop&dpr=1 600w, https://images.theconversation.com/files/341549/original/file-20200612-153817-nh8d82.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=329&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/341549/original/file-20200612-153817-nh8d82.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=329&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/341549/original/file-20200612-153817-nh8d82.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=414&fit=crop&dpr=1 754w, https://images.theconversation.com/files/341549/original/file-20200612-153817-nh8d82.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=414&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/341549/original/file-20200612-153817-nh8d82.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=414&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Epidemic spread with a distribution of secondary cases with low dispersion and value of K much larger than 1.</span>
<span class="attribution"><span class="source">Adam Kleczkowski</span></span>
</figcaption>
</figure>
<p>Simply put, a low K value suggests that a small number of infected people are responsible for large amounts of disease transmission. For the 1918 influenza, the number K is thought to be around 1, and perhaps 40% of infected people might not pass on the virus to anybody else. But for diseases like <a href="https://www.nature.com/articles/nature04153#MOESM1">Sars</a>, <a href="https://www.sciencemag.org/news/2020/05/why-do-some-covid-19-patients-infect-many-others-whereas-most-don-t-spread-virus-all">Mers</a> and <a href="https://wellcomeopenresearch.org/articles/5-67">COVID-19</a> with K as low as 0.1, this proportion rises to 70%. In contrast, large outbreaks will be initiated by only few super-spreaders, as shown below. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/341544/original/file-20200612-153858-1oxuf6a.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/341544/original/file-20200612-153858-1oxuf6a.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=320&fit=crop&dpr=1 600w, https://images.theconversation.com/files/341544/original/file-20200612-153858-1oxuf6a.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=320&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/341544/original/file-20200612-153858-1oxuf6a.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=320&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/341544/original/file-20200612-153858-1oxuf6a.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=402&fit=crop&dpr=1 754w, https://images.theconversation.com/files/341544/original/file-20200612-153858-1oxuf6a.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=402&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/341544/original/file-20200612-153858-1oxuf6a.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=402&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Epidemic spread with a distribution of secondary cases with high dispersion and value of K around or below 1.</span>
<span class="attribution"><span class="source">Adam Kleczkowski</span></span>
</figcaption>
</figure>
<h2>Why is K so important?</h2>
<p>There are two reasons why scientists are looking into the <a href="https://www.ft.com/content/2418ff87-1d41-41b5-b638-38f5164a2e94">role of variability</a> in controlling coronavirus transmission. First, super-spreading events are critical in the late stages of the epidemic when the virus is almost eradicated. Small values of K mean that one infected person can trigger many new cases in a very short time. If this happens, the epidemic can quickly rebound, even if locally eradicated. </p>
<p>Outbreaks in <a href="https://www.cbsnews.com/news/south-korea-coronavirus-cluster-linked-to-seoul-nightclubs-fueling-homophobia-fears-gay-men/">Seoul nightclubs in South Korea</a>, <a href="https://blogs.lse.ac.uk/covid19/2020/05/05/covid-19-contributes-to-the-crisis-of-occupational-safety-and-health-in-meatpacking/">meatpacking plants in the US</a>, and <a href="https://uk.reuters.com/article/us-health-coronavirus-poland-coal/poland-will-temporarily-close-a-dozen-mines-to-stop-coronavirus-idUKKBN23F0TK?rpc=401">coal mines in Poland</a> show how damaging super-spreading events can be. So governments need to be <a href="https://www.sciencedirect.com/science/article/pii/S0262407920309477">diligent in identifying the risks</a> associated with the reopening of industries and entertainment. A way to identify and track potential super-spreaders is fundamental to prevent future outbreaks.</p>
<p>But there is also a glimmer of hope. If indeed <a href="https://wellcomeopenresearch.org/articles/5-67">K is as low as 0.1</a>, <a href="https://europepmc.org/article/ppr/ppr165671">70% of infected individuals fail to pass on the virus</a>. As a result, most cases arriving from outside the country or region might recover without starting a new outbreak. It might, therefore, be easier to eradicate the disease and to maintain the disease-free status than suggested by the average reproductive number, R. </p>
<p>While R is not going to be replaced by K in the daily press briefing, both are needed to understand how COVID-19 spreads.</p><img src="https://counter.theconversation.com/content/140286/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Adam Kleczkowski has received funding from BBSRC, NSF, Academy of Medical Sciences, and the Scottish Government.</span></em></p>K is all about the super-spreaders.Adam Kleczkowski, Professor of Mathematics and Statistics, University of Strathclyde Licensed as Creative Commons – attribution, no derivatives.