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What Happens Next? COVID-19 Futures, Explained With Playable Simulations
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🔬 Here's a real deep dive! 28 min read/play:
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<article>
<div class="section">
<div>
<h1>What Happens Next?</h1>
<h2>COVID-19 Futures, Explained With Playable Simulations</h2>
<h3>(28 min play/read)</h2>
</div>
</div>
<p><strong>{WIP, DON&#39;T SHARE YET THX!}</strong></p>
<p>&quot;The only thing to fear is fear itself&quot; was stupid advice.</p>
<p>Sure, don&#39;t hoard toilet paper but if policymakers fear fear itself, they&#39;ll downplay dangers to us to avoid &quot;mass panic&quot;. Fear&#39;s not the problem, it&#39;s how we <em>channel</em> our fear. Fear gives us energy to deal with dangers now, and prepare for dangers later.</p>
<p>Honestly, we (Marcel, epidemiologist + Nicky, art/code) are worried. We bet you are, too! That&#39;s why we&#39;ve channelled our fear into making these <strong>playable simulations</strong>, so that <em>you</em> can channel your fear into understanding:</p>
<ul>
<li><strong>The Last Few Months</strong> (epidemiology 101, SEIR model, R &amp; R<sub>0</sub>)</li>
<li><strong>The Next Few Months</strong> (lockdowns, contact tracing, masks?)</li>
<li><strong>The Next Few Years</strong> (loss of immunity? no vaccine?)</li>
</ul>
<p>This guide (published April 30th, 2020<sup id="fnref1"><a href="#fn1" rel="footnote">1</a></sup>) is meant to give you hope <em>and</em> fear. To beat COVID-19 <strong>in a way that also protects our mental &amp; financial health</strong>, we need optimism to create plans, and pessimism to create backup plans. As Gladys Bronwyn Stern once said, <em>“The optimist invents the airplane and the pessimist the parachute.”</em></p>
<p>So, buckle in: we&#39;re about to experience some turbulence.</p>
<div class="section">
<div>
<h1>The Last Few Months</h1>
</div>
</div>
<p>Pilots use flight simulators to learn how not to crash planes.</p>
<p><strong>Epidemiologists use epidemic simulators to learn how not to crash humanity.</strong></p>
<p>So, let&#39;s make a simple &quot;epidemic flight simulator&quot;! In this simulation, <icon i></icon> Infectious people can turn <icon s></icon> Susceptible people into more <icon i></icon> Infectious people:</p>
<p><img src="pics/spread.png" alt=""></p>
<p>It&#39;s estimated that, <em>at the start</em> of a COVID-19 outbreak, the virus jumps from an <icon i></icon> to an <icon s></icon> <em>approximately</em> every 4 days.<sup id="fnref2"><a href="#fn2" rel="footnote">2</a></sup></p>
<p>[TODO: Actually fill out source / footnotes]</p>
<p>If we simulate &quot;double every 4 days&quot; <em>and nothing else</em>, on a population starting with just 0.001% <icon i></icon>, what happens? </p>
<p><strong>Click &quot;Start&quot; to play the simulation! You can re-play it later with different settings:</strong> (technical caveats: <sup id="fnref3"><a href="#fn3" rel="footnote">3</a></sup>)</p>
<div class="sim">
<iframe src="sim?stage=epi-1" width="800" height="540"></iframe>
</div>
<p>This is the <strong>exponential growth curve.</strong> Starts small, then explodes. &quot;Oh it&#39;s just a flu&quot; to &quot;Oh right, flus don&#39;t create <em>mass graves in rich cities</em>&quot;. </p>
<p><img src="pics/exponential.png" alt=""></p>
<p>But, this simulation is wrong. Exponential growth, thankfully, can&#39;t go on forever. One thing that stops a virus from spreading is if others <em>already</em> have the virus:</p>
<p><img src="pics/susceptibles.png" alt=""></p>
<p>The more <icon i></icon>s there are, the faster <icon s></icon>s become <icon i></icon>s, <strong>but the fewer <icon s></icon>s there are, the <em>slower</em> <icon s></icon>s become <icon i></icon>s.</strong></p>
<p>How&#39;s this change the growth of an epidemic? Let&#39;s find out:</p>
<div class="sim">
<iframe src="sim?stage=epi-2" width="800" height="540"></iframe>
</div>
<p>This is the &quot;S-shaped&quot; <strong>logistic growth curve.</strong> Starts small, explodes, then slows down again.</p>
<p>But, this simulation is <em>still</em> wrong. We&#39;re missing the fact that <icon i></icon> Infectious people eventually stop being infectious, either by 1) recovering, 2) &quot;recovering&quot; with lung damage, or 3) dying.</p>
<p>For simplicity&#39;s sake, let&#39;s pretend that all <icon i></icon> Infectious people become <icon r></icon> Recovered. (Just remember that, in reality, some of them are dying.) <icon r></icon>s can&#39;t be infected again, and let&#39;s pretend <em>for now!</em> that they stay immune for life.</p>
<p>With COVID-19, it&#39;s estimated you&#39;re <icon i></icon> Infectious for <em>approximately</em> 10 days.<sup id="fnref4"><a href="#fn4" rel="footnote">4</a></sup> Let&#39;s simulate a population starting at 100% <icon i></icon>, most of whom recover after 10 days, then most of the remainder recover after another 10 days, then most of <em>that</em> remainder recover after another 10 days, etc:</p>
<div class="sim">
<iframe src="sim?stage=epi-3" width="800" height="540"></iframe>
</div>
<p>This is the opposite of exponential growth, the <strong>exponential decay curve</strong>.</p>
<p>Now, what happens if you simulate S-shaped logistic growth <em>with</em> recovery?</p>
<p><img src="pics/graphs_q.png" alt=""></p>
<p>Let&#39;s find out:</p>
<div class="sim">
<iframe src="sim?stage=epi-4" width="800" height="540"></iframe>
</div>
<p>And <em>that&#39;s</em> where that famous curve comes from! It&#39;s not a bell curve, it&#39;s not even a &quot;log-normal&quot; curve. It has no name. But you&#39;ve seen it a zillion times, and beseeched to flatten.</p>
<p>This is the the <strong>SIR Model</strong><sup id="fnref5"><a href="#fn5" rel="footnote">5</a></sup><br>
(<icon s></icon><strong>S</strong>usceptible <icon i></icon><strong>I</strong>nfectious <icon r></icon><strong>R</strong>ecovered)<br>
the second-most important idea in Epidemiology 101:</p>
<p><img src="pics/sir.png" alt=""></p>
<p>NOTE: The simulations that inform policy are <em>far</em> more sophisticated than this! But the SIR Model can still explain the same findings, even if missing the nuances.</p>
<p>Actually, let&#39;s add one more nuance: before an <icon s></icon> becomes an <icon i></icon>, they first become <icon e></icon> Exposed. This is when they have the virus but can&#39;t pass it on yet infect<em>ed</em> but not yet infect<em>ious</em>.</p>
<p><img src="pics/seir.png" alt=""></p>
<p>(This variant is called the <strong>SEIR Model</strong><sup id="fnref6"><a href="#fn6" rel="footnote">6</a></sup>, where the &quot;E&quot; stands for <icon e></icon> &quot;Exposed&quot;. Note this <em>isn&#39;t</em> the everyday meaning of &quot;exposed&quot;, when you might or might not have the virus. In this technical definition, &quot;Exposed&quot; means you definitely have it. Science terminology is bad.)</p>
<p>For COVID-19, it&#39;s estimated that you&#39;re <icon e></icon> infected-but-not-yet-infectious for <em>approximately</em> 3 days.<sup id="fnref7"><a href="#fn7" rel="footnote">7</a></sup> What happens if we add that to the simulation?</p>
<div class="sim">
<iframe src="sim?stage=epi-5" width="800" height="540"></iframe>
</div>
<p>Not much, actually! How long you stay <icon e></icon> Exposed changes the ratio of <icon e></icon>-to-<icon i></icon>, and <em>when</em> the peak of current cases (<icon e></icon>+<icon i></icon>) happens... but the <em>height</em> of that peak, and the total % of people infected in the end, stays the same.</p>
<p>Why&#39;s that? Because of the <em>first</em>-most important idea in Epidemiology 101:</p>
<p><img src="pics/r.png" alt=""></p>
<p>Short for &quot;Reproduction number&quot;. It&#39;s the <em>average</em> number of people an <icon i></icon> infects <em>before</em> they recover (or die).</p>
<p><img src="pics/r2.png" alt=""></p>
<p><strong>R</strong> changes over the course of an outbreak, as we get more immunity &amp; interventions.</p>
<p><strong>R<sub>0</sub></strong> (pronounced R-nought) is what R is <em>at the start of an outbreak, before immunity or interventions</em>. R<sub>0</sub> more closely reflects the power of the virus itself, but it still changes from place to place. For example, R<sub>0</sub> is higher in dense cities than sparse rural areas.</p>
<p>(Most news articles and even some scientific papers! confuse R and R<sub>0</sub>. Again, science terminology is bad)</p>
<p>The R<sub>0</sub> for &quot;the&quot; seasonal flu is around 1.28<sup id="fnref8"><a href="#fn8" rel="footnote">8</a></sup>. This means, at the <em>start</em> of a flu outbreak, each <icon i></icon> infects 1.28 others <em>on average.</em> (If it sounds weird that this isn&#39;t a whole number, remember that the &quot;average&quot; mom has 2.4 children. This doesn&#39;t mean there&#39;s half-children running about.)</p>
<p>The R<sub>0</sub> for COVID-19 is estimated to be around 2.2<sup id="fnref9"><a href="#fn9" rel="footnote">9</a></sup>, though a not-yet-finalized CDC study estimates it was 5.7(!) in Wuhan.<sup id="fnref10"><a href="#fn10" rel="footnote">10</a></sup></p>
<p>In our simulations <em>at the start &amp; on average</em> an <icon i></icon> infects someone every 4 days, over 10 days. &quot;4 days&quot; goes into &quot;10 days&quot; two-and-a-half times. This means <em>at the start &amp; on average</em> each <icon i></icon> infects 2.5 others. Therefore, R<sub>0</sub> = 2.5. (caveats:<sup id="fnref11"><a href="#fn11" rel="footnote">11</a></sup>)</p>
<p><strong>Play with this R<sub>0</sub> calculator, to see how R<sub>0</sub> depends on recovery time &amp; new-infection time:</strong></p>
<div class="sim">
<iframe src="sim?stage=epi-6a&format=calc" width="285" height="255"></iframe>
</div>
<p>But remember, the fewer <icon s></icon>s there are, the <em>slower</em> <icon s></icon>s become <icon i></icon>s. The <em>current</em> reproduction number (R) depends not just on the <em>basic</em> reproduction number (R<sub>0</sub>), but <em>also</em> on how many people are no longer <icon s></icon> Susceptible. (For example, by recovering &amp; getting natural immunity.)</p>
<div class="sim">
<iframe src="sim?stage=epi-6b&format=calc" width="285" height="390"></iframe>
</div>
<p>When enough people have natural immunity, R &lt; 1, and the virus is contained! This is called <strong>herd immunity</strong>, and while it&#39;s <em>terrible</em> policy (we&#39;ll explain why later it&#39;s not for the reason you may think!), it&#39;s essential to understanding Epidemiology 101.</p>
<p>Now, let&#39;s play the SEIR Model again, but showing R<sub>0</sub>, R over time, and the herd immunity threshold:</p>
<div class="sim">
<iframe src="sim?stage=epi-7" width="800" height="540"></iframe>
</div>
<p>Note: Total cases (gray curve) does not stop at herd immunity, but <em>overshoots</em> it! And it does this <em>exactly when</em> current cases (pink curve) peaks. (This happens no matter how you change the settings try it for yourself!)</p>
<p>This is because when there are more non-<icon s></icon>s than the herd immunity threshold, you get R &lt; 1. And when R &lt; 1, new cases stop growing: a peak.</p>
<p><strong>If there&#39;s only one lesson you take away from this guide, here it is</strong> it&#39;s an extremely complex diagram so please take time to fully absorb it:</p>
<p><img src="pics/r3.png" alt=""></p>
<p><strong>This means: we do NOT need to catch all transmissions, or even nearly all transmissions, to stop COVID-19!</strong></p>
<p>It&#39;s a paradox. COVID-19 is extremely contagious, yet to contain it, we &quot;only&quot; need to stop more than 60% of infections. 60%?! If that was a school grade, that&#39;s a D-. But if R<sub>0</sub> = 2.5, cutting that by 61% gives us R = 0.975, which is R &lt; 1, virus is contained!<sup id="fnref12"><a href="#fn12" rel="footnote">12</a></sup></p>
<p><img src="pics/r4.png" alt=""></p>
<p>(If you think R<sub>0</sub> or the other numbers in our simulations are too low/high, that&#39;s good you&#39;re challenging our assumptions! There&#39;ll be a &quot;Sandbox Mode&quot; at the end of this guide, where you can plug in your <em>own</em> numbers, and simulate what happens.)</p>
<p><em>Every</em> COVID-19 intervention you&#39;ve heard of handwashing, social/physical distancing, lockdowns, self-isolation, contact tracing &amp; quarantining, face masks, even &quot;herd immunity&quot; they&#39;re <em>all</em> doing the same thing:</p>
<p>Getting R &lt; 1.</p>
<p>So now, let&#39;s use our &quot;epidemic flight simulator&quot; to figure this out: How can we get R &lt; 1 in a way <strong>that also protects our mental health <em>and</em> financial health?</strong></p>
<p>Brace yourselves for an emergency landing...</p>
<div class="section">
<div>
<h1>The Next Few Months</h1>
</div>
</div>
<p>...could have been worse. Here&#39;s a parallel universe we avoided:</p>
<h3 id="toc_0">Scenario 0: Do Absolutely Nothing</h3>
<p>Around 1 in 20 people infected with COVID-19 need to go to an ICU (Intensive Care Unit).<sup id="fnref13"><a href="#fn13" rel="footnote">13</a></sup> In a rich country like the USA, there&#39;s 1 ICU per 3400 people.<sup id="fnref14"><a href="#fn14" rel="footnote">14</a></sup> Therefore, the USA can handle 20 out of 3400 people being <em>simultaneously</em> infected or, 0.6% of the population.</p>
<p>Even if we <em>more than tripled</em> that capacity to 2%, here&#39;s what would&#39;ve happened <em>if we did absolutely nothing:</em></p>
<div class="sim">
<iframe src="sim?stage=int-1&format=lines" width="800" height="540"></iframe>
</div>
<p>Not good.</p>
<p>That&#39;s what <a href="http://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-9-impact-of-npis-on-covid-19/">the March 16 Imperial College report</a> found: do nothing, and we run out of ICUs with 80%+ of the population infected.</p>
<p>Even if only 0.5% of infected die a generous assumption when there&#39;s no more ICUs in a large country like the US, with 300 million people, 0.5% of 80% of 300 million = still 1.2 million dead... <em>IF we did nothing.</em></p>
<p>(Lots of news &amp; social media reported &quot;80%+ will be infected&quot; <em>without</em> &quot;IF WE DO NOTHING&quot;. Fear was channelled into clicks, not understanding. <em>Sigh.</em>)</p>
<h3 id="toc_1">Scenario 1: Flatten The Curve / Herd Immunity</h3>
<p>The &quot;Flatten The Curve&quot; plan was touted by every public health organization, while the United Kingdom&#39;s original &quot;herd immunity&quot; plan was universally booed. They were <em>the same plan.</em> The UK just communicated theirs poorly.<sup id="fnref15"><a href="#fn15" rel="footnote">15</a></sup></p>
<p>Both plans, though, are horribly flawed.</p>
<p>First, let&#39;s look at the two main ways to &quot;flatten the curve&quot;: handwashing &amp; physical distancing.</p>
<p>Increased handwashing cuts flus &amp; colds in high-income countries by ~25%<sup id="fnref16"><a href="#fn16" rel="footnote">16</a></sup>, while the city-wide lockdown in London cut close contacts by ~70%<sup id="fnref17"><a href="#fn17" rel="footnote">17</a></sup>. So, let&#39;s assume handwashing can reduce R by <em>up to</em> 25%, and distancing can reduce R by <em>up to</em> 70%:</p>
<p><strong>Play with this calculator to see how % of non-<icon s></icon>, handwashing, and distancing reduce R:</strong> (this calculator visualizes their <em>relative</em> effects, which is why increasing one <em>looks</em> like it decreases the effect of the others.<sup id="fnref18"><a href="#fn18" rel="footnote">18</a></sup>)</p>
<div class="sim">
<iframe src="sim?stage=int-2a&format=calc" width="285" height="260"></iframe>
</div>
<p>Now, let&#39;s simulate what happens to a COVID-19 epidemic if, starting March 2020, we had increased handwashing but only <em>mild</em> physical distancing so that R is lower, but still above 1:</p>
<div class="sim">
<iframe src="sim?stage=int-2&format=lines" width="800" height="540"></iframe>
</div>
<p>Three notes:</p>
<ol>
<li><p>This <em>reduces</em> total cases! Lots of folks think &quot;Flatten The Curve&quot; spread outs cases without reducing the total. This is impossible in <em>any</em> Epidemiology 101 model. But because the news reported &quot;80%+ will be infected&quot; as inevitable, folks thought total cases will be the same no matter what. <em>Sigh.</em></p></li>
<li><p>Due to the extra interventions, current cases (pink curve) peaks <em>before</em> herd immunity is reached. And in fact, total cases doesn&#39;t overshoot, but <em>goes to</em> herd immunity the UK&#39;s plan! At that point, R &lt; 1, you can let go of all other interventions, and COVID-19 stays contained! Well, except for one problem...</p></li>
<li><p>You still run out of ICUs. For several months. (and remember, we <em>already</em> tripled ICUs for these simulations)</p></li>
</ol>
<p>That was the other finding of the March 16 Imperial College report, which convinced the UK to abandon its original plan. Any attempt at <strong>mitigation</strong> (reduce R, but R &gt; 1) will fail. The only way out is <strong>suppression</strong> (reduce R so that R &lt; 1).</p>
<p>That is, don&#39;t merely &quot;flatten&quot; the curve, <em>crush</em> the curve. For example, with a...</p>
<h3 id="toc_2">Scenario 2: Months-Long Lockdown</h3>
<p>Let&#39;s see what happens if we <em>crush</em> the curve with a 5-month lockdown, reduce <icon i></icon> to nearly nothing, then finally <em>finally</em> return to normal life:</p>
<div class="sim">
<iframe src="sim?stage=int-3&format=lines" width="800" height="540"></iframe>
</div>
<p>Oh.</p>
<p>This is the &quot;second wave&quot; everyone&#39;s talking about. As soon as we remove the lockdown, we get R &gt; 1 again. So, a single leftover <icon i></icon> (or imported <icon i></icon>) can cause a spike in cases that&#39;s almost as bad as if we&#39;d done Scenario 0: Absolutely Nothing.</p>
<p><strong>A lockdown isn&#39;t a cure, it&#39;s just a restart.</strong></p>
<p>So, what, do we just lockdown again &amp; again?</p>
<h3 id="toc_3">Scenario 3: Intermittent Lockdown</h3>
<p>This solution was first suggested by the Imperial College report, and later again by a Harvard paper<sup id="fnref19"><a href="#fn19" rel="footnote">19</a></sup>.</p>
<p><strong>Here&#39;s a simulation:</strong> (After playing the &quot;recorded scenario&quot;, you can try simulating your <em>own</em> lockdown schedule, by changing the sliders <em>while</em> the simulation is running! Remember you can pause &amp; continue the sim, and change the simulation speed)</p>
<div class="sim">
<iframe src="sim?stage=int-4&format=lines" width="800" height="540"></iframe>
</div>
<p>This <em>would</em> keep cases below ICU capacity! We&#39;d just need to... shut everything down for few months, open up for a few, shut down for a few, open up for a few... and repeat until a vaccine is available. (And if there&#39;s no vaccine, repeat until herd immunity is reached... in 2022.)</p>
<p>Look, it&#39;s nice to draw a line saying &quot;ICU capacity&quot;, but there&#39;s lots of important things we <em>can&#39;t</em> simulate here. Like:</p>
<p><strong>Mental Health:</strong> Loneliness is one of the biggest risk factors for depression, anxiety, and suicide. And it&#39;s as associated with an early death as smoking 15 cigarettes a day.<sup id="fnref20"><a href="#fn20" rel="footnote">20</a></sup></p>
<p><strong>Financial Health:</strong> &quot;What about the economy&quot; sounds like you care more about dollars than lives, but &quot;the economy&quot; isn&#39;t just stocks: it&#39;s people&#39;s ability to provide food &amp; shelter for their loved ones, to invest in their kids&#39; futures, and enjoy arts, foods, videogames the stuff makes life worth living. And besides, poverty <em>itself</em> has horrible impacts on mental and physical health.</p>
<p>Not saying we <em>shouldn&#39;t</em> lock down again! We&#39;ll look at &quot;circuit breaker&quot; lockdowns later. Still, it&#39;s not ideal.</p>
<p>But wait... haven&#39;t Taiwan and South Korea <em>already</em> contained COVID-19? For 4 whole months, <em>without</em> long-term lockdowns?</p>
<p>How?</p>
<h3 id="toc_4">Scenario 4: Test, Trace, Isolate</h3>
<p><em>&quot;Sure, we *could&#39;ve* done what Taiwan &amp; South Korea did at the start, but it&#39;s too late now. We missed the start.&quot;</em></p>
<p>But that&#39;s exactly it! “A lockdown isn&#39;t a cure, it&#39;s just a restart”... <strong>and a fresh start is what we need.</strong></p>
<p>To understand how Taiwan &amp; South Korea contained COVID-19, we need to understand the exact timeline of a typical COVID-19 infection<sup id="fnref21"><a href="#fn21" rel="footnote">21</a></sup>:</p>
<p><img src="pics/timeline1.png" alt=""></p>
<p>If cases only self-isolate when they know they&#39;re sick (that is, they feel symptoms), the virus can still spread:</p>
<p><img src="pics/timeline2.png" alt=""></p>
<p>And in fact, 44% of all transmissions are like this: <em>pre</em>-symptomatic! <sup id="fnref22"><a href="#fn22" rel="footnote">22</a></sup></p>
<p>But, if we find <em>and quarantine</em> a symptomatic case&#39;s recent close contacts... we stop the spread, by staying one step ahead!</p>
<p><img src="pics/timeline3.png" alt=""></p>
<p>This is called <strong>contact tracing</strong>, and it&#39;s a core part of Taiwan &amp; South Korea&#39;s successful strategies.</p>
<p>Traditionally, contact tracing is done with in-person interviews, but that&#39;s too slow for COVID-19&#39;s ~48 hour window. That&#39;s why on March 31st, <a href="https://science.sciencemag.org/content/early/2020/04/09/science.abb6936">an Oxford study</a> recommended helping contact tracers with <em>contact tracing apps</em>.</p>
<p>Does that mean giving up privacy, giving in to Big Brother? Heck no! <a href="https://github.com/DP-3T/documents#decentralized-privacy-preserving-proximity-tracing">DP-3T</a>, a team of epidemiologists &amp; cryptographers (including one of us, Marcel Salathé) is <em>already</em> making a contact tracing app that reveals <strong>no info about your identity, location, who your contacts are, or even <em>how many contacts</em> you&#39;ve had.</strong></p>
<p>Here&#39;s how it works:</p>
<p><img src="pics/dp3t.png" alt=""></p>
<p>(<a href="https://ncase.me/contact-tracing/">Here&#39;s the full comic</a>, and <a href="">here&#39;s a video adaptation by 3Blue1Brown</a>)</p>
<p>Along with similar teams like <a href="https://github.com/TCNCoalition/TCN#tcn-protocol">TCN Protocol</a> and <a href="https://pact.mit.edu/">MIT PACT</a>, they&#39;ve inspired Apple &amp; Google to bake privacy-first contact tracing <a href="https://www.apple.com/ca/newsroom/2020/04/apple-and-google-partner-on-covid-19-contact-tracing-technology/">directly into Android/iOS</a>. Next month, your local public health agency may ask you to download an app. If it&#39;s privacy-first &amp; open-source, please do!</p>
<p>But what about folks without smartphones? Or infections through doorknobs? Or &quot;true&quot; asymptomatic cases? Contact tracing apps can&#39;t catch all transmissions... <em>and that&#39;s okay!</em> We don&#39;t need to catch <em>all</em> transmissions, just 60%+ to get R &lt; 1.</p>
<p>(rant about the confusion about pre-symptomatic vs. &quot;true&quot; asymptomatic:<sup id="fnref23"><a href="#fn23" rel="footnote">23</a></sup>)</p>
<p>Anyway, isolating cases would reduce R by up to 40%, and quarantining their contacts would reduce R by up to 50%<sup id="fnref24"><a href="#fn24" rel="footnote">24</a></sup>:</p>
<div class="sim">
<iframe src="sim?stage=int-4a&format=calc" width="285" height="340"></iframe>
</div>
<p>Thus, even without 100% contact quarantining, we can get R &lt; 1 <em>without a lockdown!</em> Much better for our mental &amp; financial health. (As for the cost to folks who have to self-isolate/quarantine, <em>governments should support them</em> subsidized paid leave, job protection, etc. Still way cheaper than intermittent lockdown.)</p>
<p>We then keep R &lt; 1 until we have a vaccine, which turns susceptible <icon s></icon>s into immune <icon r></icon>s. Herd immunity, the <em>right</em> way:</p>
<div class="sim">
<iframe src="sim?stage=int-4b&format=calc" width="285" height="230"></iframe>
</div>
<p>Okay, enough talk. Here&#39;s a simulation of:</p>
<ol>
<li>A few-month lockdown, until we can...</li>
<li>Switch to &quot;Test, Trace, Isolate&quot; until we can...</li>
<li>Vaccinate enough people, which means...</li>
<li>We win.</li>
</ol>
<div class="sim">
<iframe src="sim?stage=int-5&format=lines" width="800" height="540"></iframe>
</div>
<p>So that&#39;s it! That&#39;s how we make an emergency landing on this plane.</p>
<p>That&#39;s how we beat COVID-19.</p>
<p>...</p>
<p>But what if things <em>still</em> go wrong? Things have gone horribly wrong already. That&#39;s fear, and that&#39;s good! Fear gives us energy to create <em>backup plans</em>.</p>
<p>The pessimist invents the parachute.</p>
<h3 id="toc_5">Scenario 4+: Masks For All, Summer, Circuit Breakers</h3>
<p>What if R<sub>0</sub> is way higher than we thought, and the above interventions, even with mild distancing, <em>still</em> aren&#39;t enough to get R &lt; 1?</p>
<p>If so, here&#39;s a few supplements:</p>
<p><strong>Masks For All:</strong></p>
<p><em>&quot;Wait,&quot;</em> you might ask, <em>&quot;I thought face masks don&#39;t stop you from getting sick?&quot;</em></p>
<p>You&#39;re right. Masks don&#39;t stop you from getting sick... they stop you from getting <em>others</em> sick.</p>
<p><img src="pics/masks.png" alt=""></p>
<p>(sources for the comic: <sup id="fnref25"><a href="#fn25" rel="footnote">25</a></sup> <sup id="fnref26"><a href="#fn26" rel="footnote">26</a></sup> <sup id="fnref27"><a href="#fn27" rel="footnote">27</a></sup> <sup id="fnref28"><a href="#fn28" rel="footnote">28</a></sup>)</p>
<p>Still, in science, one should only publish a finding if you&#39;re 95% sure of it. (...<em>should.</em><sup id="fnref29"><a href="#fn29" rel="footnote">29</a></sup>) Admittedly, the current evidence for face masks on COVID-19 <em>specifically</em>, rather than &quot;just&quot; colds and flus, is less than &quot;95% sure&quot;.</p>
<p>But, pandemics are like poker. <strong>Make bets only when you&#39;re 95% sure, and you&#39;ll lose everything at stake.</strong> We <em>have</em> to make cost/benefit analyses under uncertainty.<sup id="fnref30"><a href="#fn30" rel="footnote">30</a></sup> Like so:</p>
<p>Cost: If homemade cloth masks, same as the cost of all that soap for handwashing. If surgical masks, more expensive but still pretty cheap.</p>
<p>Benefit: Even if it&#39;s a 5050 chance of surgical masks reducing transmission by 0% or 70%<sup id="fnref31"><a href="#fn31" rel="footnote">31</a></sup>, the average &quot;expected value&quot; is still 35%, same as a half-lockdown! So let&#39;s guess-timate that surgical masks reduce R by up to 35%. (Again, you can challenge our assumptions by turning the sliders up/down)</p>
<p><strong>Here&#39;s a calculator of how masks reduce R! You can switch between cloth &amp; surgical:</strong> (assumes cloth masks are half as effective as surgical masks<sup id="fnref32"><a href="#fn32" rel="footnote">32</a></sup>)</p>
<p>[TODO: Actually allow toggling between cloth/surgical. Currently locked to cloth]</p>
<div class="sim">
<iframe src="sim?stage=int-6a&format=calc" width="285" height="380"></iframe>
</div>
<p>(other arguments for/against masks:<sup id="fnref33"><a href="#fn33" rel="footnote">33</a></sup>)</p>
<p>Masks <em>alone</em> won&#39;t get R &lt; 1. But if handwashing &amp; &quot;Test, Trace, Isolate&quot; only gets us to R = 1.10, having just 2/3 of people wear <em>cloth</em> masks would tip that over to R &lt; 1, virus contained!</p>
<p><strong>Summer:</strong></p>
<p>Okay, this isn&#39;t an &quot;intervention&quot; we can control, but it will help! Some news outlets report that summer won&#39;t do anything to COVID-19. They&#39;re half right: summer won&#39;t get R &lt; 1, but it <em>will</em> reduce R.</p>
<p>For COVID-19, every extra 1° Celsius (2.2° Fahrenheit) makes R drop by 1.2%.<sup id="fnref34"><a href="#fn34" rel="footnote">34</a></sup> The summer-winter difference in New York City is 15°C (60°F), so summer will make R drop by 18%.</p>
<p>[TODO: Fix weird arrow glitch]</p>
<div class="sim">
<iframe src="sim?stage=int-6b&format=calc" width="285" height="220"></iframe>
</div>
<p>Summer alone won&#39;t make R &lt; 1, but if we have limited resources, we can scale back some interventions in the summer so we can scale them <em>higher</em> in the winter.</p>
<p><strong>A &quot;Circuit Breaker&quot; Lockdown:</strong></p>
<p>And if all that <em>still</em> isn&#39;t enough to get R &lt; 1... we can do another lockdown.</p>
<p>But we wouldn&#39;t have to be 2-months-closed / 1-month-open over &amp; over! Because R is reduced, we&#39;d only need one or two more &quot;circuit breaker&quot; lockdowns before a vaccine is available. (Singapore had to do this recently, &quot;despite&quot; having controlled COVID-19 for 4 months. That&#39;s not failure: this <em>is</em> what success takes.)</p>
<p>Here&#39;s a simulation a &quot;lazy case&quot; scenario:</p>
<ol>
<li>Lockdown, then</li>
<li>A moderate amount of hygiene + &quot;Test, Trace, Isolate&quot; + <em>cloth</em> &quot;Masks For All&quot;, then...</li>
<li>One more &quot;circuit breaker&quot; lockdown before a vaccine&#39;s found.</li>
</ol>
<div class="sim">
<iframe src="sim?stage=int-7&format=lines&height=620" width="800" height="620"></iframe>
</div>
<p>[TODO: Other options like temperature testing at malls, quarantines for travellers, replacing handshaking, etc]</p>
<p>. . .</p>
<p>We hope these plans give you hope. </p>
<p><strong>Even under a pessimistic scenario, it <em>is</em> possible to beat COVID-19, while protecting our mental and financial health.</strong> Use the lockdown as a restart, keep R &lt; 1 with privacy-protecting contract tracing, supplemented with at <em>least</em> cloth masks... and life can get back to a normal-ish!</p>
<p>Sure, your hands may be dry. But you&#39;ll get to invite a date out to a comics bookstore! You&#39;ll get to go out with friends to watch the latest Hollywood cash-grab. You&#39;ll get to people-watch at a library, taking joy in people going about the simple business of <em>being alive.</em></p>
<p>Even under the worst-case scenario... life perseveres.</p>
<p>So now, let&#39;s plan for some <em>worse</em> worst-case scenarios. Water landing, get your life jacket, and please follow the lights to the emergency exits:</p>
<div class="section">
<div>
<h1>The Next Few Years</h1>
</div>
</div>
<p>You get COVID-19, and recover. Or you get the COVID-19 vaccine. Either way, you&#39;re now immune...</p>
<p>...<em>for how long?</em></p>
<p>There&#39;s been reports of folks who test positive again after recovering, but those were false positives. Still, the possibility of <strong>waning immunity</strong> is very real. Either a new mutant strain evolves, or your immune system just... forgets.</p>
<p>The coronavirus responsible for COVID-19 is most closely related to the coronavirus responsible for SARS. SARS (probably) gave its survivors around 2 years of immunity.<sup id="fnref35"><a href="#fn35" rel="footnote">35</a></sup> The coronaviruses that cause &quot;the&quot; common cold give you 1 year of immunity<sup id="fnref36"><a href="#fn36" rel="footnote">36</a></sup>. So:</p>
<p><em>What if COVID-19 immunity doesn&#39;t last?</em></p>
<p>Here&#39;s a simulation starting with 100% <icon i></icon>, exponentially decaying into <icon r></icon>s after 10 days... but then back to susceptible, no-immunity <icon s></icon>s after 1 year:</p>
<div class="sim">
<iframe src="sim?stage=yrs-1" width="800" height="540"></iframe>
</div>
<p>Return of the exponential decay!</p>
<p>This is the <strong>SEIRS Model</strong>. The final &quot;S&quot; stands for <icon s></icon> Susceptible, again.</p>
<p><img src="pics/seirs.png" alt=""></p>
<p>Now let&#39;s simulate a COVID-19 outbreak, over 10 years, with no interventions... <em>if immunity only lasts a year:</em></p>
<div class="sim">
<iframe src="sim?stage=yrs-2&format=lines&height=600" width="800" height="600"></iframe>
</div>
<p>Previously, we only had <em>one</em> ICU-overwhelming spike. Now, we have several, <em>and</em> <icon i></icon> cases come to a rest <em>permanently at</em> ICU capacity. (Which, remember, we <em>tripled</em> for these simulations)</p>
<p>R = 1, it&#39;s <strong>endemic.</strong></p>
<p>Thankfully, because summer reduces R, it&#39;ll make the situation better:</p>
<div class="sim">
<iframe src="sim?stage=yrs-3&format=lines&height=640" width="800" height="640"></iframe>
</div>
<p>Oh.</p>
<p>Counterintuitively, summer makes the spikes worse <em>and</em> regular! This is because summer reduces new <icon i></icon>s, but that in turn reduces new immune <icon r></icon>s. Which means immunity plummets in the summer, <em>creating</em> large regular spikes in the winter.</p>
<p>Thankfully, the solution to this is pretty straightforward just vaccinate people every fall/winter, like we do with flu shots:</p>
<p><strong>(After playing the recording, try simulating your own vaccination campaigns! Remember you can pause/continue the sim at any time)</strong></p>
<div class="sim">
<iframe src="sim?stage=yrs-4&format=lines" width="800" height="540"></iframe>
</div>
<p>But here&#39;s the scarier question:</p>
<p>What if there&#39;s no vaccine for <em>years</em>? Or <em>ever?</em></p>
<p><strong>To be clear: this is unlikely.</strong> Sure, there&#39;s never been a vaccine for any of the other coronaviruses before, but that&#39;s because SARS was eradicated quickly, and &quot;the&quot; common cold wasn&#39;t worth the investment. Coronaviruses aren&#39;t any more complex than the viruses we already have vaccines for, so most infectious disease researchers expect a vaccine in 1 to 2 years.</p>
<p>Still, they&#39;ve expressed worries about a vaccine: What if we can&#39;t make enough?<sup id="fnref37"><a href="#fn37" rel="footnote">37</a></sup> What if we rush it, and it&#39;s not safe?<sup id="fnref38"><a href="#fn38" rel="footnote">38</a></sup></p>
<p>Even in the nightmare &quot;no-vaccine&quot; scenario, we still have 3 ways out. From most to least terrible:</p>
<p>1) Do intermittent or loose R &lt; 1 interventions, to reach &quot;natural herd immunity&quot;. (Warning: this will result in many deaths &amp; damaged lungs. <em>And</em> won&#39;t work if immunity doesn&#39;t last.)</p>
<p>2) Do the R &lt; 1 interventions forever. Contact tracing &amp; wearing masks just becomes a new norm in the post-COVID-19 world, like how STI tests &amp; wearing condoms became a new norm in the post-HIV world. (Nobody suggested &quot;herd immunity&quot; for HIV...)</p>
<p>3) Do the R &lt; 1 interventions until we develop treatments that make COVID-19 way, way less likely to need critical care. (Which we should be doing <em>anyway!</em>) Reducing ICU use by 10x is the same as increasing our ICU capacity by 10x:</p>
<p><strong>Here&#39;s a simulation of <em>no</em> lasting immunity, <em>no</em> vaccine, and not even any interventions just slowly increasing capacity to survive the long-term spikes:</strong></p>
<div class="sim">
<iframe src="sim?stage=yrs-5&format=lines" width="800" height="540"></iframe>
</div>
<p>Even under the <em>worst</em> worst-case scenario... life perseveres.</p>
<p>. . .</p>
<p>Maybe you&#39;d like to challenge our assumptions, and try different R<sub>0</sub>&#39;s or numbers. Or try simulating your <em>own</em> combination of intervention plans!</p>
<p><strong>Here&#39;s an (optional) Sandbox Mode, with <em>everything</em> available. Simulate &amp; play around to your heart&#39;s content:</strong></p>
<p>[TODO: EMBED THIS IN A WAY THAT DOESN&#39;T SUCK]</p>
<div class="sim">
<iframe src="sim?stage=SB&format=sb&height=1000" width="800" height="1000"></iframe>
</div>
<p>This basic &quot;epidemic flight simulator&quot; has taught us so much. It&#39;s let us answer questions about the past few months, next few months, and next few years.</p>
<p>So finally, let&#39;s return to...</p>
<div class="section">
<div>
<h1>The Now</h1>
</div>
</div>
<p>Plane&#39;s in the ocean. We&#39;ve scrambled onto the life rafts. It&#39;s time to find dry land.<sup id="fnref39"><a href="#fn39" rel="footnote">39</a></sup></p>
<p>Teams of epidemiologists and policymakers (<a href="https://www.americanprogress.org/issues/healthcare/news/2020/04/03/482613/national-state-plan-end-coronavirus-crisis/">left</a>, <a href="https://www.aei.org/research-products/report/national-coronavirus-response-a-road-map-to-reopening/">right</a>, and <a href="https://ethics.harvard.edu/covid-roadmap">multi-partisan</a>) have come to a consensus on how to beat COVID-19, while protecting our lives <em>and</em> liberties.</p>
<p>Here&#39;s the rough idea, with some (less-consensus) backup plans:</p>
<p><img src="pics/plan.png" alt=""></p>
<p>So what does this mean for YOU, right now?</p>
<p><strong>For everyone:</strong> Respect the lockdown so we can get out of Phase I asap. Keep washing those hands. Make your own masks. Download a <em>privacy-protecting</em> contact tracing app when those are available next month. Stay healthy, physically &amp; mentally! And write your local policymaker to get off their butt and...</p>
<p><strong>For policymakers:</strong> Make laws to support folks who have to self-isolate/quarantine. Hire more manual contact tracers, <em>supported</em> by privacy-protecting contact tracing apps. Direct more funds into the stuff we should be building, like...</p>
<p><strong>For builders:</strong> Build tests. Build ventilators. Build personal protective equipment for hospitals. Build tests. Build masks. Build apps. Build antivirals, prophylactics, and other treatments that aren&#39;t vaccines. Build vaccines. Build tests. Build tests. Build tests. Build hope. </p>
<p>Don&#39;t downplay fear to build up hope. Our fear should <em>team up</em> with our hope, like the inventors of airplanes &amp; parachutes. Preparing for horrible futures is how we <em>create</em> a hopeful future.</p>
<p>The only thing to fear is the idea that the only thing to fear is fear itself.</p>
<p><strong>{ Please let me know what you think! How did it feel overall, any parts in particular that went too slow or were too confusing, factual inaccuracies, nuances I missed, stuff I oughta mention, etc. Thank you! }</strong></p>
<div class="footnotes">
<hr>
<ol>
<li id="fn1">
<p>(NOTE: This guide was published on April 30th, 2020. Many details will become outdated, but Epidemiology 101 will remain true, and we&#39;re confident this guide will cover 95% of possible futures.)&nbsp;<a href="#fnref1" rev="footnote">&#8617;</a></p>
</li>
<li id="fn2">
<p>https://wwwnc.cdc.gov/eid/article/26/6/20-0357_article&nbsp;<a href="#fnref2" rev="footnote">&#8617;</a></p>
</li>
<li id="fn3">
<p>source&nbsp;<a href="#fnref3" rev="footnote">&#8617;</a></p>
</li>
<li id="fn4">
<p>https://link.springer.com/article/10.1007/s11427-020-1661-4&nbsp;<a href="#fnref4" rev="footnote">&#8617;</a></p>
</li>
<li id="fn5">
<p>source, and sidenote on &#39;infectious&#39;&nbsp;<a href="#fnref5" rev="footnote">&#8617;</a></p>
</li>
<li id="fn6">
<p>source&nbsp;<a href="#fnref6" rev="footnote">&#8617;</a></p>
</li>
<li id="fn7">
<p>source&nbsp;<a href="#fnref7" rev="footnote">&#8617;</a></p>
</li>
<li id="fn8">
<p>https://bmcinfectdis.biomedcentral.com/articles/10.1186/1471-2334-14-480&nbsp;<a href="#fnref8" rev="footnote">&#8617;</a></p>
</li>
<li id="fn9">
<p>https://pubmed.ncbi.nlm.nih.gov/31995857/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7001239/&nbsp;<a href="#fnref9" rev="footnote">&#8617;</a></p>
</li>
<li id="fn10">
<p>https://wwwnc.cdc.gov/eid/article/26/7/20-0282_article&nbsp;<a href="#fnref10" rev="footnote">&#8617;</a></p>
</li>
<li id="fn11">
<p>sas&nbsp;<a href="#fnref11" rev="footnote">&#8617;</a></p>
</li>
<li id="fn12">
<p>exact formula...&nbsp;<a href="#fnref12" rev="footnote">&#8617;</a></p>
</li>
<li id="fn13">
<p>https://www.statista.com/statistics/1105420/covid-icu-admission-rates-us-by-age-group/ Lower end, 5%.&nbsp;<a href="#fnref13" rev="footnote">&#8617;</a></p>
</li>
<li id="fn14">
<p>https://sccm.org/Blog/March-2020/United-States-Resource-Availability-for-COVID-19&nbsp;<a href="#fnref14" rev="footnote">&#8617;</a></p>
</li>
<li id="fn15">
<p>https://www.theatlantic.com/health/archive/2020/03/coronavirus-pandemic-herd-immunity-uk-boris-johnson/608065/&nbsp;<a href="#fnref15" rev="footnote">&#8617;</a></p>
</li>
<li id="fn16">
<p>https://onlinelibrary.wiley.com/doi/full/10.1111/j.1365-3156.2006.01568.x&nbsp;<a href="#fnref16" rev="footnote">&#8617;</a></p>
</li>
<li id="fn17">
<p>https://cmmid.github.io/topics/covid19/comix-impact-of-physical-distance-measures-on-transmission-in-the-UK.html&nbsp;<a href="#fnref17" rev="footnote">&#8617;</a></p>
</li>
<li id="fn18">
<p>log scale&nbsp;<a href="#fnref18" rev="footnote">&#8617;</a></p>
</li>
<li id="fn19">
<p>https://science.sciencemag.org/content/early/2020/04/14/science.abb5793?&nbsp;<a href="#fnref19" rev="footnote">&#8617;</a></p>
</li>
<li id="fn20">
<p>https://journals.sagepub.com/doi/abs/10.1177/1745691614568352&nbsp;<a href="#fnref20" rev="footnote">&#8617;</a></p>
</li>
<li id="fn21">
<p>sources plz, esp for incubation period 5 days&nbsp;<a href="#fnref21" rev="footnote">&#8617;</a></p>
</li>
<li id="fn22">
<p>https://www.nature.com/articles/s41591-020-0869-5&nbsp;<a href="#fnref22" rev="footnote">&#8617;</a></p>
</li>
<li id="fn23">
<p>asds&nbsp;<a href="#fnref23" rev="footnote">&#8617;</a></p>
</li>
<li id="fn24">
<p>https://science.sciencemag.org/content/early/2020/04/09/science.abb6936&nbsp;<a href="#fnref24" rev="footnote">&#8617;</a></p>
</li>
<li id="fn25">
<p>incoming&nbsp;<a href="#fnref25" rev="footnote">&#8617;</a></p>
</li>
<li id="fn26">
<p>outgoing_aerosols&nbsp;<a href="#fnref26" rev="footnote">&#8617;</a></p>
</li>
<li id="fn27">
<p>outgoing_droplets&nbsp;<a href="#fnref27" rev="footnote">&#8617;</a></p>
</li>
<li id="fn28">
<p>homemade&nbsp;<a href="#fnref28" rev="footnote">&#8617;</a></p>
</li>
<li id="fn29">
<p>ss&nbsp;<a href="#fnref29" rev="footnote">&#8617;</a></p>
</li>
<li id="fn30">
<p>That BMJ article&nbsp;<a href="#fnref30" rev="footnote">&#8617;</a></p>
</li>
<li id="fn31">
<p>s&nbsp;<a href="#fnref31" rev="footnote">&#8617;</a></p>
</li>
<li id="fn32">
<p>ss&nbsp;<a href="#fnref32" rev="footnote">&#8617;</a></p>
</li>
<li id="fn33">
<p>s&nbsp;<a href="#fnref33" rev="footnote">&#8617;</a></p>
</li>
<li id="fn34">
<p>https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=3551767 The average R-value of these 100 cities is 1.83 , One-degree Celsius increase in temperature and one percent increase in relative humidity lower R by 0.0225 &nbsp;<a href="#fnref34" rev="footnote">&#8617;</a></p>
</li>
<li id="fn35">
<p>https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2851497/&nbsp;<a href="#fnref35" rev="footnote">&#8617;</a></p>
</li>
<li id="fn36">
<p>https://pubmed.ncbi.nlm.nih.gov/2170159/&nbsp;<a href="#fnref36" rev="footnote">&#8617;</a></p>
</li>
<li id="fn37">
<p>https://www.nature.com/articles/d41586-020-01063-8&nbsp;<a href="#fnref37" rev="footnote">&#8617;</a></p>
</li>
<li id="fn38">
<p>https://www.nature.com/articles/d41586-020-00751-9&nbsp;<a href="#fnref38" rev="footnote">&#8617;</a></p>
</li>
<li id="fn39">
<p>https://www.statnews.com/2020/04/01/navigating-covid-19-pandemic/&nbsp;<a href="#fnref39" rev="footnote">&#8617;</a></p>
</li>
</ol>
</div>
</article>
-->
<article>
<div class="section">
<div>
<h1>What Happens Next?</h1>
<h2>COVID-19 Futures, Explained With Playable Simulations</h2>
<h3>by Marcel Salathé (epidemiologist) and Nicky Case (art/code)</h3>
<h3>🕐 28 min play/read</h3>
</div>
</div>
<p>foo bar foo bar foo bar</p>
<p>foo bar foo bar foo bar</p>
<p>foo bar foo bar foo bar</p>
<p>foo bar foo bar foo bar</p>
<p>foo bar foo bar foo bar</p>
<p>foo bar foo bar foo bar</p>
<p>foo bar foo bar foo bar</p>
<p>foo bar foo bar foo bar</p>
<div class="footnotes">
<hr>
<ol>
<li id="fn1">
<p>(NOTE: This guide was published on April 30th, 2020. Many details will become outdated, but Epidemiology 101 will remain true, and we&#39;re confident this guide will cover 95% of possible futures.)&nbsp;<a href="#fnref1" rev="footnote">&#8617;</a></p>
</li>
<li id="fn2">
<p>https://wwwnc.cdc.gov/eid/article/26/6/20-0357_article&nbsp;<a href="#fnref2" rev="footnote">&#8617;</a></p>
</li>
<li id="fn3">
<p>source&nbsp;<a href="#fnref3" rev="footnote">&#8617;</a></p>
</li>
<li id="fn4">
<p>https://link.springer.com/article/10.1007/s11427-020-1661-4&nbsp;<a href="#fnref4" rev="footnote">&#8617;</a></p>
</li>
<li id="fn5">
<p>source, and sidenote on &#39;infectious&#39;&nbsp;<a href="#fnref5" rev="footnote">&#8617;</a></p>
</li>
<li id="fn6">
<p>source&nbsp;<a href="#fnref6" rev="footnote">&#8617;</a></p>
</li>
<li id="fn7">
<p>source&nbsp;<a href="#fnref7" rev="footnote">&#8617;</a></p>
</li>
<li id="fn8">
<p>https://bmcinfectdis.biomedcentral.com/articles/10.1186/1471-2334-14-480&nbsp;<a href="#fnref8" rev="footnote">&#8617;</a></p>
</li>
<li id="fn9">
<p>https://pubmed.ncbi.nlm.nih.gov/31995857/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7001239/&nbsp;<a href="#fnref9" rev="footnote">&#8617;</a></p>
</li>
<li id="fn10">
<p>https://wwwnc.cdc.gov/eid/article/26/7/20-0282_article&nbsp;<a href="#fnref10" rev="footnote">&#8617;</a></p>
</li>
<li id="fn11">
<p>sas&nbsp;<a href="#fnref11" rev="footnote">&#8617;</a></p>
</li>
<li id="fn12">
<p>exact formula...&nbsp;<a href="#fnref12" rev="footnote">&#8617;</a></p>
</li>
<li id="fn13">
<p>https://www.statista.com/statistics/1105420/covid-icu-admission-rates-us-by-age-group/ Lower end, 5%.&nbsp;<a href="#fnref13" rev="footnote">&#8617;</a></p>
</li>
<li id="fn14">
<p>https://sccm.org/Blog/March-2020/United-States-Resource-Availability-for-COVID-19&nbsp;<a href="#fnref14" rev="footnote">&#8617;</a></p>
</li>
<li id="fn15">
<p>https://www.theatlantic.com/health/archive/2020/03/coronavirus-pandemic-herd-immunity-uk-boris-johnson/608065/&nbsp;<a href="#fnref15" rev="footnote">&#8617;</a></p>
</li>
<li id="fn16">
<p>https://onlinelibrary.wiley.com/doi/full/10.1111/j.1365-3156.2006.01568.x&nbsp;<a href="#fnref16" rev="footnote">&#8617;</a></p>
</li>
<li id="fn17">
<p>https://cmmid.github.io/topics/covid19/comix-impact-of-physical-distance-measures-on-transmission-in-the-UK.html&nbsp;<a href="#fnref17" rev="footnote">&#8617;</a></p>
</li>
<li id="fn18">
<p>log scale&nbsp;<a href="#fnref18" rev="footnote">&#8617;</a></p>
</li>
<li id="fn19">
<p>https://science.sciencemag.org/content/early/2020/04/14/science.abb5793?&nbsp;<a href="#fnref19" rev="footnote">&#8617;</a></p>
</li>
<li id="fn20">
<p>https://journals.sagepub.com/doi/abs/10.1177/1745691614568352&nbsp;<a href="#fnref20" rev="footnote">&#8617;</a></p>
</li>
<li id="fn21">
<p>sources plz, esp for incubation period 5 days&nbsp;<a href="#fnref21" rev="footnote">&#8617;</a></p>
</li>
<li id="fn22">
<p>https://www.nature.com/articles/s41591-020-0869-5&nbsp;<a href="#fnref22" rev="footnote">&#8617;</a></p>
</li>
<li id="fn23">
<p>asds&nbsp;<a href="#fnref23" rev="footnote">&#8617;</a></p>
</li>
<li id="fn24">
<p>https://science.sciencemag.org/content/early/2020/04/09/science.abb6936&nbsp;<a href="#fnref24" rev="footnote">&#8617;</a></p>
</li>
<li id="fn25">
<p>incoming&nbsp;<a href="#fnref25" rev="footnote">&#8617;</a></p>
</li>
<li id="fn26">
<p>outgoing_aerosols&nbsp;<a href="#fnref26" rev="footnote">&#8617;</a></p>
</li>
<li id="fn27">
<p>outgoing_droplets&nbsp;<a href="#fnref27" rev="footnote">&#8617;</a></p>
</li>
<li id="fn28">
<p>homemade&nbsp;<a href="#fnref28" rev="footnote">&#8617;</a></p>
</li>
<li id="fn29">
<p>ss&nbsp;<a href="#fnref29" rev="footnote">&#8617;</a></p>
</li>
<li id="fn30">
<p>That BMJ article&nbsp;<a href="#fnref30" rev="footnote">&#8617;</a></p>
</li>
<li id="fn31">
<p>s&nbsp;<a href="#fnref31" rev="footnote">&#8617;</a></p>
</li>
<li id="fn32">
<p>ss&nbsp;<a href="#fnref32" rev="footnote">&#8617;</a></p>
</li>
<li id="fn33">
<p>s&nbsp;<a href="#fnref33" rev="footnote">&#8617;</a></p>
</li>
<li id="fn34">
<p>https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=3551767 The average R-value of these 100 cities is 1.83 , One-degree Celsius increase in temperature and one percent increase in relative humidity lower R by 0.0225 &nbsp;<a href="#fnref34" rev="footnote">&#8617;</a></p>
</li>
<li id="fn35">
<p>https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2851497/&nbsp;<a href="#fnref35" rev="footnote">&#8617;</a></p>
</li>
<li id="fn36">
<p>https://pubmed.ncbi.nlm.nih.gov/2170159/&nbsp;<a href="#fnref36" rev="footnote">&#8617;</a></p>
</li>
<li id="fn37">
<p>https://www.nature.com/articles/d41586-020-01063-8&nbsp;<a href="#fnref37" rev="footnote">&#8617;</a></p>
</li>
<li id="fn38">
<p>https://www.nature.com/articles/d41586-020-00751-9&nbsp;<a href="#fnref38" rev="footnote">&#8617;</a></p>
</li>
<li id="fn39">
<p>https://www.statnews.com/2020/04/01/navigating-covid-19-pandemic/&nbsp;<a href="#fnref39" rev="footnote">&#8617;</a></p>
</li>
</ol>
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