Add nowrap spans around icons and adjacent text
This commit is contained in:
Tim Scalzo
parent
a0561b1e47
commit
c379c2b1df
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@ -95,6 +95,10 @@ icon[r]{
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background-image: url(../icons/r.png);
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}
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.nowrap{
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white-space: nowrap;
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}
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p > img{
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width: 100%;
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border: 1px solid #ddd;
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38
index.html
38
index.html
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@ -119,7 +119,7 @@
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<p>It'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> every 4 days, <em>on average</em>.<sup id="fnref2"><a href="#fn2" rel="footnote">2</a></sup> (remember, there's a lot of variation)</p>
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<p>If we simulate "double every 4 days" <em>and nothing else</em>, on a population starting with just 0.001% <icon i></icon>, what happens? </p>
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<p>If we simulate "double every 4 days" <em>and nothing else</em>, on a population starting with just 0.001% <span class="nowrap"><icon i></icon>,</span> what happens? </p>
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<p><strong>Click "Start" 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>
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@ -135,7 +135,7 @@
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<p><img src="pics/susceptibles.png" alt=""></p>
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<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>
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<p>The more <span class="nowrap"><icon i></icon>s</span> there are, the faster <span class="nowrap"><icon s></icon>s</span> become <span class="nowrap"><icon i></icon>s,</span> <strong>but the fewer <span class="nowrap"><icon s></icon>s</span> there are, the <em>slower</em> <span class="nowrap"><icon s></icon>s</span> become <span class="nowrap"><icon i></icon>s.</span></strong></p>
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<p>How's this change the growth of an epidemic? Let's find out:</p>
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@ -147,9 +147,9 @@
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<p>But, this simulation is <em>still</em> wrong. We're missing the fact that <icon i></icon> Infectious people eventually stop being infectious, either by 1) recovering, 2) "recovering" with lung damage, or 3) dying.</p>
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<p>For simplicity's sake, let's pretend that all <icon i></icon> Infectious people become <icon r></icon> Recovered. (Just remember that in reality, some are dead.) <icon r></icon>s can't be infected again, and let's pretend – <em>for now!</em> – that they stay immune for life.</p>
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<p>For simplicity's sake, let's pretend that all <icon i></icon> Infectious people become <icon r></icon> Recovered. (Just remember that in reality, some are dead.) <span class="nowrap"><icon r></icon>s</span> can't be infected again, and let's pretend – <em>for now!</em> – that they stay immune for life.</p>
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<p>With COVID-19, it's estimated you're <icon i></icon> Infectious for 10 days, <em>on average</em>.<sup id="fnref4"><a href="#fn4" rel="footnote">4</a></sup> That means some folks will recover before 10 days, some after. <strong>Here's what that looks like, with a simulation <em>starting</em> with 100% <icon i></icon>:</strong></p>
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<p>With COVID-19, it's estimated you're <icon i></icon> Infectious for 10 days, <em>on average</em>.<sup id="fnref4"><a href="#fn4" rel="footnote">4</a></sup> That means some folks will recover before 10 days, some after. <strong>Here's what that looks like, with a simulation <em>starting</em> with 100% <span class="nowrap"><icon i></icon>:</span></strong></p>
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<div class="sim">
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<iframe src="sim?stage=epi-3" width="800" height="540"></iframe>
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@ -163,9 +163,9 @@
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<p>Let's find out.</p>
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<p><b style='color:#ff4040'>Red curve</b> is <em>current</em> cases <icon i></icon>,<br>
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<b style='color:#999999'>Gray curve</b> is <em>total</em> cases (current + recovered <icon r></icon>),
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starts at just 0.001% <icon i></icon>:</p>
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<p><b style='color:#ff4040'>Red curve</b> is <em>current</em> cases <span class="nowrap"><icon i></icon>,</span><br>
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<b style='color:#999999'>Gray curve</b> is <em>total</em> cases (current + recovered <span class="nowrap"><icon r></icon>),</span>
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starts at just 0.001% <span class="nowrap"><icon i></icon>:</span></p>
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<div class="sim">
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<iframe src="sim?stage=epi-4" width="800" height="540"></iframe>
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@ -181,7 +181,7 @@
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<p><strong>NOTE: The simulations that inform policy are way, <em>way</em> more sophisticated than this!</strong> But the SIR Model can still explain the same general findings, even if missing the nuances.</p>
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<p>Actually, let'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't pass it on yet – infect<em>ed</em> but not yet infect<em>ious</em>.</p>
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<p>Actually, let's add one more nuance: before an <icon s></icon> becomes an <span class="nowrap"><icon i></icon>,</span> they first become <icon e></icon> Exposed. This is when they have the virus but can't pass it on yet – infect<em>ed</em> but not yet infect<em>ious</em>.</p>
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<p><img src="pics/seir.png" alt=""></p>
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@ -189,14 +189,14 @@
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<p>For COVID-19, it's estimated that you're <icon e></icon> infected-but-not-yet-infectious for 3 days, <em>on average</em>.<sup id="fnref7"><a href="#fn7" rel="footnote">7</a></sup> What happens if we add that to the simulation?</p>
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<p><b style='color:#ff4040'>Red <b style='color:#FF9393'>+ Pink</b> curve</b> is <em>current</em> cases (infectious <icon i></icon> + exposed <icon e></icon>),<br>
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<b style='color:#888'>Gray curve</b> is <em>total</em> cases (current + recovered <icon r></icon>):</p>
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<p><b style='color:#ff4040'>Red <b style='color:#FF9393'>+ Pink</b> curve</b> is <em>current</em> cases (infectious <icon i></icon> + exposed <span class="nowrap"><icon e></icon>),</span><br>
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<b style='color:#888'>Gray curve</b> is <em>total</em> cases (current + recovered <span class="nowrap"><icon r></icon>):</span></p>
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<div class="sim">
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<iframe src="sim?stage=epi-5" width="800" height="540"></iframe>
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</div>
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<p>Not much changes! How long you stay <icon e></icon> Exposed changes the ratio of <icon e></icon>-to-<icon i></icon>, and <em>when</em> current cases peak... but the <em>height</em> of that peak, and total cases in the end, stays the same.</p>
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<p>Not much changes! How long you stay <icon e></icon> Exposed changes the ratio of <span class="nowrap"><icon e></icon>-to-<icon i></icon>,</span> and <em>when</em> current cases peak... but the <em>height</em> of that peak, and total cases in the end, stays the same.</p>
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<p>Why's that? Because of the <em>first</em>-most important idea in Epidemiology 101:</p>
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@ -224,7 +224,7 @@
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<iframe src="sim?stage=epi-6a&format=calc" width="285" height="255"></iframe>
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</div>
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<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 & getting natural immunity.)</p>
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<p>But remember, the fewer <span class="nowrap"><icon s></icon>s</span> there are, the <em>slower</em> <span class="nowrap"><icon s></icon>s</span> become <span class="nowrap"><icon i>s.</icon></span> 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 & getting natural immunity.)</p>
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<div class="sim">
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<iframe src="sim?stage=epi-6b&format=calc" width="285" height="390"></iframe>
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@ -240,7 +240,7 @@
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<p><strong>NOTE: Total cases <em>does not stop</em> at herd immunity, but overshoots it!</strong> And it crosses the threshold <em>exactly</em> when current cases peak. (This happens no matter how you change the settings – try it for yourself!)</p>
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<p>This is because when there are more non-<icon s></icon>s than the herd immunity threshold, you get R < 1. And when R < 1, new cases stop growing: a peak.</p>
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<p>This is because when there are more <span class="nowrap">non-<icon s></icon>s</span> than the herd immunity threshold, you get R < 1. And when R < 1, new cases stop growing: a peak.</p>
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<p><strong>If there's only one lesson you take away from this guide, here it is</strong> – it's an extremely complex diagram so please take time to fully absorb it:</p>
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@ -300,7 +300,7 @@
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<p>Increased handwashing cuts flus & 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's assume handwashing can reduce R by <em>up to</em> 25%, and distancing can reduce R by <em>up to</em> 70%:</p>
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<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>
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<p><strong>Play with this calculator to see how % of <span class="nowrap">non-<icon s></icon>,</span> 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>
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<div class="sim">
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<iframe src="sim?stage=int-2a&format=calc" width="285" height="260"></iframe>
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@ -336,7 +336,7 @@
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<p>Oh.</p>
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<p>This is the "second wave" everyone's talking about. As soon as we remove the lockdown, we get R > 1 again. So, a single leftover <icon i></icon> (or imported <icon i></icon>) can cause a spike in cases that's almost as bad as if we'd done Scenario 0: Absolutely Nothing.</p>
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<p>This is the "second wave" everyone's talking about. As soon as we remove the lockdown, we get R > 1 again. So, a single leftover <icon i></icon> (or imported <span class="nowrap"><icon i></icon>)</span> can cause a spike in cases that's almost as bad as if we'd done Scenario 0: Absolutely Nothing.</p>
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<p><strong>A lockdown isn't a cure, it's just a restart.</strong></p>
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@ -388,7 +388,7 @@
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<p>This is called <strong>contact tracing</strong>. It's an old idea, was used at an unprecedented scale to contain Ebola<sup id="fnref23"><a href="#fn23" rel="footnote">23</a></sup>, and now it's core part of how Taiwan & South Korea are containing COVID-19!</p>
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<p>(It also lets us use our limited tests more efficiently, to find pre-symptomatic <icon i></icon>s without needing to test almost everyone.)</p>
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<p>(It also lets us use our limited tests more efficiently, to find pre-symptomatic <span class="nowrap"><icon i></icon>s</span> without needing to test almost everyone.)</p>
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<p>Traditionally, contacts are found with in-person interviews, but those <em>alone</em> are too slow for COVID-19's ~48 hour window. That's why contact tracers need help, and be supported by – <em>NOT</em> replaced by – contact tracing apps.</p>
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@ -418,7 +418,7 @@
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<p>Thus, even without 100% contact quarantining, we can get R < 1 <em>without a lockdown!</em> Much better for our mental & financial health. (As for the cost to folks who have to self-isolate/quarantine, <em>governments should support them</em> – pay for the tests, job protection, subsidized paid leave, etc. Still way cheaper than intermittent lockdown.)</p>
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<p>We then keep R < 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>
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<p>We then keep R < 1 until we have a vaccine, which turns susceptible <span class="nowrap"><icon s></icon>s</span> into immune <span class="nowrap"><icon r></icon>s.</span> Herd immunity, the <em>right</em> way:</p>
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<div class="sim">
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<iframe src="sim?stage=int-4b&format=calc" width="285" height="230"></iframe>
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@ -554,7 +554,7 @@
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<p>But for COVID-19 <em>in humans</em>, as of May 1st 2020, "how long" is the big unknown.</p>
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<p>For these simulations, let's say it's 1 year.
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<strong>Here's a simulation starting with 100% <icon r></icon></strong>, exponentially decaying into susceptible, no-immunity <icon s></icon>s after 1 year, on <em>average</em>, with variation:</p>
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<strong>Here's a simulation starting with 100% <span class="nowrap"><icon r></icon></strong>,</span> exponentially decaying into susceptible, no-immunity <span class="nowrap"><icon s></icon>s</span> after 1 year, on <em>average</em>, with variation:</p>
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<div class="sim">
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<iframe src="sim?stage=yrs-1&format=lines&height=600" width="800" height="600"></iframe>
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@ -584,7 +584,7 @@
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<p>Oh.</p>
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<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>
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<p>Counterintuitively, summer makes the spikes worse <em>and</em> regular! This is because summer reduces new <span class="nowrap"><icon i></icon>s,</span> but that in turn reduces new immune <span class="nowrap"><icon r></icon>s.</span> Which means immunity plummets in the summer, <em>creating</em> large regular spikes in the winter.</p>
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<p>Thankfully, the solution to this is pretty straightforward – just vaccinate people every fall/winter, like we do with flu shots:</p>
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@ -69,7 +69,7 @@
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<p>It'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> every 4 days, <em>on average</em>.<sup id="fnref2"><a href="#fn2" rel="footnote">2</a></sup> (remember, there's a lot of variation)</p>
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<p>If we simulate "double every 4 days" <em>and nothing else</em>, on a population starting with just 0.001% <icon i></icon>, what happens? </p>
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<p>If we simulate "double every 4 days" <em>and nothing else</em>, on a population starting with just 0.001% <span class="nowrap"><icon i></icon>,</span> what happens? </p>
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<p><strong>Click "Start" 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>
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<p><img src="pics/susceptibles.png" alt=""></p>
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<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>
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<p>The more <span class="nowrap"><icon i></icon>s</span> there are, the faster <span class="nowrap"><icon s></icon>s</span> become <span class="nowrap"><icon i></icon>s,</span> <strong>but the fewer <span class="nowrap"><icon s></icon>s</span> there are, the <em>slower</em> <span class="nowrap"><icon s></icon>s</span> become <span class="nowrap"><icon i></icon>s.</span></strong></p>
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<p>How's this change the growth of an epidemic? Let's find out:</p>
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@ -97,9 +97,9 @@
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<p>But, this simulation is <em>still</em> wrong. We're missing the fact that <icon i></icon> Infectious people eventually stop being infectious, either by 1) recovering, 2) "recovering" with lung damage, or 3) dying.</p>
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<p>For simplicity's sake, let's pretend that all <icon i></icon> Infectious people become <icon r></icon> Recovered. (Just remember that in reality, some are dead.) <icon r></icon>s can't be infected again, and let's pretend – <em>for now!</em> – that they stay immune for life.</p>
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<p>For simplicity's sake, let's pretend that all <icon i></icon> Infectious people become <icon r></icon> Recovered. (Just remember that in reality, some are dead.) <span class="nowrap"><icon r></icon>s</span> can't be infected again, and let's pretend – <em>for now!</em> – that they stay immune for life.</p>
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<p>With COVID-19, it's estimated you're <icon i></icon> Infectious for 10 days, <em>on average</em>.<sup id="fnref4"><a href="#fn4" rel="footnote">4</a></sup> That means some folks will recover before 10 days, some after. <strong>Here's what that looks like, with a simulation <em>starting</em> with 100% <icon i></icon>:</strong></p>
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<p>With COVID-19, it's estimated you're <icon i></icon> Infectious for 10 days, <em>on average</em>.<sup id="fnref4"><a href="#fn4" rel="footnote">4</a></sup> That means some folks will recover before 10 days, some after. <strong>Here's what that looks like, with a simulation <em>starting</em> with 100% <span class="nowrap"><icon i></icon>:</span></strong></p>
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<div class="sim">
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<iframe src="sim?stage=epi-3" width="800" height="540"></iframe>
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<p>Let's find out.</p>
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<p><b style='color:#ff4040'>Red curve</b> is <em>current</em> cases <icon i></icon>,<br>
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<b style='color:#999999'>Gray curve</b> is <em>total</em> cases (current + recovered <icon r></icon>),
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starts at just 0.001% <icon i></icon>:</p>
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<p><b style='color:#ff4040'>Red curve</b> is <em>current</em> cases <span class="nowrap"><icon i></icon>,</span><br>
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<b style='color:#999999'>Gray curve</b> is <em>total</em> cases (current + recovered <span class="nowrap"><icon r></icon>),</span>
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starts at just 0.001% <span class="nowrap"><icon i></icon>:</span></p>
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<div class="sim">
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<iframe src="sim?stage=epi-4" width="800" height="540"></iframe>
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@ -131,7 +131,7 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
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<p><strong>NOTE: The simulations that inform policy are way, <em>way</em> more sophisticated than this!</strong> But the SIR Model can still explain the same general findings, even if missing the nuances.</p>
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<p>Actually, let'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't pass it on yet – infect<em>ed</em> but not yet infect<em>ious</em>.</p>
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<p>Actually, let's add one more nuance: before an <icon s></icon> becomes an <span class="nowrap"><icon i></icon>,</span> they first become <icon e></icon> Exposed. This is when they have the virus but can't pass it on yet – infect<em>ed</em> but not yet infect<em>ious</em>.</p>
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<p><img src="pics/seir.png" alt=""></p>
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@ -139,14 +139,14 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
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<p>For COVID-19, it's estimated that you're <icon e></icon> infected-but-not-yet-infectious for 3 days, <em>on average</em>.<sup id="fnref7"><a href="#fn7" rel="footnote">7</a></sup> What happens if we add that to the simulation?</p>
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<p><b style='color:#ff4040'>Red <b style='color:#FF9393'>+ Pink</b> curve</b> is <em>current</em> cases (infectious <icon i></icon> + exposed <icon e></icon>),<br>
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<b style='color:#888'>Gray curve</b> is <em>total</em> cases (current + recovered <icon r></icon>):</p>
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<p><b style='color:#ff4040'>Red <b style='color:#FF9393'>+ Pink</b> curve</b> is <em>current</em> cases (infectious <icon i></icon> + exposed <span class="nowrap"><icon e></icon>),</span><br>
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<b style='color:#888'>Gray curve</b> is <em>total</em> cases (current + recovered <span class="nowrap"><icon r></icon>):</span></p>
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<div class="sim">
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<iframe src="sim?stage=epi-5" width="800" height="540"></iframe>
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</div>
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<p>Not much changes! How long you stay <icon e></icon> Exposed changes the ratio of <icon e></icon>-to-<icon i></icon>, and <em>when</em> current cases peak... but the <em>height</em> of that peak, and total cases in the end, stays the same.</p>
|
||||
<p>Not much changes! How long you stay <icon e></icon> Exposed changes the ratio of <span class="nowrap"><icon e></icon>-to-<icon i></icon>,</span> and <em>when</em> current cases peak... but the <em>height</em> of that peak, and total cases in the end, stays the same.</p>
|
||||
|
||||
<p>Why's that? Because of the <em>first</em>-most important idea in Epidemiology 101:</p>
|
||||
|
||||
|
|
@ -174,7 +174,7 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
|
|||
<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 & getting natural immunity.)</p>
|
||||
<p>But remember, the fewer <span class="nowrap"><icon s></icon>s</span> there are, the <em>slower</em> <span class="nowrap"><icon s></icon>s</span> become <span class="nowrap"><icon i>s.</icon></span> 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 & getting natural immunity.)</p>
|
||||
|
||||
<div class="sim">
|
||||
<iframe src="sim?stage=epi-6b&format=calc" width="285" height="390"></iframe>
|
||||
|
|
@ -190,7 +190,7 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
|
|||
|
||||
<p><strong>NOTE: Total cases <em>does not stop</em> at herd immunity, but overshoots it!</strong> And it crosses the threshold <em>exactly</em> when current cases peak. (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 < 1. And when R < 1, new cases stop growing: a peak.</p>
|
||||
<p>This is because when there are more <span class="nowrap">non-<icon s></icon>s</span> than the herd immunity threshold, you get R < 1. And when R < 1, new cases stop growing: a peak.</p>
|
||||
|
||||
<p><strong>If there's only one lesson you take away from this guide, here it is</strong> – it's an extremely complex diagram so please take time to fully absorb it:</p>
|
||||
|
||||
|
|
@ -250,7 +250,7 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
|
|||
|
||||
<p>Increased handwashing cuts flus & 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'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>
|
||||
<p><strong>Play with this calculator to see how % of <span class="nowrap">non-<icon s></icon>,</span> 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>
|
||||
|
|
@ -286,7 +286,7 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
|
|||
|
||||
<p>Oh.</p>
|
||||
|
||||
<p>This is the "second wave" everyone's talking about. As soon as we remove the lockdown, we get R > 1 again. So, a single leftover <icon i></icon> (or imported <icon i></icon>) can cause a spike in cases that's almost as bad as if we'd done Scenario 0: Absolutely Nothing.</p>
|
||||
<p>This is the "second wave" everyone's talking about. As soon as we remove the lockdown, we get R > 1 again. So, a single leftover <icon i></icon> (or imported <span class="nowrap"><icon i></icon>)</span> can cause a spike in cases that's almost as bad as if we'd done Scenario 0: Absolutely Nothing.</p>
|
||||
|
||||
<p><strong>A lockdown isn't a cure, it's just a restart.</strong></p>
|
||||
|
||||
|
|
@ -338,7 +338,7 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
|
|||
|
||||
<p>This is called <strong>contact tracing</strong>. It's an old idea, was used at an unprecedented scale to contain Ebola<sup id="fnref23"><a href="#fn23" rel="footnote">23</a></sup>, and now it's core part of how Taiwan & South Korea are containing COVID-19!</p>
|
||||
|
||||
<p>(It also lets us use our limited tests more efficiently, to find pre-symptomatic <icon i></icon>s without needing to test almost everyone.)</p>
|
||||
<p>(It also lets us use our limited tests more efficiently, to find pre-symptomatic <icon i></icon>s without needing to test almost everyone.)</p><p>(It also lets us use our limited tests more efficiently, to find pre-symptomatic <span class="nowrap"><icon i></icon>s</span> without needing to test almost everyone.)</p>
|
||||
|
||||
<p>Traditionally, contacts are found with in-person interviews, but those <em>alone</em> are too slow for COVID-19's ~48 hour window. That's why contact tracers need help, and be supported by – <em>NOT</em> replaced by – contact tracing apps.</p>
|
||||
|
||||
|
|
@ -368,7 +368,7 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
|
|||
|
||||
<p>Thus, even without 100% contact quarantining, we can get R < 1 <em>without a lockdown!</em> Much better for our mental & financial health. (As for the cost to folks who have to self-isolate/quarantine, <em>governments should support them</em> – pay for the tests, job protection, subsidized paid leave, etc. Still way cheaper than intermittent lockdown.)</p>
|
||||
|
||||
<p>We then keep R < 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>
|
||||
<p>We then keep R < 1 until we have a vaccine, which turns susceptible <span class="nowrap"><icon s></icon>s</span> into immune <span class="nowrap"><icon r></icon>s.</span> Herd immunity, the <em>right</em> way:</p>
|
||||
|
||||
<div class="sim">
|
||||
<iframe src="sim?stage=int-4b&format=calc" width="285" height="230"></iframe>
|
||||
|
|
@ -504,7 +504,7 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
|
|||
<p>But for COVID-19 <em>in humans</em>, as of May 1st 2020, "how long" is the big unknown.</p>
|
||||
|
||||
<p>For these simulations, let's say it's 1 year.
|
||||
<strong>Here's a simulation starting with 100% <icon r></icon></strong>, exponentially decaying into susceptible, no-immunity <icon s></icon>s after 1 year, on <em>average</em>, with variation:</p>
|
||||
<strong>Here's a simulation starting with 100% <span class="nowrap"><icon r></icon></strong>,</span> exponentially decaying into susceptible, no-immunity <span class="nowrap"><icon s></icon>s</span> after 1 year, on <em>average</em>, with variation:</p>
|
||||
|
||||
<div class="sim">
|
||||
<iframe src="sim?stage=yrs-1&format=lines&height=600" width="800" height="600"></iframe>
|
||||
|
|
@ -534,7 +534,7 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
|
|||
|
||||
<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>Counterintuitively, summer makes the spikes worse <em>and</em> regular! This is because summer reduces new <span class="nowrap"><icon i></icon>s,</span> but that in turn reduces new immune <span class="nowrap"><icon r></icon>s.</span> 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>
|
||||
|
||||
|
|
|
|||
|
|
@ -59,7 +59,7 @@ It's estimated that, *at the start* of a COVID-19 outbreak, the virus jumps from
|
|||
|
||||
[^serial_interval]: “The mean [serial] interval was 3.96 days (95% CI 3.53–4.39 days)”. [Du Z, Xu X, Wu Y, Wang L, Cowling BJ, Ancel Meyers L](https://wwwnc.cdc.gov/eid/article/26/6/20-0357_article) (Disclaimer: Early release articles are not considered as final versions)
|
||||
|
||||
If we simulate "double every 4 days" *and nothing else*, on a population starting with just 0.001% <icon i></icon>, what happens?
|
||||
If we simulate "double every 4 days" *and nothing else*, on a population starting with just 0.001% <span class="nowrap"><icon i></icon>,</span> what happens?
|
||||
|
||||
**Click "Start" to play the simulation! You can re-play it later with different settings:** (technical caveats: [^caveats])
|
||||
|
||||
|
|
@ -81,7 +81,7 @@ But, this simulation is wrong. Exponential growth, thankfully, can't go on forev
|
|||
|
||||
|
||||
|
||||
The more <icon i></icon>s there are, the faster <icon s></icon>s become <icon i></icon>s, **but the fewer <icon s></icon>s there are, the *slower* <icon s></icon>s become <icon i></icon>s.**
|
||||
The more <span class="nowrap"><icon i></icon>s</span> there are, the faster <span class="nowrap"><icon s></icon>s</span> become <span class="nowrap"><icon i></icon>s,</span> **but the fewer <span class="nowrap"><icon s></icon>s</span> there are, the *slower* <span class="nowrap"><icon s></icon>s</span> become <span class="nowrap"><icon i></icon>s.</span>**
|
||||
|
||||
How's this change the growth of an epidemic? Let's find out:
|
||||
|
||||
|
|
@ -93,9 +93,9 @@ This is the "S-shaped" **logistic growth curve.** Starts small, explodes, then s
|
|||
|
||||
But, this simulation is *still* wrong. We're missing the fact that <icon i></icon> Infectious people eventually stop being infectious, either by 1) recovering, 2) "recovering" with lung damage, or 3) dying.
|
||||
|
||||
For simplicity's sake, let's pretend that all <icon i></icon> Infectious people become <icon r></icon> Recovered. (Just remember that in reality, some are dead.) <icon r></icon>s can't be infected again, and let's pretend – *for now!* – that they stay immune for life.
|
||||
For simplicity's sake, let's pretend that all <icon i></icon> Infectious people become <icon r></icon> Recovered. (Just remember that in reality, some are dead.) <span class="nowrap"><icon r></icon>s</span> can't be infected again, and let's pretend – *for now!* – that they stay immune for life.
|
||||
|
||||
With COVID-19, it's estimated you're <icon i></icon> Infectious for 10 days, *on average*.[^infectiousness] That means some folks will recover before 10 days, some after. **Here's what that looks like, with a simulation *starting* with 100% <icon i></icon>:**
|
||||
With COVID-19, it's estimated you're <icon i></icon> Infectious for 10 days, *on average*.[^infectiousness] That means some folks will recover before 10 days, some after. **Here's what that looks like, with a simulation *starting* with 100% <span class="nowrap"><icon i></icon>:</span>**
|
||||
|
||||
[^infectiousness]: “The median communicable period \[...\] was 9.5 days.” [Hu, Z., Song, C., Xu, C. et al](https://link.springer.com/article/10.1007/s11427-020-1661-4) Yes, we know "median" is not the same as "average". For simplified educational purposes, close enough.
|
||||
|
||||
|
|
@ -111,9 +111,9 @@ Now, what happens if you simulate S-shaped logistic growth *with* recovery?
|
|||
|
||||
Let's find out.
|
||||
|
||||
<b style='color:#ff4040'>Red curve</b> is *current* cases <icon i></icon>,
|
||||
<b style='color:#999999'>Gray curve</b> is *total* cases (current + recovered <icon r></icon>),
|
||||
starts at just 0.001% <icon i></icon>:
|
||||
<b style='color:#ff4040'>Red curve</b> is *current* cases <span class="nowrap"><icon i></icon>,</span>
|
||||
<b style='color:#999999'>Gray curve</b> is *total* cases (current + recovered <span class="nowrap"><icon r></icon>),</span>
|
||||
starts at just 0.001% <span class="nowrap"><icon i></icon>:</span>
|
||||
|
||||
<div class="sim">
|
||||
<iframe src="sim?stage=epi-4" width="800" height="540"></iframe>
|
||||
|
|
@ -131,7 +131,7 @@ the *second*-most important idea in Epidemiology 101:
|
|||
|
||||
**NOTE: The simulations that inform policy are way, *way* more sophisticated than this!** But the SIR Model can still explain the same general findings, even if missing the nuances.
|
||||
|
||||
Actually, let'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't pass it on yet – infect*ed* but not yet infect*ious*.
|
||||
Actually, let's add one more nuance: before an <icon s></icon> becomes an <span class="nowrap"><icon i></icon>,</span> they first become <icon e></icon> Exposed. This is when they have the virus but can't pass it on yet – infect*ed* but not yet infect*ious*.
|
||||
|
||||
|
||||
|
||||
|
|
@ -143,14 +143,14 @@ For COVID-19, it's estimated that you're <icon e></icon> infected-but-not-yet-in
|
|||
|
||||
[^latent]: “Assuming an incubation period distribution of mean 5.2 days from a separate study of early COVID-19 cases, we inferred that infectiousness started from 2.3 days (95% CI, 0.8–3.0 days) before symptom onset” (translation: Assuming symptoms start at 5 days, infectiousness starts 2 days before = Infectiousness starts at 3 days) [He, X., Lau, E.H.Y., Wu, P. et al.](https://www.nature.com/articles/s41591-020-0869-5)
|
||||
|
||||
<b style='color:#ff4040'>Red <b style='color:#FF9393'>+ Pink</b> curve</b> is *current* cases (infectious <icon i></icon> + exposed <icon e></icon>),
|
||||
<b style='color:#888'>Gray curve</b> is *total* cases (current + recovered <icon r></icon>):
|
||||
<b style='color:#ff4040'>Red <b style='color:#FF9393'>+ Pink</b> curve</b> is *current* cases (infectious <icon i></icon> + exposed <span class="nowrap"><icon e></icon>),</span>
|
||||
<b style='color:#888'>Gray curve</b> is *total* cases (current + recovered <span class="nowrap"><icon r></icon>):</span>
|
||||
|
||||
<div class="sim">
|
||||
<iframe src="sim?stage=epi-5" width="800" height="540"></iframe>
|
||||
</div>
|
||||
|
||||
Not much changes! How long you stay <icon e></icon> Exposed changes the ratio of <icon e></icon>-to-<icon i></icon>, and *when* current cases peak... but the *height* of that peak, and total cases in the end, stays the same.
|
||||
Not much changes! How long you stay <icon e></icon> Exposed changes the ratio of <span class="nowrap"><icon e></icon>-to-<icon i></icon>,</span> and *when* current cases peak... but the *height* of that peak, and total cases in the end, stays the same.
|
||||
|
||||
Why's that? Because of the *first*-most important idea in Epidemiology 101:
|
||||
|
||||
|
|
@ -186,7 +186,7 @@ In our simulations – *at the start & on average* – an <icon i></icon> infect
|
|||
<iframe src="sim?stage=epi-6a&format=calc" width="285" height="255"></iframe>
|
||||
</div>
|
||||
|
||||
But remember, the fewer <icon s></icon>s there are, the *slower* <icon s></icon>s become <icon i></icon>s. The *current* reproduction number (R) depends not just on the *basic* reproduction number (R<sub>0</sub>), but *also* on how many people are no longer <icon s></icon> Susceptible. (For example, by recovering & getting natural immunity.)
|
||||
But remember, the fewer <span class="nowrap"><icon s></icon>s</span> there are, the *slower* <span class="nowrap"><icon s></icon>s</span> become <span class="nowrap"><icon i></icon>s.</span> The *current* reproduction number (R) depends not just on the *basic* reproduction number (R<sub>0</sub>), but *also* on how many people are no longer <icon s></icon> Susceptible. (For example, by recovering & getting natural immunity.)
|
||||
|
||||
<div class="sim">
|
||||
<iframe src="sim?stage=epi-6b&format=calc" width="285" height="390"></iframe>
|
||||
|
|
@ -202,7 +202,7 @@ Now, let's play the SEIR Model again, but showing R<sub>0</sub>, R over time, an
|
|||
|
||||
**NOTE: Total cases *does not stop* at herd immunity, but overshoots it!** And it crosses the threshold *exactly* when current cases peak. (This happens no matter how you change the settings – try it for yourself!)
|
||||
|
||||
This is because when there are more non-<icon s></icon>s than the herd immunity threshold, you get R < 1. And when R < 1, new cases stop growing: a peak.
|
||||
This is because when there are more <span class="nowrap">non-<icon s></icon>s</span> than the herd immunity threshold, you get R < 1. And when R < 1, new cases stop growing: a peak.
|
||||
|
||||
**If there's only one lesson you take away from this guide, here it is** – it's an extremely complex diagram so please take time to fully absorb it:
|
||||
|
||||
|
|
@ -286,7 +286,7 @@ Increased handwashing cuts flus & colds in high-income countries by ~25%[^handwa
|
|||
|
||||
[^london]: “We found a 73% reduction in the average daily number of contacts observed per participant. This would be sufficient to reduce R0 from a value from 2.6 before the lockdown to 0.62 (0.37 - 0.89) during the lockdown”. We rounded it down to 70% in these simulations for simplicity. [Jarvis and Zandvoort et al](https://cmmid.github.io/topics/covid19/comix-impact-of-physical-distance-measures-on-transmission-in-the-UK.html)
|
||||
|
||||
**Play with this calculator to see how % of non-<icon s></icon>, handwashing, and distancing reduce R:** (this calculator visualizes their *relative* effects, which is why increasing one *looks* like it decreases the effect of the others.[^log_caveat])
|
||||
**Play with this calculator to see how % of <span class="nowrap">non-<icon s></icon>,</span> handwashing, and distancing reduce R:** (this calculator visualizes their *relative* effects, which is why increasing one *looks* like it decreases the effect of the others.[^log_caveat])
|
||||
|
||||
[^log_caveat]: This distortion would go away if we plotted R on a logarithmic scale... but then we'd have to explain *logarithmic scales.*
|
||||
|
||||
|
|
@ -324,7 +324,7 @@ Let's see what happens if we *crush* the curve with a 5-month lockdown, reduce <
|
|||
|
||||
Oh.
|
||||
|
||||
This is the "second wave" everyone's talking about. As soon as we remove the lockdown, we get R > 1 again. So, a single leftover <icon i></icon> (or imported <icon i></icon>) can cause a spike in cases that's almost as bad as if we'd done Scenario 0: Absolutely Nothing.
|
||||
This is the "second wave" everyone's talking about. As soon as we remove the lockdown, we get R > 1 again. So, a single leftover <icon i></icon> (or imported <span class="nowrap"><icon i></icon>)</span> can cause a spike in cases that's almost as bad as if we'd done Scenario 0: Absolutely Nothing.
|
||||
|
||||
**A lockdown isn't a cure, it's just a restart.**
|
||||
|
||||
|
|
@ -390,7 +390,7 @@ This is called **contact tracing**. It's an old idea, was used at an unprecedent
|
|||
|
||||
[^ebola]: “Contact tracing was a critical intervention in Liberia and represented one of the largest contact tracing efforts during an epidemic in history.” [Swanson KC, Altare C, Wesseh CS, et al.](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6152989/)
|
||||
|
||||
(It also lets us use our limited tests more efficiently, to find pre-symptomatic <icon i></icon>s without needing to test almost everyone.)
|
||||
(It also lets us use our limited tests more efficiently, to find pre-symptomatic <span class="nowrap"><icon i></icon>s</span> without needing to test almost everyone.)
|
||||
|
||||
Traditionally, contacts are found with in-person interviews, but those *alone* are too slow for COVID-19's ~48 hour window. That's why contact tracers need help, and be supported by – *NOT* replaced by – contact tracing apps.
|
||||
|
||||
|
|
@ -441,7 +441,7 @@ Isolating *symptomatic* cases would reduce R by up to 40%, and quarantining thei
|
|||
|
||||
Thus, even without 100% contact quarantining, we can get R < 1 *without a lockdown!* Much better for our mental & financial health. (As for the cost to folks who have to self-isolate/quarantine, *governments should support them* – pay for the tests, job protection, subsidized paid leave, etc. Still way cheaper than intermittent lockdown.)
|
||||
|
||||
We then keep R < 1 until we have a vaccine, which turns susceptible <icon s></icon>s into immune <icon r></icon>s. Herd immunity, the *right* way:
|
||||
We then keep R < 1 until we have a vaccine, which turns susceptible <span class="nowrap"><icon s></icon>s</span> into immune <span class="nowrap"><icon r></icon>s.</span> Herd immunity, the *right* way:
|
||||
|
||||
<div class="sim">
|
||||
<iframe src="sim?stage=int-4b&format=calc" width="285" height="230"></iframe>
|
||||
|
|
@ -597,7 +597,7 @@ But for COVID-19 *in humans*, as of May 1st 2020, "how long" is the big unknown.
|
|||
[^monkeys]: From [Bao et al.](https://www.biorxiv.org/content/10.1101/2020.03.13.990226v1.abstract) *Disclaimer: This article is a preprint and has not been certified by peer review (yet).* Also, to emphasize: they only tested re-infection 28 days later.
|
||||
|
||||
For these simulations, let's say it's 1 year.
|
||||
**Here's a simulation starting with 100% <icon r></icon>**, exponentially decaying into susceptible, no-immunity <icon s></icon>s after 1 year, on *average*, with variation:
|
||||
**Here's a simulation starting with 100% <span class="nowrap"><icon r></icon>**,</span> exponentially decaying into susceptible, no-immunity <span class="nowrap"><icon s></icon>s</span> after 1 year, on *average*, with variation:
|
||||
|
||||
<div class="sim">
|
||||
<iframe src="sim?stage=yrs-1&format=lines&height=600" width="800" height="600"></iframe>
|
||||
|
|
@ -627,7 +627,7 @@ Thankfully, because summer reduces R, it'll make the situation better:
|
|||
|
||||
Oh.
|
||||
|
||||
Counterintuitively, summer makes the spikes worse *and* 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, *creating* large regular spikes in the winter.
|
||||
Counterintuitively, summer makes the spikes worse *and* regular! This is because summer reduces new <span class="nowrap"><icon i></icon>s,</span> but that in turn reduces new immune <span class="nowrap"><icon r></icon>s.</span> Which means immunity plummets in the summer, *creating* large regular spikes in the winter.
|
||||
|
||||
Thankfully, the solution to this is pretty straightforward – just vaccinate people every fall/winter, like we do with flu shots:
|
||||
|
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Reference in New Issue