<p>It's estimated that, <em>at the start</em> of a COVID-19 outbreak, the virus jumps from an <iconi></icon> to an <icons></icon> every 4 days, <em>on average</em>.<supid="fnref2"><ahref="#fn2"rel="footnote">2</a></sup> (remember, there's a lot of variation)</p>
<p>If we simulate "double every 4 days"<em>and nothing else</em>, on a population starting with just 0.001% <iconi></icon>, what happens? </p>
<p>If we simulate "double every 4 days"<em>and nothing else</em>, on a population starting with just 0.001% <spanclass="nowrap"><iconi></icon>,</span> what happens? </p>
<p><strong>Click "Start" to play the simulation! You can re-play it later with different settings:</strong> (technical caveats: <supid="fnref3"><ahref="#fn3"rel="footnote">3</a></sup>)</p>
@ -135,7 +135,7 @@
<p><imgsrc="pics/susceptibles.png"alt=""></p>
<p>The more <iconi></icon>s there are, the faster <icons></icon>s become <iconi></icon>s, <strong>but the fewer <icons></icon>s there are, the <em>slower</em><icons></icon>s become <iconi></icon>s.</strong></p>
<p>The more <spanclass="nowrap"><iconi></icon>s</span> there are, the faster <spanclass="nowrap"><icons></icon>s</span> become <spanclass="nowrap"><iconi></icon>s,</span><strong>but the fewer <spanclass="nowrap"><icons></icon>s</span> there are, the <em>slower</em><spanclass="nowrap"><icons></icon>s</span> become <spanclass="nowrap"><iconi></icon>s.</span></strong></p>
<p>How's this change the growth of an epidemic? Let's find out:</p>
@ -147,9 +147,9 @@
<p>But, this simulation is <em>still</em> wrong. We're missing the fact that <iconi></icon> Infectious people eventually stop being infectious, either by 1) recovering, 2) "recovering" with lung damage, or 3) dying.</p>
<p>For simplicity's sake, let's pretend that all <iconi></icon> Infectious people become <iconr></icon> Recovered. (Just remember that in reality, some are dead.) <iconr></icon>s can't be infected again, and let's pretend – <em>for now!</em> – that they stay immune for life.</p>
<p>For simplicity's sake, let's pretend that all <iconi></icon> Infectious people become <iconr></icon> Recovered. (Just remember that in reality, some are dead.) <spanclass="nowrap"><iconr></icon>s</span> can't be infected again, and let's pretend – <em>for now!</em> – that they stay immune for life.</p>
<p>With COVID-19, it's estimated you're <iconi></icon> Infectious for 10 days, <em>on average</em>.<supid="fnref4"><ahref="#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% <iconi></icon>:</strong></p>
<p>With COVID-19, it's estimated you're <iconi></icon> Infectious for 10 days, <em>on average</em>.<supid="fnref4"><ahref="#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% <spanclass="nowrap"><iconi></icon>:</span></strong></p>
<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>
<p>Actually, let's add one more nuance: before an <icons></icon> becomes an <iconi></icon>, they first become <icone></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>
<p>Actually, let's add one more nuance: before an <icons></icon> becomes an <spanclass="nowrap"><iconi></icon>,</span> they first become <icone></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>
<p><imgsrc="pics/seir.png"alt=""></p>
@ -189,14 +189,14 @@
<p>For COVID-19, it's estimated that you're <icone></icon> infected-but-not-yet-infectious for 3 days, <em>on average</em>.<supid="fnref7"><ahref="#fn7"rel="footnote">7</a></sup> What happens if we add that to the simulation?</p>
<p>Not much changes! How long you stay <icone></icon> Exposed changes the ratio of <icone></icon>-to-<iconi></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 <icone></icon> Exposed changes the ratio of <spanclass="nowrap"><icone></icon>-to-<iconi></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>
<p>But remember, the fewer <icons></icon>s there are, the <em>slower</em><icons></icon>s become <iconi></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 <icons></icon> Susceptible. (For example, by recovering & getting natural immunity.)</p>
<p>But remember, the fewer <spanclass="nowrap"><icons></icon>s</span> there are, the <em>slower</em><spanclass="nowrap"><icons></icon>s</span> become <spanclass="nowrap"><iconi>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 <icons></icon> Susceptible. (For example, by recovering & getting natural immunity.)</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-<icons></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 <spanclass="nowrap">non-<icons></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>
@ -300,7 +300,7 @@
<p>Increased handwashing cuts flus & colds in high-income countries by ~25%<supid="fnref16"><ahref="#fn16"rel="footnote">16</a></sup>, while the city-wide lockdown in London cut close contacts by ~70%<supid="fnref17"><ahref="#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-<icons></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.<supid="fnref18"><ahref="#fn18"rel="footnote">18</a></sup>)</p>
<p><strong>Play with this calculator to see how % of <spanclass="nowrap">non-<icons></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.<supid="fnref18"><ahref="#fn18"rel="footnote">18</a></sup>)</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 <iconi></icon> (or imported <iconi></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 <iconi></icon> (or imported <spanclass="nowrap"><iconi></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>
@ -388,7 +388,7 @@
<p>This is called <strong>contact tracing</strong>. It's an old idea, was used at an unprecedented scale to contain Ebola<supid="fnref23"><ahref="#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 <iconi></icon>s without needing to test almost everyone.)</p>
<p>(It also lets us use our limited tests more efficiently, to find pre-symptomatic <spanclass="nowrap"><iconi></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>
@ -418,7 +418,7 @@
<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 <icons></icon>s into immune <iconr></icon>s. Herd immunity, the <em>right</em> way:</p>
<p>We then keep R < 1 until we have a vaccine, which turns susceptible <spanclass="nowrap"><icons></icon>s</span> into immune <spanclass="nowrap"><iconr></icon>s.</span> Herd immunity, the <em>right</em> way:</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% <iconr></icon></strong>, exponentially decaying into susceptible, no-immunity <icons></icon>s after 1 year, on <em>average</em>, with variation:</p>
<strong>Here's a simulation starting with 100% <spanclass="nowrap"><iconr></icon></strong>,</span> exponentially decaying into susceptible, no-immunity <spanclass="nowrap"><icons></icon>s</span> after 1 year, on <em>average</em>, with variation:</p>
<p>Counterintuitively, summer makes the spikes worse <em>and</em> regular! This is because summer reduces new <iconi></icon>s, but that in turn reduces new immune <iconr></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 <spanclass="nowrap"><iconi></icon>s,</span> but that in turn reduces new immune <spanclass="nowrap"><iconr></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>
<p>It's estimated that, <em>at the start</em> of a COVID-19 outbreak, the virus jumps from an <iconi></icon> to an <icons></icon> every 4 days, <em>on average</em>.<supid="fnref2"><ahref="#fn2"rel="footnote">2</a></sup> (remember, there's a lot of variation)</p>
<p>If we simulate "double every 4 days"<em>and nothing else</em>, on a population starting with just 0.001% <iconi></icon>, what happens? </p>
<p>If we simulate "double every 4 days"<em>and nothing else</em>, on a population starting with just 0.001% <spanclass="nowrap"><iconi></icon>,</span> what happens? </p>
<p><strong>Click "Start" to play the simulation! You can re-play it later with different settings:</strong> (technical caveats: <supid="fnref3"><ahref="#fn3"rel="footnote">3</a></sup>)</p>
@ -85,7 +85,7 @@
<p><imgsrc="pics/susceptibles.png"alt=""></p>
<p>The more <iconi></icon>s there are, the faster <icons></icon>s become <iconi></icon>s, <strong>but the fewer <icons></icon>s there are, the <em>slower</em><icons></icon>s become <iconi></icon>s.</strong></p>
<p>The more <spanclass="nowrap"><iconi></icon>s</span> there are, the faster <spanclass="nowrap"><icons></icon>s</span> become <spanclass="nowrap"><iconi></icon>s,</span><strong>but the fewer <spanclass="nowrap"><icons></icon>s</span> there are, the <em>slower</em><spanclass="nowrap"><icons></icon>s</span> become <spanclass="nowrap"><iconi></icon>s.</span></strong></p>
<p>How's this change the growth of an epidemic? Let's find out:</p>
@ -97,9 +97,9 @@
<p>But, this simulation is <em>still</em> wrong. We're missing the fact that <iconi></icon> Infectious people eventually stop being infectious, either by 1) recovering, 2) "recovering" with lung damage, or 3) dying.</p>
<p>For simplicity's sake, let's pretend that all <iconi></icon> Infectious people become <iconr></icon> Recovered. (Just remember that in reality, some are dead.) <iconr></icon>s can't be infected again, and let's pretend – <em>for now!</em> – that they stay immune for life.</p>
<p>For simplicity's sake, let's pretend that all <iconi></icon> Infectious people become <iconr></icon> Recovered. (Just remember that in reality, some are dead.) <spanclass="nowrap"><iconr></icon>s</span> can't be infected again, and let's pretend – <em>for now!</em> – that they stay immune for life.</p>
<p>With COVID-19, it's estimated you're <iconi></icon> Infectious for 10 days, <em>on average</em>.<supid="fnref4"><ahref="#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% <iconi></icon>:</strong></p>
<p>With COVID-19, it's estimated you're <iconi></icon> Infectious for 10 days, <em>on average</em>.<supid="fnref4"><ahref="#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% <spanclass="nowrap"><iconi></icon>:</span></strong></p>
@ -131,7 +131,7 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
<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>
<p>Actually, let's add one more nuance: before an <icons></icon> becomes an <iconi></icon>, they first become <icone></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>
<p>Actually, let's add one more nuance: before an <icons></icon> becomes an <spanclass="nowrap"><iconi></icon>,</span> they first become <icone></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>
<p><imgsrc="pics/seir.png"alt=""></p>
@ -139,14 +139,14 @@ the <em>second</em>-most important idea in Epidemiology 101:</p>
<p>For COVID-19, it's estimated that you're <icone></icon> infected-but-not-yet-infectious for 3 days, <em>on average</em>.<supid="fnref7"><ahref="#fn7"rel="footnote">7</a></sup> What happens if we add that to the simulation?</p>
<p>Not much changes! How long you stay <icone></icon> Exposed changes the ratio of <icone></icon>-to-<iconi></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 <icone></icon> Exposed changes the ratio of <spanclass="nowrap"><icone></icon>-to-<iconi></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>
<p>But remember, the fewer <icons></icon>s there are, the <em>slower</em><icons></icon>s become <iconi></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 <icons></icon> Susceptible. (For example, by recovering & getting natural immunity.)</p>
<p>But remember, the fewer <spanclass="nowrap"><icons></icon>s</span> there are, the <em>slower</em><spanclass="nowrap"><icons></icon>s</span> become <spanclass="nowrap"><iconi>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 <icons></icon> Susceptible. (For example, by recovering & getting natural immunity.)</p>
@ -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-<icons></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 <spanclass="nowrap">non-<icons></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%<supid="fnref16"><ahref="#fn16"rel="footnote">16</a></sup>, while the city-wide lockdown in London cut close contacts by ~70%<supid="fnref17"><ahref="#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-<icons></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.<supid="fnref18"><ahref="#fn18"rel="footnote">18</a></sup>)</p>
<p><strong>Play with this calculator to see how % of <spanclass="nowrap">non-<icons></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.<supid="fnref18"><ahref="#fn18"rel="footnote">18</a></sup>)</p>
@ -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 <iconi></icon> (or imported <iconi></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 <iconi></icon> (or imported <spanclass="nowrap"><iconi></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<supid="fnref23"><ahref="#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 <iconi></icon>s without needing to test almost everyone.)</p>
<p>(It also lets us use our limited tests more efficiently, to find pre-symptomatic <iconi></icon>s without needing to test almost everyone.)</p><p>(It also lets us use our limited tests more efficiently, to find pre-symptomatic <spanclass="nowrap"><iconi></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 <icons></icon>s into immune <iconr></icon>s. Herd immunity, the <em>right</em> way:</p>
<p>We then keep R < 1 until we have a vaccine, which turns susceptible <spanclass="nowrap"><icons></icon>s</span> into immune <spanclass="nowrap"><iconr></icon>s.</span> Herd immunity, the <em>right</em> way:</p>
@ -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% <iconr></icon></strong>, exponentially decaying into susceptible, no-immunity <icons></icon>s after 1 year, on <em>average</em>, with variation:</p>
<strong>Here's a simulation starting with 100% <spanclass="nowrap"><iconr></icon></strong>,</span> exponentially decaying into susceptible, no-immunity <spanclass="nowrap"><icons></icon>s</span> after 1 year, on <em>average</em>, with variation:</p>
@ -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 <iconi></icon>s, but that in turn reduces new immune <iconr></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 <spanclass="nowrap"><iconi></icon>s,</span> but that in turn reduces new immune <spanclass="nowrap"><iconr></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% <iconi></icon>, what happens?
If we simulate "double every 4 days" *and nothing else*, on a population starting with just 0.001% <spanclass="nowrap"><iconi></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 <iconi></icon>s there are, the faster <icons></icon>s become <iconi></icon>s, **but the fewer <icons></icon>s there are, the *slower*<icons></icon>s become <iconi></icon>s.**
The more <spanclass="nowrap"><iconi></icon>s</span> there are, the faster <spanclass="nowrap"><icons></icon>s</span> become <spanclass="nowrap"><iconi></icon>s,</span> **but the fewer <spanclass="nowrap"><icons></icon>s</span> there are, the *slower*<spanclass="nowrap"><icons></icon>s</span> become <spanclass="nowrap"><iconi></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 <iconi></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 <iconi></icon> Infectious people become <iconr></icon> Recovered. (Just remember that in reality, some are dead.) <iconr></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 <iconi></icon> Infectious people become <iconr></icon> Recovered. (Just remember that in reality, some are dead.) <spanclass="nowrap"><iconr></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 <iconi></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% <iconi></icon>:**
With COVID-19, it's estimated you're <iconi></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% <spanclass="nowrap"><iconi></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.
<bstyle='color:#ff4040'>Red curve</b> is *current* cases <iconi></icon>,
<bstyle='color:#999999'>Gray curve</b> is *total* cases (current + recovered <iconr></icon>),
starts at just 0.001% <iconi></icon>:
<bstyle='color:#ff4040'>Red curve</b> is *current* cases <spanclass="nowrap"><iconi></icon>,</span>
<bstyle='color:#999999'>Gray curve</b> is *total* cases (current + recovered <spanclass="nowrap"><iconr></icon>),</span>
starts at just 0.001% <spanclass="nowrap"><iconi></icon>:</span>
@ -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 <icons></icon> becomes an <iconi></icon>, they first become <icone></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 <icons></icon> becomes an <spanclass="nowrap"><iconi></icon>,</span> they first become <icone></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)
Not much changes! How long you stay <icone></icon> Exposed changes the ratio of <icone></icon>-to-<iconi></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 <icone></icon> Exposed changes the ratio of <spanclass="nowrap"><icone></icon>-to-<iconi></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
But remember, the fewer <icons></icon>s there are, the *slower*<icons></icon>s become <iconi></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 <icons></icon> Susceptible. (For example, by recovering & getting natural immunity.)
But remember, the fewer <spanclass="nowrap"><icons></icon>s</span> there are, the *slower*<spanclass="nowrap"><icons></icon>s</span> become <spanclass="nowrap"><iconi></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 <icons></icon> Susceptible. (For example, by recovering & getting natural immunity.)
@ -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-<icons></icon>s than the herd immunity threshold, you get R <1.AndwhenR<1,newcasesstopgrowing:apeak.
This is because when there are more <spanclass="nowrap">non-<icons></icon>s</span> than the herd immunity threshold, you get R <1.AndwhenR<1,newcasesstopgrowing:apeak.
**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-<icons></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 <spanclass="nowrap">non-<icons></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 <iconi></icon> (or imported <iconi></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 <iconi></icon> (or imported <spanclass="nowrap"><iconi></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 <iconi></icon>s without needing to test almost everyone.)
(It also lets us use our limited tests more efficiently, to find pre-symptomatic <spanclass="nowrap"><iconi></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!*Muchbetterforourmental&financialhealth.(Asforthecosttofolkswhohavetoself-isolate/quarantine,*governments should support them*–payforthetests,jobprotection,subsidizedpaidleave,etc.Stillwaycheaperthanintermittentlockdown.)
We then keep R <1untilwehaveavaccine,whichturnssusceptible<icons></icon>s into immune <iconr></icon>s. Herd immunity, the *right* way:
We then keep R <1untilwehaveavaccine,whichturnssusceptible<spanclass="nowrap"><icons></icon>s</span> into immune <spanclass="nowrap"><iconr></icon>s.</span> Herd immunity, the *right* way:
@ -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% <iconr></icon>**, exponentially decaying into susceptible, no-immunity <icons></icon>s after 1 year, on *average*, with variation:
**Here's a simulation starting with 100% <spanclass="nowrap"><iconr></icon>**,</span> exponentially decaying into susceptible, no-immunity <spanclass="nowrap"><icons></icon>s</span> after 1 year, on *average*, with variation:
@ -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 <iconi></icon>s, but that in turn reduces new immune <iconr></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 <spanclass="nowrap"><iconi></icon>s,</span> but that in turn reduces new immune <spanclass="nowrap"><iconr></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:
Tim Scalzo
2 years ago