diff --git a/css/index.css b/css/index.css index 0bc03aa..bd80272 100644 --- a/css/index.css +++ b/css/index.css @@ -95,6 +95,10 @@ icon[r]{ background-image: url(../icons/r.png); } +.nowrap{ + white-space: nowrap; +} + p > img{ width: 100%; border: 1px solid #ddd; diff --git a/index.html b/index.html index d420ccf..689fce5 100644 --- a/index.html +++ b/index.html @@ -119,7 +119,7 @@

It's estimated that, at the start of a COVID-19 outbreak, the virus jumps from an to an every 4 days, on average.2 (remember, there's a lot of variation)

-

If we simulate "double every 4 days" and nothing else, on a population starting with just 0.001% , what happens?

+

If we simulate "double every 4 days" and nothing else, on a population starting with just 0.001% , what happens?

Click "Start" to play the simulation! You can re-play it later with different settings: (technical caveats: 3)

@@ -135,7 +135,7 @@

-

The more s there are, the faster s become s, but the fewer s there are, the slower s become s.

+

The more s there are, the faster s become s, but the fewer s there are, the slower s become s.

How's this change the growth of an epidemic? Let's find out:

@@ -147,9 +147,9 @@

But, this simulation is still wrong. We're missing the fact that 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 Infectious people become Recovered. (Just remember that in reality, some are dead.) 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 Infectious people become Recovered. (Just remember that in reality, some are dead.) s 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 Infectious for 10 days, on average.4 That means some folks will recover before 10 days, some after. Here's what that looks like, with a simulation starting with 100% :

+

With COVID-19, it's estimated you're Infectious for 10 days, on average.4 That means some folks will recover before 10 days, some after. Here's what that looks like, with a simulation starting with 100% :

@@ -163,9 +163,9 @@

Let's find out.

-

Red curve is current cases ,
- Gray curve is total cases (current + recovered ), - starts at just 0.001% :

+

Red curve is current cases ,
+ Gray curve is total cases (current + recovered ), + starts at just 0.001% :

@@ -181,7 +181,7 @@

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 becomes an , they first become Exposed. This is when they have the virus but can't pass it on yet – infected but not yet infectious.

+

Actually, let's add one more nuance: before an becomes an , they first become Exposed. This is when they have the virus but can't pass it on yet – infected but not yet infectious.

@@ -189,14 +189,14 @@

For COVID-19, it's estimated that you're infected-but-not-yet-infectious for 3 days, on average.7 What happens if we add that to the simulation?

-

Red + Pink curve is current cases (infectious + exposed ),
- Gray curve is total cases (current + recovered ):

+

Red + Pink curve is current cases (infectious + exposed ),
+ Gray curve is total cases (current + recovered ):

-

Not much changes! How long you stay Exposed changes the ratio of -to-, 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 Exposed changes the ratio of -to-, 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:

@@ -224,7 +224,7 @@
-

But remember, the fewer s there are, the slower s become s. The current reproduction number (R) depends not just on the basic reproduction number (R0), but also on how many people are no longer Susceptible. (For example, by recovering & getting natural immunity.)

+

But remember, the fewer s there are, the slower s become s. The current reproduction number (R) depends not just on the basic reproduction number (R0), but also on how many people are no longer Susceptible. (For example, by recovering & getting natural immunity.)

@@ -240,7 +240,7 @@

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-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 non-s 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:

@@ -300,7 +300,7 @@

Increased handwashing cuts flus & colds in high-income countries by ~25%16, while the city-wide lockdown in London cut close contacts by ~70%17. So, let's assume handwashing can reduce R by up to 25%, and distancing can reduce R by up to 70%:

-

Play with this calculator to see how % of non-, 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.18)

+

Play with this calculator to see how % of non-, 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.18)

@@ -336,7 +336,7 @@

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 (or imported ) 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 (or imported ) 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.

@@ -388,7 +388,7 @@

This is called contact tracing. It's an old idea, was used at an unprecedented scale to contain Ebola23, and now it's core part of how Taiwan & South Korea are containing COVID-19!

-

(It also lets us use our limited tests more efficiently, to find pre-symptomatic s without needing to test almost everyone.)

+

(It also lets us use our limited tests more efficiently, to find pre-symptomatic s 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.

@@ -418,7 +418,7 @@

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 s into immune s. Herd immunity, the right way:

+

We then keep R < 1 until we have a vaccine, which turns susceptible s into immune s. Herd immunity, the right way:

@@ -554,7 +554,7 @@

But for COVID-19 in humans, as of May 1st 2020, "how long" is the big unknown.

For these simulations, let's say it's 1 year. - Here's a simulation starting with 100% , exponentially decaying into susceptible, no-immunity s after 1 year, on average, with variation:

+ Here's a simulation starting with 100% , exponentially decaying into susceptible, no-immunity s after 1 year, on average, with variation:

@@ -584,7 +584,7 @@

Oh.

-

Counterintuitively, summer makes the spikes worse and regular! This is because summer reduces new s, but that in turn reduces new immune 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 s, but that in turn reduces new immune s. 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:

diff --git a/words/words.html b/words/words.html index 396aa37..459f09e 100644 --- a/words/words.html +++ b/words/words.html @@ -69,7 +69,7 @@

It's estimated that, at the start of a COVID-19 outbreak, the virus jumps from an to an every 4 days, on average.2 (remember, there's a lot of variation)

-

If we simulate "double every 4 days" and nothing else, on a population starting with just 0.001% , what happens?

+

If we simulate "double every 4 days" and nothing else, on a population starting with just 0.001% , what happens?

Click "Start" to play the simulation! You can re-play it later with different settings: (technical caveats: 3)

@@ -85,7 +85,7 @@

-

The more s there are, the faster s become s, but the fewer s there are, the slower s become s.

+

The more s there are, the faster s become s, but the fewer s there are, the slower s become s.

How's this change the growth of an epidemic? Let's find out:

@@ -97,9 +97,9 @@

But, this simulation is still wrong. We're missing the fact that 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 Infectious people become Recovered. (Just remember that in reality, some are dead.) 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 Infectious people become Recovered. (Just remember that in reality, some are dead.) s 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 Infectious for 10 days, on average.4 That means some folks will recover before 10 days, some after. Here's what that looks like, with a simulation starting with 100% :

+

With COVID-19, it's estimated you're Infectious for 10 days, on average.4 That means some folks will recover before 10 days, some after. Here's what that looks like, with a simulation starting with 100% :

@@ -113,9 +113,9 @@

Let's find out.

-

Red curve is current cases ,
-Gray curve is total cases (current + recovered ), -starts at just 0.001% :

+

Red curve is current cases ,
+Gray curve is total cases (current + recovered ), +starts at just 0.001% :

@@ -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 becomes an , they first become Exposed. This is when they have the virus but can't pass it on yet – infected but not yet infectious.

+

Actually, let's add one more nuance: before an becomes an , they first become Exposed. This is when they have the virus but can't pass it on yet – infected but not yet infectious.

@@ -139,14 +139,14 @@ the second-most important idea in Epidemiology 101:

For COVID-19, it's estimated that you're infected-but-not-yet-infectious for 3 days, on average.7 What happens if we add that to the simulation?

-

Red + Pink curve is current cases (infectious + exposed ),
-Gray curve is total cases (current + recovered ):

+

Red + Pink curve is current cases (infectious + exposed ),
+Gray curve is total cases (current + recovered ):

-

Not much changes! How long you stay Exposed changes the ratio of -to-, 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 Exposed changes the ratio of -to-, 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:

@@ -174,7 +174,7 @@ the second-most important idea in Epidemiology 101:

-

But remember, the fewer s there are, the slower s become s. The current reproduction number (R) depends not just on the basic reproduction number (R0), but also on how many people are no longer Susceptible. (For example, by recovering & getting natural immunity.)

+

But remember, the fewer s there are, the slower s become s. The current reproduction number (R) depends not just on the basic reproduction number (R0), but also on how many people are no longer Susceptible. (For example, by recovering & getting natural immunity.)

@@ -190,7 +190,7 @@ the second-most important idea in Epidemiology 101:

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-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 non-s 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:

@@ -250,7 +250,7 @@ the second-most important idea in Epidemiology 101:

Increased handwashing cuts flus & colds in high-income countries by ~25%16, while the city-wide lockdown in London cut close contacts by ~70%17. So, let's assume handwashing can reduce R by up to 25%, and distancing can reduce R by up to 70%:

-

Play with this calculator to see how % of non-, 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.18)

+

Play with this calculator to see how % of non-, 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.18)

@@ -286,7 +286,7 @@ the second-most important idea in Epidemiology 101:

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 (or imported ) 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 (or imported ) 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.

@@ -338,7 +338,7 @@ the second-most important idea in Epidemiology 101:

This is called contact tracing. It's an old idea, was used at an unprecedented scale to contain Ebola23, and now it's core part of how Taiwan & South Korea are containing COVID-19!

-

(It also lets us use our limited tests more efficiently, to find pre-symptomatic s without needing to test almost everyone.)

+

(It also lets us use our limited tests more efficiently, to find pre-symptomatic s without needing to test almost everyone.)

(It also lets us use our limited tests more efficiently, to find pre-symptomatic s 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.

@@ -368,7 +368,7 @@ the second-most important idea in Epidemiology 101:

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 s into immune s. Herd immunity, the right way:

+

We then keep R < 1 until we have a vaccine, which turns susceptible s into immune s. Herd immunity, the right way:

@@ -504,7 +504,7 @@ the second-most important idea in Epidemiology 101:

But for COVID-19 in humans, as of May 1st 2020, "how long" is the big unknown.

For these simulations, let's say it's 1 year. -Here's a simulation starting with 100% , exponentially decaying into susceptible, no-immunity s after 1 year, on average, with variation:

+Here's a simulation starting with 100% , exponentially decaying into susceptible, no-immunity s after 1 year, on average, with variation:

@@ -534,7 +534,7 @@ the second-most important idea in Epidemiology 101:

Oh.

-

Counterintuitively, summer makes the spikes worse and regular! This is because summer reduces new s, but that in turn reduces new immune 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 s, but that in turn reduces new immune s. 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:

diff --git a/words/words.md b/words/words.md index 691356b..d5ba3aa 100644 --- a/words/words.md +++ b/words/words.md @@ -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% , what happens? +If we simulate "double every 4 days" *and nothing else*, on a population starting with just 0.001% , 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 ![](pics/susceptibles.png) -The more s there are, the faster s become s, **but the fewer s there are, the *slower* s become s.** +The more s there are, the faster s become s, **but the fewer s there are, the *slower* s become s.** 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 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 Infectious people become Recovered. (Just remember that in reality, some are dead.) 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 Infectious people become Recovered. (Just remember that in reality, some are dead.) s 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 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% :** +With COVID-19, it's estimated you're 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% :** [^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. -Red curve is *current* cases , -Gray curve is *total* cases (current + recovered ), -starts at just 0.001% : +Red curve is *current* cases , +Gray curve is *total* cases (current + recovered ), +starts at just 0.001% :
@@ -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 becomes an , they first become 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 becomes an , they first become Exposed. This is when they have the virus but can't pass it on yet – infect*ed* but not yet infect*ious*. ![](pics/seir.png) @@ -143,14 +143,14 @@ For COVID-19, it's estimated that you're 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) -Red + Pink curve is *current* cases (infectious + exposed ), -Gray curve is *total* cases (current + recovered ): +Red + Pink curve is *current* cases (infectious + exposed ), +Gray curve is *total* cases (current + recovered ):
-Not much changes! How long you stay Exposed changes the ratio of -to-, 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 Exposed changes the ratio of -to-, 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 infect
-But remember, the fewer s there are, the *slower* s become s. The *current* reproduction number (R) depends not just on the *basic* reproduction number (R0), but *also* on how many people are no longer Susceptible. (For example, by recovering & getting natural immunity.) +But remember, the fewer s there are, the *slower* s become s. The *current* reproduction number (R) depends not just on the *basic* reproduction number (R0), but *also* on how many people are no longer Susceptible. (For example, by recovering & getting natural immunity.)
@@ -202,7 +202,7 @@ Now, let's play the SEIR Model again, but showing R0, 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-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 non-s 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-, 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 non-, 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 (or imported ) 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 (or imported ) 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 s without needing to test almost everyone.) +(It also lets us use our limited tests more efficiently, to find pre-symptomatic s 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 s into immune s. Herd immunity, the *right* way: +We then keep R < 1 until we have a vaccine, which turns susceptible s into immune s. 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% **, exponentially decaying into susceptible, no-immunity s after 1 year, on *average*, with variation: +**Here's a simulation starting with 100% **, exponentially decaying into susceptible, no-immunity s 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 s, but that in turn reduces new immune 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 s, but that in turn reduces new immune s. 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: