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Future scenarios of COVID-19: a playable simulation

"The only thing to fear is fear itself" (see footnote! →1) was stupid advice.

Sure you don't hoard toilet paper - but if politicians fear fear itself, they will downplay real dangers in order to avoid "mass panic". Fear is not the problem, but the way that we manage our fear channel. Fear gives us the energy to deal with the current dangers and to prepare for the dangers to come.

We (Marcel, Epidemiologist + Nicky, Art / Code) are honestly concerned too. And we bet you are too! That is why we used our fear to avoid this playable simulations to create. Our goal is that you don't panic, but try to understand and learn something:

  • Over the past few months (1x1 of epidemiology, SEIR model, R & R0)
  • Over the next few months (Lockdown, contact tracing, masks)
  • Over the next few years (Loss of Immunity? No Vaccine?)

This guide (published on May 1, 20202) should give you hope and scare at the same time. Because to beat COVID-19 in a way that too protects our sanity and financial condition, we need on the one hand optimism to make plans and on the other hand pessimism to make backup plans. As Gladys Bronwyn Stern once said: "The optimist invents the airplane and the pessimist the parachute."

So buckle up: we expect some turbulence.

Pilots train with flight simulators to prevent future crashes.

Epidemiologists train in epidemic simulators to prevent humanity from falling.

So let's take a very very simple "epidemic flight simulator"! In this simulation, contagious people can turn unprotected people into contagious people:

It is believed that at the start of a COVID-19 outbreak, the virus on average Jumps from an infectious human to an unprotected human every 4 days.3 (note that there are many variations)

If we have "doubling every 4 days", for a population that starts with only 0.001%, and nothing else simulate what happens then?

Click on start to start the simulation! You can restart it later with various settings: (technical reservations: 4)

this is the exponential growth curve. It starts small and then explodes. From "Oh, it's just the flu" to "Oh right, the flu doesn't make it Mass graves in rich cities".

But this simulation is wrong. Fortunately, exponential growth cannot last forever. The spread of a virus is stopped, for example, when others let it already to have:

The more there is, the faster it becomes but the fewer there are, the more slower become to.

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

This is an "S-shaped" logistic growth curve. It starts small, explodes, and then slows down again.

But even this simulation is still not correct. We overlook the fact that contagious people eventually cease to be contagious, either by 1) recovering, 2) "recovering" with lung damage, or 3) dying.

For the sake of simplicity, let's pretend that all contagious people have recovered. (Remember, some of them are actually dying.) Can't get infected again, let's-- provisionally! - pretend to stay immune for a lifetime.

It is believed that people with COVID-19 on average Are contagious for 10 days.5 This means that some people recover sooner than 10 days, others later. This is what it looks like in a simulation that is 100% begins:

This is the opposite of exponential growth that exponential decay curve.

Well, what if we have S-shaped logistical growth With Simulate recovery?

Let's find out:

the Red curve give the current Falls again,
the Gray curve give the entire Cases (current + recovered) again) and starts at just 0.001%. :

And so this famous curve comes about! It's not a bell curve, it's not even a "log-normal" curve. She has no name. But you've seen it umpteen times and have been implored to flatten it.

This is this SIR model,6
(S.usceptible vulnerable / unprotectedI.nfectious contagious / infectiousR.ecovered recovered / recovered),
the second- most important idea in the 1x1 of epidemiology:

NOTE: The simulations on the basis of which the policy makes decisions are essential more sophisticated than this! The SIR model can nevertheless explain the same general results, even if the nuances are missing.

Actually, we should add one more nuance: Before one becomes one, it is first exposed. That's when he or she already has the virus but can't pass it on yet - infected, but not yet infectious.

(This variant will be the SEIR model7 called, where the "E" stands for E.xposed (exposed) stands. Please note that this Not the everyday meaning of "exposed" is what it would be: You may or may not have the virus. In this technical definition, "exposed" means that you definitely have the virus. Scientific terminology is a difficult thing).

For COVID-19 it is assumed that it is infected for 3 days but not yet infectious, on average. 8 What if we add that to the simulation?

The Red + Pink Curve give the current Cases (infectious + exposed) again,
the Gray curve give the entire Cases (current + recovered) again:

Not much changes! How long one remains exposed changes the relationship between to and when the current cases are peaking ... but the height this peak and the total number of cases stays the same at the end.

Why this? Because of the main Idea in the 1x1 of epidemiology:

Short for reproduction number. She describes the average Number of people infected by one before he recovers (or dies).

R. changes in the course of the outbreak due to increased immunity and measures.

R.0 (pronounced R-zero, also "base reproduction number") is the reproduction number Beginning of an outbreak, i.e. before immunity and before interventions. R.0 This reflects the strength of the virus, but this number varies from place to place. For example, it is higher in densely populated cities than in rural areas.

(Most newspaper articles - and sometimes even scientific publications! - confuse R and R0. As I said - scientific terminology is a difficult field.)

The basic reproduction number R0 the seasonal flu is around 1.289. That means that at the beginning of a flu outbreak everyone on average 1.28 infects others. (In case you're wondering why 1.28 is not a whole number: An "average" mother has 2.4 children. That doesn't mean that half children are walking around somewhere.)

The R0-Value for COVID-19 is estimated at around 2.210although there is a not yet finished Study gives a value of 5.7 (!) For Wuhan.11

Infected in our simulations - at the beginning and average - a different person every 4 days for 10 days. The ratio of 10 to 4 days is exactly 2.5, which means that - at the beginning and average - each and every 2.5 other people infected. So R applies here0 = 2.5. (Reservations:12)

Games to R0 in the calculator below to see how R0 depends on the recovery time and the rate of new infections:

As a reminder: the less there are, the more slower become to. The current Reproduction number R not only depends on the Base reproduction number (R0), but also on the number of potentially infected people. (For example, through recovery and natural immunity.)

Once enough people have gained immunity and R <1, the virus is under control. This is called Herd immunity. For flu viruses, herd immunity is determined by means of a Vaccine reached. The idea of ​​achieving "natural herd immunity" through targeted infections is extremely bad! (But not for the reason you might assume - we'll explain that later!)

Now let's look at the SEIR model, which is now R0 shows R over time, as well as the herd immunity threshold shows:

NOTE: The total number of infected people does not stop at the limit of herd immunity, but goes beyond that! In addition, the total number of infected people exceeds the herd immunity threshold exactly at the time of the highest current number of cases. (This is independent of the choice of parameters - test it yourself!)

Why is that? If there is more non- than the herd immunity threshold, then R <1. And if R <1, the growth of new cases stops: a high point has been reached.

If there's only one thing to remember from this guide, it's this one - it's an extremely complex diagram so take your time to internalize it:

It means: We do NOT have to intercept all transmissions, not even almost all of them, in order to stop COVID-19!

This seems paradoxical! COVID-19 is an extremely contagious disease, but preventing "only" more than 60% of infections is sufficient to contain them. 60% ?! As a school grade that would be "satisfactory". But if R0 = 2.5 and one subtracts 61% from it, one obtains R = 0.975. Since then R <1, the virus would be contained! (exact formula: 13))

(If you think R0 or some of the other numbers in our simulations are too small or too large - great! In doing so, you are questioning our assumptions. At the end there is a "sandbox mode" in which you can use your own Pick numbers and simulate what happens next.)

Each Doing the COVID-19 measure you've heard of - be it hand washing, keeping your distance, "lockdown", self-isolation, "contact tracing", quarantine, face masks or herd immunity all the same thing:

You should achieve that R <1.

Let us now start our "epidemic flight simulator" in order to be able to answer the following question: How do we achieve that R <1, taking into account our health and financial interests?

Prepare for an emergency landing ...

... could have been much worse. Here is a parallel universe that we avoided:

Scenario 0: Do nothing at all

About 1 in 20 people who are infected with COVID-19 will need intensive care treatment.14 In a rich country like the USA, there is one intensive care place for every 3,400 people.15 Hence, the US can handle that 20 out of 3,400 people at the same time are infected - or 0.6% of the population.

Even if we reduce this capacity to 2% more than tripled would have happened if we had done absolutely nothing:

Not good at all.

This is what the Imperial College report of March 16 found out: If we do nothing, we will run out of beds in the intensive care units and more than 80% of the population will be infected. (As a reminder: the total number of cases exceeds herd immunity)

Even if only 0.5% of those infected die - a very optimistic assumption when there are no more beds in intensive care units - then in a large country like the US with 300 million people, 0.5% of 80% of the 300 million die. So still 1.2 million people ... IF we don't do anything.

(It has been reported on many news and social media that "80% will be infected" without the addition "IF WE DO NOTHING". In this way, fear channeled itself into clicks, not understanding. Sigh.)

Scenario 1: "Flatten the Curve" / Herd immunity

The "Flatten The Curve" plan was touted by all health organizations, while the original British "herd immunity" plan was widely booed. However, it was actually about same plan. Great Britain communicated him poorly.16

However, both plans had a fatal flaw.

First, let's look at the two main ways that flatten the curve: hand washing and social distancing.

Increased hand washing reduces flu and colds in high-income countries by ~ 25%17 reduced, while citywide lockdown in London close contacts by ~ 70%18 restricts. So let's assume that by washing hands, R can be up to 25% and by distancing R can be reduced by up to 70% reduced:

Try this calculator to see how hand washing and distancing reduce R with different% of nons: (this calculator visualizes your relative Effects, which is why the increase in one characteristic is so looks likeas if it diminishes the effect of the other.19)

Now let's simulate what would happen to a COVID-19 epidemic if we had increased hand washing from March 2020, but only little Kept their distance - so that R is lower but still greater than 1:

Three notes:

  1. This decreased the total number of cases! Even if R <1 is not achieved, reducing R will still save lives by reducing the 'excess' to herd immunity. Many people think that as the curve flattens out, the cases are stretched out in time without reducing the total number. But that is a contradiction in terms each basic epidemiology model. But because the news portrayed "80% + will be infected" as inevitable, it was widely believed that the total number of cases would stay the same either way. Sigh.

  2. Due to the additional measures, the current case numbers are reaching their peak before herd immunity is achieved. In fact, in this simulation the total number of cases just shoots little bit Beyond Herd Immunity - The UK's Plan! At this point, R <1, all other measures can be let go and COVID-19 will remain contained! There's only one problem ...

  3. There are no beds in the intensive care units. And that for several months. (and we have the beds in the intensive care units for this simulation, yes already tripled)

That was the other finding of the March 16 Imperial College Report that persuaded Britain to abandon its original plan. Every attempt one Weakening (Reduce R, but R> 1) will fail. The only way out is Containment (Reduce R so that R <1).

That means: It is not enough to simply "flatten" the curve. The curve must crushed become. For example with ...

Scenario 2: Lockdown lasting for months

Let's see what happens when we turn the curve with a 5 month lockdown to pressthat reduce to almost zero and then finally - at last - return to our normal life:


This is the "second wave" everyone is talking about. As soon as we unlock the lockdown, we get R> 1. A single remaining (or an imported one) can cause a spike in the number of cases that is almost as bad as if we had followed scenario 0: done absolutely nothing.

A lockdown isn't a cure, it's just a restart.

So what to do One lockdown after another?

Scenario 3: Periodic lockdown

This option was first suggested in the Imperial College report of March 16 and later again in a Harvard paper 20.

Here is a simulation for this option: (First play the recording. Then you can try your own Simulate lockdown plan by changing the slider while the simulation is running! You can interrupt the simulation, continue it and change the simulation speed)

This would keep the number of cases below the capacity of the intensive care units! And it is much better than an 18 month lockdown until a vaccine is available. So we'd just have to ... lockdown for a couple of months, open it for a couple of months, and repeat that until a vaccine is available.(And if there isn't a vaccine, we'll repeat it until herd immunity is achieved ... in 2022).

At first it seems reasonable to make such a plan based on the capacities of the intensive care units, but in doing so we are overlooking a number of essential things that we are here Not can simulate. For example:

Mental health: Loneliness is one of the biggest risk factors for depression, anxiety, and suicide. And statistically speaking, it leads to early death just as often as smoking 15 cigarettes a day 21.

Economic aspects: When asked about the economy, it sounds like you care more about your money than your life, but "the economy" isn't just about stocks: it's about people's ability to care for their loved ones in the future investing their children and enjoying arts, food and video games. So everything that makes life worth living. In addition, there is poverty per se has serious effects on mental and physical health.

This is not a plea against new lockdowns! We'll look at possible ways to do this later. Still, it's not ideal.

Wait a minute ... Taiwan and South Korea don't have it already Get a grip on COVID-19? For four whole months and without long-term lockdowns?

How is that possible?

Scenario 4: test, track, isolate

"Certainly we could * have done what Taiwan and South Korea did in the beginning. But it's too late for that now. We missed the beginning. "*

But that is exactly it! "A lockdown is not a cure, it's just a restart" ... and a restart is what we need

To understand how Taiwan and South Korea got a grip on COVID-19, we need to understand the exact timing of a typical COVID-19 infection22:

If people don't self-isolate until they know they are sick (i.e., when they experience symptoms), the virus can still spread:

In fact, 44% of all broadcasts go like this: You find in front the appearance of the symptoms instead!23

But when we find the last few close contacts of a person who is experiencing symptoms and quarantine ... let's stop the spread by staying one step ahead!

This idea is called the contact tracing (Contact tracking). It's an old idea that was first introduced on a large scale to contain Ebola24 was used. Now it is central to the COVID-19 containment strategy in Taiwan & South Korea!

(This also allows us to use our limited testing capabilities more efficiently to find pre-symptom onset without having to test almost everyone.)

Usually contacts are found through face-to-face interviews, but that alone is going too slow for the ~ 48 hour window of COVID-19. Therefore the seekers need help and are supported by - NOT replaced by - contact tracing apps.

(This idea didn't come from "nerds": using an app to fight COVID-19 was first suggested by a team of epidemiologists from Oxford.)

Wait a minute, apps that track who you've been in contact with? ... Does that mean giving up your privacy and sacrificing it to Big Brother?

No damn it! DP-3T, a team of epidemiologists & encryption experts (including one of us, Marcel Salathé) already a contact tracking application - with a code accessible to the public - that does not reveal any information about your identity, your location, who your contacts are and not even about how many contacts you had.

It works like this:

(Here you can find the full comic. Details on "pranking" / false positives / etc. in the footnote:25)

Together with teams similar to TCN Protocol26 and WITH PACT27 they got Apple & Google to implement contact tracking directly in Android / iOS while maintaining privacy.28 (You don't trust Google / Apple? Good! The nice thing about this system is that there is no trust needed). Soon your local health authority may ask you to download an app. If the protection of privacy is ensured and the code is publicly available, then please do that!

But what about people without smartphones? Or infections from doorknobs? Or "real" asymptomatic cases? Contact tracing apps cannot capture all transmissions ... and that's okay! We do not have to all Capture transmissions, only over 60% to achieve R <1.

(Also a rant about the confusion between presymptomatic and "real" asymptomatic - "real" asymptomatics are rare:29)

The isolation more symptomatic Cases would reduce R by up to 40%, and quarantine their pre- or asymptomatic Contacts would reduce R by up to 50%30:

This means that we can get R <1 even without 100% contact quarantine, and that without lockdown! And therefore much better for our psychological and economic situation. (People who isolate themselves, should get support from their governments - Assumption of costs for the tests, securing jobs, subsidizing paid leave, etc. That is still significantly cheaper than periodic lockdowns).

We then keep R <1 until we have a vaccine that turns vulnerable s into immunized. Herd immunity to the right one Type:

(Note: This calculator simulates 100% effective vaccines. In reality, would have to above the "herd immunity" to be vaccinated away indeed To maintain herd immunity)

Okay, enough of the words. This is a simulation of ...

  1. ... a lockdown for a few months until we ...
  2. toggle to "test, track, isolate" until we ...
  3. vaccinate enough people, which means that ...
  4. we win.

So that's it! So we make an emergency landing with our plane.

This is how we beat COVID-19.


But what if things still go wrong? Things have already gone terribly wrong. This is where fear speaks - and that's a good thing! Fear gives us energy to Backup plans to create.

The pessimist invents the parachute.

Scenario 4+: masks for everyone, summer, emergency switch lockdown!

What if R0 would be much bigger than we think and despite the measures we would not be able to push R below 1?

Even if we fail to get R <1, lowering the reproductive number will reduce the number of cases and thereby save lives. However, R <1 remains our goal and here are a few more ways we can do it:

Masks for everyone:

You may be wondering: "Wait a minute, I thought face masks don't protect against infection at all?" That's true. Everyday masks do not protect you from infection.31... they reduce the risk of you other infect.

To back it up with numbers: wear one infected person a surgical face mask, this reduces the number of cold and flu viruses in aerosols by 70%.32 A reduction in infection by 70% roughly corresponds to the effect of a Lockdowns!

Nevertheless, we still do not know that specific Influence of masks on the infection rate of COVID-19. A result is only considered scientifically valid if it is 95% certain. Only then should it be published. (...should.)33 As of May 1st, 2020, everyday masks are less than "95% safe".

Pandemics are like poker: Only bet when you are 95% sure and you will lose everything else. Like from a recent article34 about masks in the British Medical Journal, have to our cost / benefit analyzes are calculated with an uncertainty factor. Like this:

Cost: Are these homemade cloth masks (which are about ~ 2/3 as effective as surgical masks35), then it's super cheap. When it comes to surgical masks it gets more expensive but still pretty cheap.

Benefit: Even if there is a 50:50 chance that surgical masks will reduce transmission by either 0% or 70%, the expected value is 35%, which is half of one Lockdowns. So, using our uncertainty factor, we estimate that surgical masks reduce R by up to 35%. (Here, too, the assumptions can be questioned and checked by changing the slider.)

(further arguments for / against masks:36)

"It's hard to wear properly." It's just as difficult to wash your hands according to WHO guidelines - seriously, "Step 3) the right palm over the back of the hand" ?! - and yet we recommend hand washing because it is better not to do it perfectly than not at all.

"Wearing a mask makes people more carefree when it comes to hand washing and keeping their distance." Sure, seat belts make some people disregard stop signs, and flossing allows people to eat stones. We should seriously argue the opposite: masks are one permanent physical reminder to be careful - and in East Asia also a symbol of solidarity!

Masks alone will not ensure that R <1 is achieved. But if regular hand washing and "testing - tracking - isolating" got us to R = 1.10, and then only a third of people were wearing masks, it would tip to R <1. Virus contained!


Okay, this is not a "measure" that we can control, but it will help! There are some reports claiming that summer won't change anything about COVID-19. They are only partially correct: summer will not bring R below 1, but it will becomes reduce it.

For COVID-19, every 1 ° Celsius (1.8 ° Fahrenheit) increase in temperature results in a 1.2% reduction in the R-value.37 The temperature difference between summer and winter in New York City is about 26 ° C (47 ° F), so that summer causes a reduction in the R-value of about 31%.

Summer alone won't bring R below 1, but if we have limited resources we can relax some measures in summer and again in winter stronger attract.

An "emergency switch" -Lockdown:

And if that's all still is not enough to bring R below 1, we can try another lockdown.

But we wouldn't have to close 2 months and open a month over and over again. Because R would be reduced, just one or two more "kill switch" lockdowns would be enough before a vaccine is available. (Singapore had to do this "despite" the 4-month control of COVID-19. This is not a failure, on the contrary: through it becomes make it a success.)

Here is a simulation of a "lazy case" scenario:

  1. Lockdown, after that
  2. A moderate mix of hygiene, "testing, tracking & isolating" and an acceptable mask requirement, then ...
  3. another "kill switch" lockdown before a vaccine is developed.

And then there are those further Actions we could take to lower R further:

  • Travel restrictions / quarantine
  • Fever checks in supermarkets and schools
  • Professional disinfection of public places
  • Greeting by foot instead of a handshake
  • And all the other things that people will think of

We hope these plans create some hope.

Even in a pessimistic scenario is it is possible to fight COVID-19 and protect our health and economy. Through the Lockdown as a "restart", the simultaneous lowering of the reproductive factor (R <1), the case isolation as well as the broad use of a data protection compliant app to track the contacts and the mask requirement ... life can be brought back to a new normal.

Sure, your hands are likely to be very brittle. But you can go on a date at the comic book store again. You can watch a new Hollywood flick in the cinema with friends. You can watch people in the library again or just enjoy it with others, alive to be.

Even if it comes to the worst-case scenario ... life goes on.

So let's really get ready for a few bad Worst case scenarios. Ditching! Take your life jacket and go to the emergency exits:

You get COVID-19 and you recover. Or you can get the COVID-19 vaccination. Either way you're immune now ...

...for how long?

  • COVID-19 is most closely related to SARS, which made survivors immune for 2 years.38
  • The coronaviruses that cause normal colds will make you immune for 8 months.39
  • There have been reports of people recovering from COVID-19 but then testing positive again. It is still unclear whether these were false positives.40
  • A not yet professionally assessed Study in monkeys showed immunity to COVID-19 coronavirus for at least 28 days.41

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

For the following simulations, let's assume it is 1 year. Here is a simulation that starts at 100% and decays exponentially, with s no longer immune on average after one year, susceptible again with deviations:

Return of exponential decay!

This is the SEIRS model. The last "S" stands for "susceptible" again.

Now let's simulate a COVID-19 outbreak over 10 years without any action ... if immunity lasts only a year:

In previous simulations we only had a the intensive care units overwhelming tip. Now we have several and the falls are commuting permanent in the capacity of the intensive care units. (Remember, we had these for these simulations tripled.)

R = 1, it is endemic.

Fortunately, the summer reduces R, which improves the situation:


Surprisingly, summer makes the peaks worse and regularly! This is because the summer lowers the new s, which in turn lowers the new imun s. That means immunity crashes in summer which is a big, recurring spike in winter generated.

Fortunately, the solution to this is quite clear - vaccinate people every fall / winter, just like the flu vaccinations do:

(After you've played the recording, try to simulate your own vaccination campaigns! Remember, you can pause / resume the simulation at any time.)

But here is the more terrifying question:

What if it's over Years no vaccine? Or No way?

To be clear: this is unlikely. Most epidemiologists expect a vaccine in 1 to 2 years. Yes, there has never been a vaccine for any of the other coronaviruses, but that's because SARS was quickly wiped out and the "normal" cold didn't justify the investment.

Still, infectious disease researchers have raised concerns: what if we can't make enough?42 What if we rush it and it's not safe?43

Even in the "no vaccine" nightmare scenario, we still have 3 ways out. From the worst to the least worst:

1) Do periodic lockdowns or loose R <1 measures to achieve "natural herd immunity". (Warning: That would lead to many deaths & damaged lungs. And it won't work unless immunity persists.)

2) Do the R <1 measures forever. Contact tracing & wearing masks are becoming the new normal in the post-COVID-19 world, just as STD testing & condom wearing have become the new normal in the post-HIV world.

3) Do the R <1 measures until we have developed treatment options that make it much, much less likely that COVID-19 will require intensive care measures. (We should definitely Do!) Reducing the need for intensive care units by 10 times has the same effect as increasing the capacity of the intensive care units by 10 times:

Here is a simulation without persistent immunity, without Vaccine, and even without any action - simply a slow increase in capacity to survive the long-term spikes:

Even in the worst case scenario ... life goes on.

Maybe you want to question our assumptions and share other R0Try 's or values. Or yours own Try a combination of intervention measures!

Here's an (optional) sandbox mode where everything is available.(Scroll to see all settings) Simulate and play around to your heart's content:

This simple "epidemic flight simulator" taught us a lot. It has made it possible to answer questions about the past few months, the next few months, and the next few years.

Let's finally get back to ...

The plane went down. We are huddled together in the lifeboats. It's time to find the mainland.44

Teams of epidemiologists and people in politics (left, right, and non-partisan) have reached a consensus on how we can beat COVID-19 and our lives at the same time and protect our freedoms.

Here's the rough idea, with some (less consensual) alternative plans:

What does that mean for YOU, right now?

For each and everyone: Respect the exit restrictions so we can get out of phase I as quickly as possible. Keep washing your hands. Make your own masks. Load a privacy friendly Download the app to identify contact persons as soon as they are available in the next month. Stay healthy - physically and mentally! And text the local decision-makers to get their butts up and ...

For politicians: Make laws to help people who need to self-isolate / quarantine. Hire more human contact followers supported through privacy-friendly apps. Direct more resources into the things we should be making, like ..

For makers45: Manufactures tests, ventilators, personal protective equipment for hospitals and doctor's offices. Makes tests, masks, and apps, as well as antiviral drugs, prophylactic drugs, and other non-vaccine treatments. And makes vaccines, tests, tests and more tests. Creates hope.

Don't downplay fear to build hope. Our fear should grow with our hope ally, like the inventor of the planes and parachutes. By preparing for a terrible future create we have a hopeful future.

The only thing to fear is the idea that the only thing to fear is fear itself.

  1. The footnotes in this simulation contain sources, links, or additional comments. Like that first comment!

    "The only thing to fear is fear itself" is a quote from Franklin D. Roosevelt from his speech on his inauguration in 1933 during the Great Depression

  2. This guide was published on May 1st, 2020. Many details will become obsolete, but we are confident that it covers 95% of all possible future scenarios and that the 1x1 of epidemiology with no expiration date will remain useful

  3. "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 (Note: pre-releases cannot be considered final versions of articles) ↩︎

  4. Note: all of these simulations are very simplified for educational purposes.

    A simplification: If you set the following for this simulation: "Infect a new person every X days", the number of infected people actually increases by 1 / X per day. The same goes for future settings in these simulations - "Recover every X days" actually means that the number of infected people will decrease by 1 / X every day.

    These are Not identical but similar enough and easier to see through for learning purposes than specifying the transfer / recovery rates directly

  5. "The median of the time span in which infected people were contagious [...] was 9.5 days." (“The median communicable period [...] was 9.5 days.”) Hu, Z., Song, C., Xu, C. et al. Yes, we know that "median" and "average" are not the same . But they are similar enough for didactic purposes

  6. For more technical explanations on the SIR model, see the Institute for Disease Modeling and Wikipedia↩︎

  7. Further technical explanations of the SEIR model can be found at the Institute for Disease Modeling and Wikipedia↩︎

  8. “Based on an incubation period distribution averaging over 5.2 days from another study of early COVID-19 cases, we concluded that infectivity was 2.3 days (95% CI, 0.8-3.0 days) before the occurrence of symptoms. " Translation: Assuming the symptoms start on the 5th day, then the contagiousness starts 2 days before that (i.e. on the 3rd day). (“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”) He, X., Lau, EHY, Wu, P. et al.↩︎

  9. “The median R value for seasonal influenza was 1.28 (IQR: 1.19–1.37)” (translated): “The median R value for seasonal influenza was 1.28 (IQR: 1.19–1.37)” Biggerstaff , M., Cauchemez, S., Reed, C. et al.↩︎

  10. “We estimate the base reproduction number R0 from 2019-nCoV to about 2.2 (translated): “We estimated the basic reproduction number R0 of 2019-nCoV to be around 2.2 (90% high density interval: 1.4–3.8)” Riou J, Althaus CL.↩︎

  11. “We calculated the median of the R0 value as 5.7 (95% CI 3.8–8.9)” (translated): “we calculated a median R0 value of 5.7 (95% CI 3.8–8.9)” Sanche S , Lin YT, Xu C, Romero-Severson E, Hengartner N, Ke R.↩︎

  12. We assume here that one is always consistently infectious in one's "infectious phase". Here, too, the simplifications have been made for better understanding

  13. As a reminder, R = R0 * Proportion of permitted transfers. The proportion of permitted transmissions = 1 - proportion of the foiled Transfers.

    Then to get R <1, R0 * Approved infections <1.

    So, Admitted Infections <1 / R0

    So, 1 - Foiled Infections <1 / R0

    Therefore, Foiled Infections> 1 - 1 / R0

    So need more than 1-1 / R0 of transmissions are thwarted in order to achieve R <1 and contain the virus! ↩︎

  14. Percentage of COVID-19 cases in the United States from February 12 to March 16, 2020 that required intensive care treatment, by age group (translated): "Percentage of COVID-19 cases in the United States from February 12 to March 16 , 2020 that required intensive care unit (ICU) admission, by age group ". Between 4.9% and 11.5% all COVID-19 cases required intensive care treatment. If you choose the lowest estimate, that's 5% or 1 in 20. This total is specific to the US age structure. It will be higher in countries with an older population and lower in countries with a younger population

  15. Number of beds in the intensive care unit = 96,596. Of the Society of Critical Care Medicine (Society for Intensive Care Medicine) The population of the United States in 2019 was around 328,200,000 people. 96,596 out of 328,200,000 makes about 1 in 3400.↩︎

  16. Translated quote: He says the real goal is the same as in other countries: flatten the curve by staggering the outbreak of infection. As a result, the nation can achieve herd immunity; this is a side effect, not a goal. [...] The government's current Coronavirus Action Plan available online doesn't mention herd immunity at all. (From a The Atlantic article by Ed Yong) (translated): “He says that the actual goal is the same as that of other countries: flatten the curve by staggering the onset of infections. As a consequence, the nation may achieve herd immunity; it's a side effect, not an aim. [...] The government’s actual coronavirus action plan, available online, doesn't mention herd immunity at all. " From a The Atlantic article by Ed Yong↩︎

  17. All eight eligible studies reported that hand washing reduced the risk of respiratory infection, with risk reductions ranging from 6% to 44%. Pooled value 24% (95% CI 6-40%). (For the sake of simplicity, we have rounded the pooled value to 25% in these simulations.) Rabie, T. and Curtis, V. Note: As this meta-analysis shows, the quality of the studies on hand washing (at least in high-income countries ) miserable

  18. We found a 73% decrease in the average daily number of observed contacts per participant. This would be enough to get R0 from a value of 2.6 before lockdown to 0.62 (0.37-0.89) during lockdown. (For the sake of simplicity, we have rounded down to 70% in these simulations.) Jarvis and Zandvoort et al↩︎

  19. That distortion would go away if we plotted R on a logarithmic scale ... but then we would have to logarithmic scales explain↩︎

  20. In the absence of other measures, a key metric for social distancing success is whether ICU capacities are exceeded. In order to avoid this, a longer or periodic spatial distancing up to the year 2022 may be necessary. (translated): “Absent other interventions, a key metric for the success of social distancing is whether critical care capacities are exceeded. To avoid this, prolonged or intermittent social distancing may be necessary into 2022. " [Kissler and Tedijanto et al] (↩︎

  21. See Figure 6 from Holt-Lunstad & Smith 2010. Of course, we have to restrictively point out that they are only one correlation have found. But as long as we do not want to randomly arrange lifelong loneliness for individual people, we have to fall back on such observations for our assumptions

  22. an average of 3 days until a person becomes infectious: "Assuming an incubation period distribution averaging 5.2 days from a separate study of early COVID-19 cases, we concluded that the infection was 2.3 days (95% CI, 0.8-3.0 days) ago Symptombeginn lag "(Translation:" 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 ") (This means: If the symptoms start after 5 days, you are already contagious 2 days beforehand = risk of infection 3 days after infection) [He, X., Lau, EHY, Wu, P. et al.] (Https: //

    ** Average of 4 days until another person was infected: ** "The average [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

    ** 5 days on average until symptoms appear: ** "The median incubation time was estimated to be 5.1 days (95% CI, 4.5 to 5.8 days)" Lauer SA, Grantz KH, Bi Q, et al ↩︎

  23. We estimated that 44% (95% confidence interval, 25-69%) of the secondary cases became infected during the presymptomatic stage of the index cases. (Translation: "We estimated that 44% (95% confidence interval, 25-69%) of secondary cases were infected during the index cases’ presymptomatic stage ") He, X., Lau, E.H.Y., Wu, P. et al↩︎

  24. "Contact tracing was a critical activity in Liberia and represented one of the largest epidemic contact tracing efforts in history." (Translation: “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.↩︎

  25. To prevent "pranking" (people falsely claiming to be infected), the DP-3T protocol requires that the hospital first send you a one-time access code that you can use to upload your messages.

    False alarms are a problem with both manual and digital contact tracing. But we can reduce it in two ways: 1) By only notifying Bob when the app has received messages for, say, 30 minutes or more, not just a passing message. And 2) if the app really thinks Bob was exposed, can she give him a manual * n Refer the contact follower to conduct a detailed follow-up interview.

    For other topics such as data bandwidth, source integrity and other security issues, read the open-source DP-3T whitepapers! ↩︎

  26. Temporary Contact Numbers, a decentralized contact tracing protocol for contact tracing while preserving privacy↩︎

  27. PACT: Private Automated Contact Tracing↩︎

  28. Apple and Google partner on COVID-19 contact tracing technology. Please note: You do not develop these apps selfbut only the system environments that these apps support.↩︎

  29. A lot of news stories - and frankly, a lot of scientific papers - do not distinguish between "cases that showed no symptoms when we tested them" (presymptomatic) and "cases that did always showed no symptoms ". (genuinely asymptomatic). The difference could only be determined if they followed up the cases later.

    That is exactly what [this study] ( did. (Disclaimer: "Early releases of articles are not considered definitive versions.") In a call center in South Korea that was experiencing a COVID-19 outbreak, only 4 (1.9%) cases remained asymptomatic within 14 days of the quarantine, and none of her household contacts had secondary infections.

    This means that "real asymptomatic" is rare, and infection with real asymptomatic can be even rarer! ↩︎

  30. From the same Oxford study that first recommended apps in the fight against COVID-19: Luca Ferretti & Chris Wymant et al. See Figure 2. Suppose R0 = 2.0, they found:

    • Contribution of symptomatic cases to R = 0.8 (40%)
    • Contribution of presymptomatic cases to R = 0.9 (45%)
    • Contribution of the asymptomatic cases to R = 0.1 (5%, although their model involves uncertainties and the contribution could be much lower)
    • Contribution of environmental influences such as door handles to R = 0.2 (10%)

    If you add up the pre- and asymptomatic contacts (45% + 5%), you get 50% of R! ↩︎

  31. “None of these surgical masks exhibited adequate filter performance and facial fit characteristics to be considered respiratory protection devices. ” Tara Oberg & Lisa M. Brosseau↩︎

  32. “The overall 3.4 fold reduction [70% reduction] in aerosol copy numbers we observed combined with a nearly complete elimination of large droplet spray demonstrated by Johnson et al. suggests that surgical masks worn by infected persons could have a clinically significant impact on transmission. " Milton DK, Fabian MP, Cowling BJ, Grantham ML, McDevitt JJ↩︎

  33. Real scientists have probably read the last sentence with one laughing and one crying eye. See also: p-hacking, the replication crisis ↩︎

  34. "It is time to apply the precautionary principle" (translated): "It is time to apply the precautionary principle" "Trisha Greenhalgh et al [PDF] ↩︎

  35. Davies, A., Thompson, K., Giri, K., Kafatos, G., Walker, J., & Bennett, A See Table 1: For the two bacterial aerosols tested, a 100% cotton T-shirt was approximately 2/3 of the filter efficiency of a surgical mask

  36. "We need to secure our supplies for our hospitals."In any case. But that's more of an argument in favor of increasing the production of masks, not rationing them. In the meantime, we can make cloth masks

  37. “One-degree Celsius increase in temperature [...] lower [s] R by 0.0225” and “The average R-value of these 100 cities is 1.83”. 0.0225 ÷ 1.83 = ~ 1.2%. Wang, Jingyuan and Tang, Ke and Feng, Kai and Lv, Weifeng↩︎

  38. SARS-specific antibodies were obtained for an average of 2 years [...] Therefore, SARS patients could be susceptible to re-infection ≥3 years after initial contact. Wu LP, Wang NC, Chang YH, et al. "Unfortunately," we will never know how long SARS immunity would really have lasted because we eradicated it so quickly

  39. We could not find a significant difference between the likelihood of at least one positive test and the likelihood of recurrence for the beta coronaviruses HKU1 and OC43 34 weeks after registration for study participation / initial infection. Marta Galanti & Jeffrey Shaman (PDF) ↩︎

  40. After a person fights off a virus, virus particles tend to linger for a while. These particles cannot cause infection, but they can make a test result positive. from STAT News by Andrew Joseph↩︎

  41. From Bao et al.Note: This article is a preprint and has not (yet) been peer-reviewed. Also, to emphasize: only re-infection was tested after 28 days

  42. "If a vaccine for the coronavirus comes out, can the world make enough of it?" (translated): "If a coronavirus vaccine arrives, can the world make enough?" by Roxanne Khamsi, on Nature↩︎

  43. "Do not push for the release of COVID-19 vaccines and drugs without sufficient safety guarantees" (translated): "Don’t rush to deploy COVID-19 vaccines and drugs without sufficient safety guarantees" by Shibo Jiang, on Nature↩︎

  44. Mainland Metaphor by Marc Lipsitch and Yonatan Grad, on STAT News↩︎

  45. An explanation of the term can be found here. (Https:// ↩︎