Corona Mathematics
or
the Algebra of Death
by Daniel Regenberg, Berlin, 19th-20th of March 2020
00. Introduction
This Text is written with a feeling of great urgency. The Corona virus is spreading all around the world. Many people in many different regions of the world have died already, and much more people will die. Our actions NOW determine how fatal the impact on humanity will be, how hard this virus will hit our countries, communities and families in the weeks and months to come.
In this text I try to explain some of the underlying mathematics of the virus spread, the mechanics of this pandemic outbreak. In order to fight this enemy we have to understand it.
The situation is highly volatile, we learn each day more about this virus and its behavior. This text is based on the currently available limited data. The consequences outlined here are so dramatic and sad, that I hope future developments will proof it all wrong.
Please excuse my poor English, it is my third language. This virus spreads worldwide, writing in german would limit the potential reach of this information.
I tried to explain the mechanics of the Corona spread before in a series of 13 very rough videos, which i did all in one day — we have to move fast, because so is the virus. https://www.youtube.com/watch?v=3rWBdNc5rqA&list=PLbBshZl_Yre5SXMilS2CljWQ4oJEhXjpu&index=1
And I made three short and very basic videos to explain in simple terms the most dangerous aspects of this outbreak.
https://www.youtube.com/watch?v=PXkvfSIXPKs&list=PLbBshZl_Yre7U8iRTFK8d9xfav8do1Me0
There is already some good information around, I recommend for example strongly this article by Tomas Pueyo: https://medium.com/@tomaspueyo/coronavirus-act-today-or-people-will-die-f4d3d9cd99ca
There are already two simulations online where you can model the spread by yourself, change the parameter, instigate interventions and see their effect and so forth.
http://gabgoh.github.io/COVID/index.html
However, watching the daily news, listening to the statements of some politicians and some conversations with friends, I have to realize rather often, that there are many basic misconceptions about this virus and its spread. With my limited means, I will try to give useful information to you and everybody interested. If this information is valuable to you, please help passing it on to others — it may save lives, and if not yours, the lives of your parents or grandparents.
This virus is new, many things are yet unknown, and the situation worldwide is very volatile. So many numbers in this text have to be estimates, since we have only access to a limited amount of data yet. In three years everything well be much clearer, but we have to act now. Here for example you find some provisionally data https://github.com/midas-network/COVID-19/tree/master/parameter_estimates/2019_novel_coronavirus.
Some people will not understand the (hopefully) stringent or even radical measures taken by their governments. After carefully reading this text you might understand better. And if you are unlucky enough to live in a country which — for whatever reasons — does not take the necessary actions (yet), then you hopefully will understand why and how to take precautions by yourself.
So the most basic information first: The virus will affect sooner or later all regions of the world heavily. It will come to you. And it will hit hard. Most probably it is already there. Depending on how well the testing is done in our area, the official case numbers may differ hugely from the real numbers, so these numbers are not the best indicator. So what is a good indicator? If people sick with Covid-19 keep showing up in greater numbers at your hospitals, or — even worse — if the number of people who died because of Covid-19 keeps rising, then you know: There is a huge spread of the Corona virus in your community, even if the official numbers show otherwise. In this text I will propose a method how to estimate the real number of cases only by knowing the number of fatalities (chapter 10). But for now: This disease seems so be most dangerous for elderly persons, for persons with certain other diseases, and mostly for old persons with one or even multiple other diseases — these are the most vulnerable: People with high blood pressure, diabetes, chronic lung diseases and cardiovascular diseases seem to be in great danger.
https://www.cdc.gov/coronavirus/2019-ncov/specific-groups/high-risk-complications/older-adults.html
This is the most important practical information in this text:
If people sick with Covid-19 show up in higher numbers in your hospitals or if more and more people die because of the disease, please take immediate action, even if the official case numbers are still low! Take care of the old and sick, make them go in strict isolation with whatever means possible, you may save their life!
The weeks and days before a potential lockdown of your area and country are the most dangerous: Many people will already be infected without knowing it, at the same time the awareness in the population is probably still low, and a few weeks from now the healthcare system will potentially collapse — that means: people who get infected today may be in a very bad situation and suffer greatly three weeks from now. So if your country or region is in this situation right now (the deaths are ramping up, administration and/or population is in denial, official measures are weak), please hide your older and vulnerable relatives and friends indoors, persuade them with whatever means to stay safe in isolation, try to save them, even if they now do not understand — they will understand a few weeks from now, but then it might be to late.
Think of the terrible scenes in Italy: Completely overworked medical professionals have to decide who gets a respirator or ICU bed and who does not. Thousands of old people die lonely in quarantine, because they have to be isolated to stop the spread. You cannot even say goodbye. There is no proper funeral because the country is in lockdown. I hope it is safe so assure, that we do not want this to happen to our parents and grandparents.
01. Exponential growth by 27% daily
The good news first: In many countries and regions stringent and coherent countermeasures have been taken, so there the spread of the virus has at least been mitigated, ideally stopped. The measures differ greatly, and their effect will (for reasons I explain in chapter 02 in detail) only be measurable with a certain delay — at least five to ten days. The situation in different regions is different in many regards, and so are the measures. That means the spread of the virus will in different regions from now on depend strongly on the social response to the threat, and it will be harder to predict the growth of the spread. Remember: This virus with its specific properties is quite new, also measures like for example a full lockdown of a modern western society have not been done before — so we do not know their precise effect on the virus spread, we are in uncharted territory here.
But before countermeasures are taken, the virus unfolds unhindered with its own deadly logic, and first I will explain the underlying mechanics of this unmitigated exponential growth. This growth is also still important after the spread is stopped, because of the timeframe of the disease: People get infected, days later they get sick and might be tested positive, days later they might need a hospital or ICU bed, and some more days later they might die. I will explain all this in detail later, but for now please understand: If you stop the spread now, the number of infected will keep growing for at least five to ten days, the number of people in need of intensive care will grow longer, and the number of fatalities will keep growing even a longer time after you stopped the spread. So if you have an unmitigated exponential growth and stop the spread because a certain amount of people have died until now, this number might easily rise hundredfold!
If you stop the unmitigated spread because for example 100 people in your country have died, you will end up with 10.000 people dead — possibly more.
You would expect the virus to grow with different rates in different societies, depending on how close the people live and interact, how large the families are etc., as well as in different climatic conditions. But according to the available numbers the unmitigated virus spread unfolds actually quite similar everywhere. You probably will have seen the different curves for different countries and how they actually do not look very different after all (except for some countries with successful outbreak control like China, South Korea and others). Here an example from Twitter https://twitter.com/coronawatch_, which shows the development of official cases in different countries after their 100th case.
In chapter 05 I will discuss the growth rate in detail, and there is a lot of information online to understand exponential growth, for example here https://www.youtube.com/watch?v=Kas0tIxDvrg. For now: The growth rate for unmitigated growth differs of course, but not so much, it seems to be something between 25 and 30 % each day wherever you look. That is why the curves of the different outbreaks in different countries look so similar. Let´s just go with 27 % for now.
That means: If no actions are taken, the number of infected grows 27% — each day!
Imagine a bank account with 27% interest — each day…
In the beginning this growth may seem slow, but then it explodes very, very fast.
If you want to know the growth after a given number of days d, just calculate:
1,27^d
Some examples:
1) three days
1,27³ = 2,048
That means, the number of infected people doubles every three days. If you have 1.000 infected people today, you will have 2.000 in 3 days, 4.000 in 6 days, 8.000 in 9 days, 16.000 in 12 days etc.
2) a week
1,27⁷ = 5,329
That means after a weak the number of infected is at least five times higher. So if you have 1.000 infected now, in one week you will have 5.000, then one week later 25.000 and so forth.
3) a month
1,27³⁰ = 1.300
That means, if you have 1.000 infected now, one month from now there will be more than one million infected. One month later there will be more than one billion infected…
Now I will give some examples for unmitigated growth of one month from now on, considering the number of officially registered positive cases in different countries (I will show later why the real number of infected is much, much higher, so it gets worse unfortunately):
USA — 8.054 cases now — one month from now more then 10 million (10.470.200)
Great Britain — 2.689 cases now — one month from now 3,5 million (3.495.700)
Brazil — 529 cases now — one month from now 687.700
So when will the growth stop? There are different possibilities which can also be combined:
-mitigation via collective behavioral changes like (consequent) social distancing and stricter hygiene
-containment via lockdown or quarantine measures
-effective tracking and strict isolation of infected persons
-herd immunity via vaccine
-herd immunity via natural immunity (that means probably 60–70% of the population have to have been infected)
Also climatic changes (summer is coming) might help a bit to mitigate the growth, though new studies do not suggest a large effect. But if different factors are combined, the growth might actually get stopped without having to maintain a total lockdown forever: If the population is aware and disciplined, if cases are isolated and their contacts tracked immediately and quarantined consequently, if maybe a fraction of the population is already immune, if maybe the weather might help a bit, if all these factors combine, we probably could contain the spread without longterm lockdown, as South Korea or Taiwan show. But as I said: We are in uncharted territory.
One thing is certain: If we don´t act, within only a few months worldwide several billion people will be infected — and tens or in the worst case hundred of millions will die. This pandemic may claim more lives then the first and second world war combined.
02. Timeframe and latencies
As I already pointed out several times, the virus is rather new, there is only limited data available. Three years from now we will know much more and the numbers will be known. For now we have to estimate based on the knowledge we have. For this chapter I again took information from this side for example https://github.com/midas-network/COVID-19/tree/master/parameter_estimates/2019_novel_coronavirus. I will develop a simplified model based on a five-day scheme here. In the 13 videos I made a few days earlier, I used a week-based model, both seems to be possible at this time, the data is still very limited, we have to estimate a lot. And of course every individual Covid-19 case is different, here I try to estimate average time intervals.
The infection with the Corona virus develops following a certain timeframe:
1) You get infected (without knowing at first) and enter the incubation period. As it seems you can not spread the virus and you can not be tested positive in this period.
2) You get sick and may or may not have symptoms. Now you can spread the virus. It is important: There seem to be cases of asymptomatic carrying, that means you carry the virus and can spread it, but you do not know this (and may in fact never know), because you feel no symptoms. Asymptomatic carriers seem to spread the virus situationally less, because they do not sneeze or cough, but because they don´t know they carry it, they may not take precautions and seem to spread it a lot, as data from South Korea suggests. At this time nobody knows how high the percentage of these asymptomatic carriers is, we might know this only years from now, for example by statistical analysis from blood donations.
3) If you have symptoms or you had contact or for other reasons you might take a test, it has to be send to the lab, they process it and send the result. Now you are an officially confirmed case of Covid-19 and show up in the statistics.
4) You might get seriously ill and need a hospital or even ICU bed.
5) You might unfortunately die — or recover and go home.
Considering all the numbers from the page linked above this VERY simplified model seems to be not unreasonable:
day 00 — infection
day 05 — disease starts
day 10 — positive test result
day 15 — potential need for an ICU bed
day 20 — potential death
With the data currently available, the number with the greatest uncertainty in this estimation is the number of days after which you need an ICU bed — it might be a few days less, maybe even up to five days less, it is hard to tell at this point in time. Also the number of days it takes until your test can potentially show a positive result depends heavily on the testing practice in your region: If a lot of testing is done with very fast tests, this timeframe will shorten and vice versa.
What does that mean? I will discuss the hidden number in testing and the death rate in detail later, for now let us assume we find 50% of the sick people and test them positive, 5% of the sick people need an ICU bed, and 1% of the sick people die finally. All these factors are just linear, so all curves are basically the same as the curve with the number of affected people, only with a time latency and a certain percentage of the original value. But the general curve is the same. (It may become distorted if the health system is overwhelmed, see below.)
That means: The need for ICU beds also grows exponentially, as does the number of deaths. Both numbers grow 27% each day.
The numbers might get distorted finally: People don´t stay forever in the hospital, they are send home eventually, while the numbers of officially cases and deaths are cumulative. And when you have no ICU beds left, then this number obviously does not grow anymore. Then your health system will be overwhelmed, and the death rate will actually go up to probably about 4%. But before this terrible state is reached, all the curves develop the same, they grow by 27% each day, unless the growth of the virus is stopped — I will show this with the actual numbers in chapter 05.
Of course the curves get more regular with higher numbers — if only a few people died until now, then the statistical distortion is still high.
To make this more clear: See here the development of official cases and deaths in Italy from wikipedia https://www.wikiwand.com/en/2020_coronavirus_pandemic_in_Italy. Even if there will be some distortion because of the probably insufficient testing effort and statistical noise, you still see two very similar curves — and both represent the same exponential growth.
In Germany our testing is more coherent, so this curve is more regular then in Italy, but we have still only a few deaths, so you can in the curve representing the deaths clearly see the statistical noise: The growth curve of the deaths is distorted, because there are only a few. When the growth continues (wich it unfortunately will), this curve will be more and more identical to the curve with the confirmed cases, only with a time delay of about 10 days, and finally hopefully significantly flattened by the measures taken until now.
Because of the timeframe of the Corona virus, the situation is even worse, which i will explain later in greater detail: If you stop the growth now, because of the here discussed time delays the number of sick people will keep growing for at least 5 days, the number of confirmed cases (means they tested positiv) for about 10 days, the number of people in need of an ICU bed for about 10–15 days and the number of dead people for about 20 days.
Keep in mind: 27% growth a day means:
5 days later approx. 3 times higher numbers
10 days later approx. 10 times higher
15 days later approx. 33 times higher
20 days later approx. 100 times higher
That means: If you do not mitigate the spread of the infection in your region, then the other numbers (like the number of deaths) also grow with the exact 27& each day — until your healthcare system is overwhelmed, and then it gets worse.
So if the virus is in a period of unmitigated growth and you have for example already 1.000 dead people, you will, even if you stop the growth radically right now, have at least 100.000 dead people a few weeks from now, because it will keep growing for 20 days, whatever measures you take now. If your health system is overwhelmed the death count may rise to 400.000.
Countries like the US or Great Britain — which both have right now more then 100 deaths and did not change the growth of the virus significantly in the last days or weeks — will have more then 10.000 deaths a few weeks from now — and this is unfortunately a best case scenario: If they do not take urgent measures it will get worse.
03. About testing
The testing practice differs a lot between different countries. I will show later a method, how you can roughly estimate the real number of infected people in your region via the number of dead people — and then you can compare this with the official case count and find out, how well the testing in your region is. But for now: I guess it is intuitively obvious, that a country with a lot of deaths and only a few confirmed cases does a bad job in testing — while a country with only a few deaths and a lot of confirmed cases does good testing.
Some countries test more people, some do almost no testing at all. A lot of data is online, for example here https://ourworldindata.org/covid-testing. Of course not only the number of performed tests is important, but also the criteria by which it is decided to test people — if countries trace back very thoroughly all contacts of infected persons, they might need fewer tests to get a good picture than countries, which test more people randomly.
I do not want to blame countries, I just want to share my impression of the current situation, which will hopefully change soon in some countries:
Exemplary testing: South Korea
Good testing: Germany and some Scandinavian countries
mediocre testing: UK, Italy, Spain
bad testing: US, many African and South American countries
There will probably always be a hidden number of cases, persons who might have never experienced any symptoms but still have had the disease, even in countries with exemplary testing like South Korea or Taiwan. In most countries this hidden number is actually rather large, as we will see later.
But there is another way in which the picture given by the test results is distorted inevitably: You know how many people are infected at the earliest ten days after they got infected, as I showed in the last chapter.
That means, inevitably your testing shows only a picture of the situation ten days ago, there is no way around this. You can only try to bring this time down by using instant tests and by testing people very promptly, but at least the latency of the incubation period (5 days in average) is inevitable.
If the growth of the virus has not been mitigated yet (as it has not significantly in the US until maybe a few days ago, Brazil, Great Britain and other countries), we know how much the growth is in 10 days: more then ten times. So if the news talk about 5.000 confirmed cases, that means that (without the hidden number, which makes it even worse) in reality at least 50.000 people are infected right now, but only 5.000 are known as infected, 45.000 not. So 45.000 people walk around spreading the virus without anybody knowing.
If the growth is mitigated, the time delay effect stays of course the same, only the growth rate changes.
Later I will discuss this more in detail, but you can already imagine, how difficult it is to deal with this virus, because we can only monitor the situation ten days ago. In the article by Tomas Pueyo this is mentioned, as is in the following article https://jamanetwork.com/journals/jama/fullarticle/2762130. It is very important to understand the inevitable delay of monitoring, because many countries like Italy acted unfortunately too late, and the consequences are terrible. You must not wait until your numbers are bad, you have to stop the growth before they get too high. Remember: China locked down Wuhan with only 400 confirmed cases — and still more then 3.000 people died in China because of Covid-19!
For example in the US there are momentarily ca. 10.000 confirmed cases. I will show later, that the hidden number in the US is very large. Also they probably mitigated the growth in the US since a few days with the social distancing measures they have taken. Let us assume, for the sake of the argument, that the growth continued unmitigated until today with 27% and then came to a sudden stop and is now 0%. Then you know, because your testing shows the situation ten days ago, that you have now in reality (without the hidden number) 100.000 infected — and if only 1% of these people die, that means 1.000 dead people in the next weeks. Because of the hidden number the situation is much worse, as I will show in the next chapters.
04. Death rate
There are many misconceptions about the death rate (also „case fatality rate“ or CFR). Some people look for example at Italy: 35.713 confirmed cases and 2.978 deaths, does it mean 8,33% death rate? Is it so high because the population is so old? No, the whole method is wrong. First of all: You do not know the real number of infected, there is always a hidden number. And more importantly: People die in average 20 days or so after they get infected and ten days after they are tested postitiv, so you cannot compare the number of actual infected with the number of total deaths, especially if you are still in a period with rapid growth. Once the growth is stopped (or better once the whole pandemic is over) — like in China, on the Princess Diamond and hopefully in South Korea — you can finally compare the number of deaths with the number of total cases. There will still be some uncertainty because there might be hidden cases of people who never knew and probably never will know that they have been infected.
So at this time all the numbers are provisionally and some educated guessing is necessary.
The data from South Korea seems to be the most reliable right now: https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_South_Korea. Here we can also see, that the death rate differs a lot for different parts of the population: For young healthy persons it is around 0,1% or even smaller, for older people or people with certain health conditions the death rate goes up significantly. The total death rate in South Korea is about 1%, but it might still go up a bit, since the spread seems to be almost contained, but still many people are sick — that means the number of cases will (if the containment hopefully stays tight for the future) not rise significantly while the number of deaths may still raise, which will increase the death rate.
On the Princess Diamond the death rate was 1%, in China outside Wuhan a bit under 1% and in Wuhan around 4%, as the data shows, even if it may not be the most reliable https://en.wikipedia.org/wiki/2019%E2%80%9320_coronavirus_pandemic_in_mainland_China.
In countries with different demographics the death rate might be very different. In Africa more than half of the population is under 25, and because of the weaker healthcare systems and widespread diseases many old people with multiple diseases might die much earlier than in a developed country. In developed countries we have a much older population, and because of our good healthcare system we can keep many elderly persons with multiple medical conditions alive, and these people are now vulnerable to the Corona virus. At this point it is all speculation, but maybe African societies and some poorer countries might for these reasons not be affected as much from this pandemic than developed countries — let us hope this is true. Maybe the good health care system of developed countries makes them now susceptible to experiencing fatalities by Covid-19. However, the demographics and the state of the healthcare system of course influence the death rate, so a global death rate is always only a rough estimate.
At this point it seems to me a reasonable estimate, that the death toll in a country with good healthcare system and the demographics of a developed country is about 1%. Once the healthcare system is overwhelmed it will change to about 4%.
If we do not contain the spread, the virus will, as experts seem to agree on, finally infect 60 to 70% of a population. Of these infected 1% will die, if the healthcare system is not overwhelmed, and 4% if it is (which it will in every country ultimately if the virus grows unmitigated, and very fast). So let me show a few examples for the impact of an unmitigated spread of the virus in some countries and the world:
UK — ca. 45 million infected, 450.000 to 1.800.000 deaths
Germany — ca. 55 million infected, 550.000 to 2.200.000 deaths
USA — ca. 215 million infected, 2.150.000 to 8.600.000 deaths
India — ca. 900 million infected, 9 to 36 million deaths
world — ca 5 billion infected, 50 to 200 million deaths
And there is more bad news: Many people will recover but suffer an irreparable lung damage. I did not find coherent numbers for this topic, but it will probably end up being a not negligible proportion of the infected population. So the aftermath will be like when a war is finally over: many people dead and many severely damaged.
05. Calculating the universal growth rate of all different curves
As we have seen until now, the number of confirmed cases is actually an unreliable number. If you intensify your testing effort, the number of confirmed cases obviously will go up, so the growth rate is distorted to the positive side. If you test less, the growth rate will seem to be lower, even if the real number of infected people grows unchanged. But we know by now, that the growth rate of patients initially in need of an ICU bed and the growth rate of deaths should be identical to the growth rate of infected people, only with a time delay. Remember: Ca. 5% of all infected need an ICU bed (maybe less, data is still very limited) and ca. 1% of all infected die eventually — until the health system is overwhelmed: Then no ICU beds are free and the death rate grows to ca. 4%.
(For the following calculations I did not use numbers from China and South Korea: In China the officials might not have the real numbers, because the spread started there and at the beginning the situation was inevitably quite chaotic — or they might not show the real numbers, if they are politically not desirable; in any case the numbers might be unreliable. And in South Korea patient 31 was an extreme super-spreader, so here the growth curve is irregular.)
Let us run some (terrible) numbers (all data is taken from wikipedia):
In Germany we have until now only a few deaths and many confirmed cases, so testing seems to be rather good https://de.wikipedia.org/wiki/COVID-19-Pandemie_in_Deutschland.
date confirmed cases growth
11–03 1.089
12–03 1.892 +73%
13–03 2.576 +36%
14–03 3.421 +32%
15–03 4.195 +23%
16–03 5.433 +30%
17–03 7.156 +32%
18–03 8.198 +15%
Average growth: 34,4%
That seems to be quite high, either they intensified testing or we had a strong spread.
In the US the testing effort seems to be rather poor, but maybe it is consistently bad, and in wikipedia they conveniently show the daily growth in percent, so let us at least look at that https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_the_United_States. It is from 11–03 until 18–03:
33%, 35%, 31%, 24%, 25%, 29%, 42%
Average growth: 31%
Now to the more evil numbers, let us start with the development of deaths in France https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_France. Here Wikipedia also shows the growth in percent, the numbers from 13–03 until 19–03 are:
23%, 21%, 40%, 17%, 18%, 51%, 54%
Average growth: 32%
What about the growth of confirmed cases in France? The growth in the last 7 days, 13–03 until 19–03:
28%, 23%, 20%, 22%, 17%, 18%, 20%
The average growth rate is only 21%. Why is it so low? There are two major possibilities, and they are not mutually exclusive:
1) In the beginning of the pandemic the testing effort might have been more consistent, because it was still easier to trace back contacts and find possibly infected.
2) The „soft“ social distancing measures (keep your distance, wash your ands etc.) instigated at least ten days earlier already showed some effect and slowed the growth from almost 30% to almost 20% — that would actually be very good news!
For Italy wikipedia also shows the growth rate of the deaths in percent https://www.wikiwand.com/en/2020_coronavirus_pandemic_in_Italy. They sadly already suffer a longer strong outbreak, so let us look at a longer period of two weeks, from 06–03 until 19–03:
33%, 18%, 57%, 27%, 36%, 31%, 23%, 25%, 14%, 26%, 19%, 16%, 19%, 14%
Average growth: 25,5%
The German wikipedia page about the Italian outbreak also gives the numbers of people in need of an ICU bed: https://de.wikipedia.org/wiki/COVID-19-Pandemie_in_Italien. The reports from doctors from the last days unfortunately show that their health system is overloaded, so the numbers will be distorted. Also after some days people will not need an ICU bed anymore because they are either recovered or dead, so these numbers will develop differently from the accumulative numbers of confirmed cases or deaths — only the number of day by day newly needed ICU beds will behave similar. But lets look at the curve from 01–03 until 08–03.
People in need of an ICU bed:
140, 166, 229, 295, 351, 462, 567, 650.
Growth: 18%, 38%, 29%, 19%, 32%, 23%, 15%
Average Growth: 25%
Now Spain https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_Spain, first the growth rate of deaths for the last week:
55%, 47%, 50%, 16%, 56%, 20%, 30%
Average growth: 39%
That seems to be quite high, but the numbers are still not huge, so there may be some distortion here — hopefully.
For Spain they also show the number of people in intensive care, the numbers for the last week are: 190, 272, 293, 382, 432, 563, 774, 939.
So the growth is: 43%, 8%, 30%, 13%, 30%, 37%, 21%
Average growth: 26%
So all these numbers are around 25 or 30%, in parts even a bit higher. Why do they differ at all? There are several reasons, I will just discuss some of them:
-In different communities people interact obviously differently, so the rate of new infections will differ; inhabitants of northern european countries for example might even before the pandemic in their standard behavior live more distanced than people in other parts of the world; people live in families of different sizes in different parts of the world, the work is organized differently, movement and travel differ etc. etc.
-The testing effort might be increased or decreased; same with the contact tracing effort. This will affect not the number of really infected people but merely the number of official cases, and that is the number which is reported.
-Some early measures of social distancing and increased hygiene might show some effects and slow the growth weeks before a potential lockdown.
-The awareness of the population will affect the growth rate heavily: The people of many Asian countries were much more prepared for this (because they had experienced pandemics in the recent past) than e.g. the people of Europe and Northern America, so they knew to be careful and follow the rules before the death toll explodes and the government has to implement harsh measures.
-With small numbers there will be a lot of statistical distortion: A super-spreader in an early stage may lead to a sudden increase in cases; an outbreak in a home for elderly people might lead to a spike in the death rate etc.
-The death rate depends on demographics, the capacity and quality of the health system and on the fact if this system is still working normally or already overwhelmed.
-Climatic conditions might play a role.
etc.
So the surprising fact is not, that the growth rate differs, the surprising fact is how similar it is. It seems to be somewhere between 25 and 30%, maybe even a bit more. For the simplified model developed in this text I used 27%, which is an estimated guess, but of course a bit arbitrary — and a simplification.
Is it a big different between a growth rate of 25 and 30%? In exponential curves it adds up to a huge difference:
Let us say on day 0 there are 1.000 infected people, and the growth is unmitigated:
time past: 1 week 2 weeks 1 month 2 months
growth 25% 4.768 22.737 807.793 652.530.446
growth 30% 6.274 39.373 2.619.995 6.864.377.172
The last number is of course almost the population of earth, so in reality not possible — herd immunity would occur and the growth would slow naturally, but the point is: The difference between 25 and 30% daily growth, a difference of just 5%, amounts after one month to a threefold difference, after two month to a tenfold difference in the number of infections.
This is why all measures to bring down the growth rate are important, this is why seemingly trivial actions like washing your hands and keeping your distance may save lives one month later: If the growth rate is reduced only minimally, the effects after one month might be very significant! So every measure, be it individual or collective, potentially helps in bringing the growth down and thus diminishing the terrible impact this virus outbreak has on our communities.
If you bring the number of newly infected down now, this will diminish the number of people dying 20 days from now.
06. Latency of counter measures
By now it should be sufficiently clear: All measures to diminish the spread of the virus will show effects only with a certain delay or latency or time offset. You can monitor their effect approximately ten days later: Will the measures taken today slow down the spread significantly? Well, you will know ten days from now. Optimally the growth rate will reach 0%, that means no new cases are reported, as in China in the last two days (their new cases were only imported cases, which they quarantined; the domestic spread seems to be contained, at least at the moment and according to the official numbers).
Let us look at a very simple example: The growth is unmitigated 27% until a certain date, then an extrem lockdown occurs and growth comes to a sudden halt, it jumps immediately to 0%. In reality this would of course never happen, firstly before the lockdown usually other measures are taken (improved hygiene, social distancing, canceling of mass gatherings etc.), and secondly there will be many already sick but asymptomatic people and many people in the incubation period, who would even after a lockdown infect (not knowingly) their family members or other people they live or closely interact with. So in reality the curve would flatten before the lockdown and then don´t jump to zero growth immediately with the lockdown, but flatten out slowly for quite some time. In fact these effects may cancel out each other, so that the overall effect after all may be not so different from the very simple model, of course depending on the respective situation.
(Worst case: Maybe the actual partial lockdown of western societies will — in contrast to the very rigid lockdown in China — crash our economies without stopping the virus spread, since most infections don´t seem to occur in busy public places, but by people interacting closely within the family or at the workplace…)
The underlying logic of course also works if the growth was already slowed down before the lockdown, only with a different growth rate, e.g. 15% instead of 27% — which would make a huge difference.
The curves represent the (unknown) number of in reality infected people. This number might be reconstructed and thus known in hindsight, at any given moment the test results only show a fraction of the situation from ten days ago. And vice versa ten days from now your testing might reveal the situation now — if you test thoroughly. You can see this clearly in the figure from this article https://jamanetwork.com/journals/jama/fullarticle/2762130 considering the cases in Wuhan — they reconstructed later the real spread (if they got it right): The grey bars represent the real development, the orange bars the delayed picture given by the test results.
That also means, that the measures taken now show an effect with a delay. For the very simplified model from above in which the spread grows unchanged until a sudden and complete lockdown takes place and everybody is isolated, and from then on the growth is reduced to zero suddenly, that means:
-Day zero: Lockdown; no new infections occur, growth jumps to 0%, the growth curve is suddenly horizontal.
-Approx. day 5: The number of sick people (and thus of contagious people!!) stops growing. Until then this number grows, because people before in the incubation period will get sick now — or they will be asymptomatic but still contagious.
-Approx. day 10: The test results from now on show the flattening of the curve, so you can finally monitor the effect of the measures taken.
-Approx. day 15: The need for ICU beds will reach its peak.
-Approx. day 20: The death toll will stop growing.
When the growth before the lockdown was unmitigated at 27%, that means:
-Suppose you have 10.000 confirmed cases when the sudden lockdown takes place. There will be a hidden number, but even without taking that into account, the number of sick and potentially positively tested people will grow for ten more days, which is more then tenfold, so you will have more than 100.000 cases ten days after the lockdown takes place.
-Suppose you instigate the lockdown when you have no ICU beds left — the need for them will grow 15 more days after the lockdown, maybe a bit less, but probably at least 20fold. So if you wait with the lockdown or other radical measures to stop the spread until your health system is overwhelmed, it will be overwhelmed at least 20 times more. Instead you have to lock down everything and stop the spread when 5% of free ICU beds are used by Covid-19 patients!
-Worst case: Your administration instigates the lockdown because a given number of deaths occurred, for example 100. Maybe your government did not do anything until then, the spread of the virus is unmitigated, but then they have 100 victims, and this is for them a critical number, they are alarmed now, and they shut everything down. The death toll will keep growing for 20 days, which is at least a 100fold increase. So if the lockdown happens when 100 people have died and the growth until then was not mitigated, then at least 10.000 people will die in the next weeks.
In some countries this sad situation occurred and still will occur. Not so in China: Here the officials seemed to have listened to the number guy, who told them, according to a news story I read: „Sure, there are only 400 cases now, but if you do nothing you will have 100 million infected five weeks from now.“ That seems a bit excessive. 400 cases now and 100.000.000 five weeks from now? Well, their testing effort at the beginning was necessarily not perfect, it could not have been, since the disease was new and people and institutions had to adapt very fast. Let´s assume, they estimated a ratio of 1:5 found cases to real cases; that means that in reality there should be 2.000 cases, not 400. But because of the testing delay or latency discussed before, this shows the situation 10 days earlier. Five weeks are 35 days. So let´s put all this together:
2.000 x 1,27^(10+35) = 93.798.833
There you have the 100 million. It´s actually not rocket science. And with the knowledge of a death rate of 1 to 4% (which they did not have at that time), the science guys could have told the politicians: If you don´t act now, five weeks from now there will be 100 million infected, and that means, that one month later there will be one to four million casualties — if the spread is stopped five weeks from now, otherwise more. The Chinese politicians listened anyway and took drastic measures. Now they seem to have contained the spread and can carefully lift the lockdown and reopen their economy. In Italy for example the officials waited to long, for whatever reasons. Why did they not listen to the science guys? Or did nobody tell them? Or were they afraid of the consequences of drastic measures? Maybe in the future, when the dust is settled, these issues will be examined and discussed, for now it is important for other countries to learn the lesson here and act now and act consequently. The crisis is far from over in Italy, because the number of severely sick and dying people keep rising days after the shutdown — and will keep doing so for some days. Other countries seem to fall into the same trap, despite of the gloomy warning. In the next chapter I will make some predictions based on the model developed so far.
07. Dark predictions
To write this chapter is emotional very demanding. I hope I can help people understand the mechanics of the virus spread better and take measures to improve the outcome. That is my motivation to write this gloomy chapter.
As long as the growth of the spread is unmitigated, it is very easy to make predictions, because the underlying mechanics develop with the precision of a clockwork. In the last days and weeks most societies have taken some measures, so the fast exponential growth is hopefully slowed, the respective growths curve flattened. It is hard to predict the effects, because they will show in the test results ten days later and because the situation is unprecedented. Measures like this never have been taken in our modern societies. We can look back a few days, when the virus spread in many regions rather unchallenged and calculate the development from there into the future. The growth rate differs in different regions, maybe some changes in the behavior of the population already showed some effect etc., so there is of course a certain amount of uncertainty. I hope all these uncertainties play out in a good way and these predictions do not come true. But it may actually be even worse, since we do not know the future. Maybe the unfolding catastrophe is not a strong enough warning and much worse things will happen in some regions then predicted here, because insufficient measures will be taken — there is sadly always room for a development to the worse.
Some more uncertainty in the calculations: We still have only limited data, so it is just an educated guess that people die in average 20 days after infection — we will know this a few months from now. If infected persons die in reality in average 3 days earlier, then the death toll will rise only to half the amount after the growth is stopped, if they die in average 23 days after infection, then the death toll will keep rising three days more and therefore double.
(Also there might be people dying without somebody identifying them as Covid-19 victims — in the beginning of an outbreak because the spread is so small that people are not aware, in the end because so many people die, that the situation gets rather chaotic.)
Spain:
Spain locked down their society six days ago at the 14th of march. At that time 136 people had died. The next day this number jumped to 288, the day before it was 120, so there seems to be a statistical distortion, because the numbers are still small. From this day on the death toll should rise unchanged for 20 days according to our model, and the lockdown will not affect it. So we can calculate 16 days from the 18th of march and will have a better accuracy since the numbers are already higher. At this date there were 598 victims.
598 x 1,27¹⁶ = 27.388
So let us hope the soft measures instigated before the lockdown have significantly slowed the growth of the spread, otherwise in the next weeks in Spain 27.000 people will die — potentially more, because their healthcare system will be overwhelmed. In that case the death toll might grow to up to 100.000 people.
Italy: Since 10th of March Italy is under lockdown, and before the officials tried to persuade the population to practice social distancing, stricter hygiene etc., so the growth curve is not longer the unchecked curve of approximately 27% daily growth. Nobody knows at this time, how big the effect of the „soft“ measures before the lockdown and how big and sudden the effect of the lockdown will be, the next days and weeks will show. But measures like these have never been taken in a modern western society, we are in uncharted territory. Let´s assume the growth was unchanged until ten days ago and then came to a sudden halt. Of course this is very simplistic, in reality the curve might have flattened before and will continue to grow and flat out after the lockdown, because people will get infected at home in their family and at the workplace even after the lockdown. These effects may actually cancel each other out, nobody knows at this time. But assumed the growth continued since ten days ago. Until the 10th of March 632 people in Italy have died because of Covid-19. Because of the time delays, the death toll will rise for at least 20 days from that date on:
632 x 1,27²⁰ = 75.299
Again, if the average interval infection to death differs only three days, these number will be cut in half. But if the health system is overwhelmed, which it already is, the number will go up fourfold. If the growth curve was flattened significantly, the death toll might not rise that high. So nobody can tell the future for Italy right now, the situation is too complex: If everything worked out great before the lockdown, the death toll might peak at 10.000, but it is also not unrealistic that more then 100.000 people will die in Italy in the next weeks — if the spread is not stopped, maybe even more. And to me all of these numbers are terrible, and the message stays the same: The worst for Italy is unfortunately still to come, and the same situation will occur in every country in the world unless stringent measures are taken — it will happen and it will happen fast and it will be terrible!
UK:
Schools will finally be closed from today on and other measures are taken. The government seems to have changed its course, as will be discussed in the next chapter about herd immunity. For this calculation let us assume the growth was unchanged until today and then suddenly stops — even if this seems rather unrealistic, which will make the reality more terrible than this prediction. Until today in total 144 people have died because of Covid-19. This death toll will rise for at least 20 days from now on:
144 x 1,27²⁰ = 17.156
So it is an optimistic estimate that in the next few weeks 17.156 people will die in the UK because of Covid-19. Because the number is still rather small, there will be some deviation.
USA:
Here we have a similar situation than in the UK: Already many people died, 172 as of today, and the government seems to be slow, unprepared or reluctant to take measures, at least its response until now is weak. Let us optimistically assume that from today on the growth of the spread is stopped totally, then still many people will die:
172 x 1,27²⁰ = 20.492
This estimate is very optimistic for many reasons: Probably the spread is not stopped now and maybe the healthcare system will soon be overwhelmed. These factors could easily push the death toll over 100.000 in the next weeks. So rather optimistically estimated more then 20.000 Americans will die in the next weeks, in fact this is some kind of best case scenario.
But what effect will it have, if you flattened the growth curve before a lockdown? The death toll will continue rising for at least 20 days, but with a different growth rate. And this difference will be very substantial. I will discuss now three examples. Let´s assume 1.000 people have already die when a total lockdown is coming into effect and the growth comes to a sudden halt. Before it was 10, 20 or 30% respectively.
1.000 death until lockdown
30% growth: 1.000 x 1,3²⁰ = 190.049
20% growth: 1.000 x 1,2²⁰ = 38.337
10% growth: 1.000 x 1,1²⁰ = 6.727
So the different is huge: When the curve has been already flattened for the 20 days before the lockdown to 10% or when it is at an unmitigated 30% the difference is more then 180.000 people dead or alive. So please be aware and take the necessary measures, even if your government is still in denial. Every measure taken now to slow of the virus spread, may it seem insignificant, silly or trivial, will potentially save lives a few weeks from now!
08. Herd immunity
One method to win the battle against this virus is to contain it radically, stop the spread, trace all infected, isolate them, instigate lockdowns etc. But this solution is always temporary, unless the whole world succeeds in containing this virus, and in this case it would be exterminated like the small pox. Until then it seems a long way to go. Another method would be to achieve herd immunity. As I already mentioned in the 4th chapter, there seems to be a broad consensus amongst scientist, that for a virus as contagious as this one, 60 to 70% of the population had to be immune in order to stop the spread without containment and social distancing. So how to achieve that?
The best method to achieve herd immunity is obviously a vaccine. Nobody knows at this time when a vaccine will be available. Also we will need a lot of that vaccine in order to achieve herd immunity for humanity, about five billion units — less if many people have been infected and thus achieved (probably and hopefully) immunity. If all efforts are bundled and restrictions softened, if we treat this as a moonshot, then we might have it in 6 months, some experts say. But it might as well take two years, nobody knows.
There is another strategy, and until a few days ago the UK and the Netherlands seemed to be willing to follow this path: Don´t try to navigate around the storm, just steer directly into it in order to quickly come out on the other side. As discussed in chapter 04 a substantial part of the population might die (probably 0,6% to 2,6% of the total population), if not certain measures are taken: If you put all the old and vulnerable persons into isolation for some month, and if the healthy rest of the population just carries on (like a giant Corona party), then from the 60–70% of the population having to be infected to achieve herd immunity only 0,1% might die, as the death rate for healthy younger persons seems to be quite low, namely 0,1%. For the UK with its population of 66 million that would mean, that about 45.000 citizens would die — healthy younger persons out of the working population, parents and so forth, not 80 year old persons with three severe health conditions.
The UK has changed their course, and at this moment this change seems to be reasonable, since we do not know much about this new virus and Covid-19. Is the death rate really that low amongst younger persons? What if the data from south Korea was somehow statistically distorted?
There is the possibility that the death rate is even lower for healthy young people, since many of the younger casualties seemed to have had severe health problems and chronic diseases. Also healthy and not old people seem to be much less often in need of intensive care, most cases take a mild course. The next weeks will probably bring more clarity here.
Worldwide tests are done with different known drugs in the hope to find something which also works against Covid-19. At this moment there is no therapy, doctors can just provide artificial respiration and stabilize patients or fight secondary infections, but there is no real therapy for this disease. If this changes and there is a drug or therapy which works well against Covid-19, the strategy discussed here might actually be viable: Once we know the virus better and can reduce the death rate amongst healthy young people further, for example to 0,01% or even less, and the disease rarely takes a severe course with these people, then there would be in the UK for example maybe a few thousand or even only a few hundred deaths, the health system would not be overwhelmed and you could reopen the society and economy and end the quarantine of the vulnerable people.
09. Flatten the curve
As shown many times until now it is extremely sensible to flatten the curve, and every little step — individually or collectively — may save lives a few weeks later. But many people (also journalists and politicians) still seem to believe, that we could flatten the curve to not overwhelm our health care systems and thus slowly and bit by bit pass everybody through Covid-19 without overwhelming the system. By now it should be clear, that 0,6 to 2,6% of the population would die in this maneuver (1 to 4% of the 60 to 70% proportion of the whole population you need to be immune in order to achieve herd immunity). So even if your society is ready to accept this price, I will show now, that the time frame is completely unrealistic.
Let us look at Germany for example, a country with 83 million inhabitants and a very good health care system with 28.000 ICU beds. Usually in average 5.000 ICU beds are free. Even if in this extreme situation we could ramp up the capacities and dedicate 15.000 ICU beds for Covid-19 patients, that would mean, that the 5% of infected people who need in average an ICU bed could maximally amount to 15.000 people. So not more then 300.000 people at the same time should be infected in order to avoid an overload:
300.000 x 5% = 15.000
If one sick person needs an ICU bed in average for one week, that means in one month we could allow 1,2 million people to become infected, 14,4 million per year. We need 55 million people to be immune to achieve herd immunity, so that would take 3,8 years. And in order to achieve this, we would need extremely precise social engineering tools, since we would have to keep the number of infected constantly around 300.000 for 3,8 years without realtime monitoring (because of the inevitable testing-latency discussed above).
The US has actually even a higher number of ICU beds per capita (https://www.forbes.com/sites/niallmccarthy/2020/03/12/the-countries-with-the-most-critical-care-beds-per-capita-infographic/#32fe25087f86), here this approach might be doable in only three years and two month. In the UK it would take more then 16 years…
But it has to be said, that the need for an ICU bed also goes down dramatically for younger and healthy people. So if the strategy discussed in the last chapter is applied and only this part of the population is infected, the time frame might actually be feasible: If the need for ICU beds gets down the same amount as the death rate, with the factor ten, it could be done in four or five months in Germany or the US — in the UK it will still take more than two years. Maybe the need of ICU beds for healthy young people is even smaller, studies will show this, at the moment it is unknown.
10. Calculating the real number of infected people
In the chapters before I explained the mathematics and mechanics of the Corona virus as it is suggested by the data. If you did not understand the model yet please read the corresponding chapters again.
The model is of course an extreme simplification, but according to the data it seems to be quite useful. Let me give you just two examples:
1) Two weeks ago the death toll in Italy was 107. According to the model it should be today:
107 x 1,27 ^14 = 3.038
The official death toll today is 2.978, the deviation is around 2%. So with this model you could have told the Italian officials two weeks ago: „Two weeks from now 3.000 people will be dead, this is inevitable, but if you do not stop the spread immediately, the toll will rise exponentially for 20 more days after the lockdown. So for every three days you wait, the death toll will at least double.“ Maybe they might have listened, maybe not. Now probably more then 30.000 people will die in Italy in the next weeks — maybe more.
2) We have now 13.957 official cases in Germany. Our testing is not too bad, so you can actually calculate with these numbers not too unreliably. One week ago there have been 2.576 cases.
2.576 x 1,27⁷ = 13.726
The deviation is also under 2%.
In other situations the deviation might be much bigger. The model presented here is not a magic tool to exactly predict the future, since in every region and in every situation the growth rate might differ, as will other factors, like demographics, behavioral patterns, climatic conditions etc. I tried to develop this model to show the basic mechanics behind this virus spread, and these basic mechanics are the same worldwide. My intention was not to magically predict the future, I wanted to enable people to understand this invisible enemy a bit better.
With this model you can actually estimate the real number of infected people in your country or region. It is scary. The basic thought is simple: There is a time latency and a hidden number in the testing, so nobody knows how many people are really infected. There might be a hidden number in the death toll too, but it is probably much smaller. Especially in developed countries in the actual situation most people dying of Covid-19 will probably be registered. In some countries (like Iran) the officials might keep the number of deaths secret in order to conceal their poor response to the situation, in countries with poor or overwhelmed health care system dead people might not be registered as Covid-19 victims, because they lack the capacities, but in general I think it is safe to assume, that the hidden number in the death toll will be smaller than the hidden number in the official case count. And since the death rate is roughly known, you can estimate the number of infected via the death toll.
It is intuitively understandable: If you have many deaths in your region but not many official cases, then the testing is bad — like in the US or the UK. If you have not many deaths but many official cases the testing is better — like in Germany. And note: This method is only reliable before the growth rate was changed significantly. After a change this method could also be applied, but only if the growth rate was known and regular. So sometimes it is easier to go back a few days to a state in which many countries did not have strong measures in place to fight the spread, because at that time the growth was still unmitigated and the virus thus still spreading very regular. almost like a clockwork.
If the death rate is around 1% and the growth of the virus is not yet slowed, then the calculation is quite simple:
Let´s say growth is still unmitigated at 27% in your region. There are D Persons dead (and D should not be very small, otherwise the statistical distortion is too large).
20 days earlier there must have been 100 x D infected of which then 1% would eventually die.
Since that time this (100 x D) infected group would have grown 1,27²⁰ times.
1,27²⁰ = 119,145
119,145 x 100 = 11.915
That means now there will be more than 10.000 times D infected people.
That means: If you have already 100 dead people in your region and the spread is still unmitigated, you will have more then one million infected people now.
Let´s look for example at the situation in Germany five days ago, when the growth of the virus spread was still basically unchanged: On march 14th the total death toll was 12, so there should be around 120.000 infected. The official number that day was 3.421, but because of the test delay (see chapter 02), this number reflects the situation from ten days earlier, so we have to include this delay into the calculation:
3.421 x 1,27¹⁰ = 37.341
That means, the German official case number suggests, we have now 37.341 infected, the number of deaths suggests 120.000, so the rate is 31% and the ratio about 1:3. The testing thus revealed one third of the really infected population, which seems to be pretty good for a fast spreading virus with asymptomatic carriers. (Note: Because there were only 12 deaths this calculation is very unreliable, it works better with higher numbers.)
In Italy the situation is complicated now, because drastic measures have been taken about ten days ago. So the growth of the spread is hopefully diminished, the curve flattened, ideally the spread is contained. Because the measures were instigated ten days ago, the next days now are critical: Because of the ten day delay in testing, now the numbers should start to show the effects of the measures. But to plot a curve (respectively: to see a trend), you need a few numbers, you need more then one dot to plot a curve. So over the weekend the numbers might show how much the curve is flattened. Today (Friday 20th of March) the death count in Italy is unfortunately 4.032. The death rate might already be higher than 1%, because doctors had to decide who gets a ventilator and who does not, the system is overwhelmed, despite the incredible effort of the Italian medical professionals. If 4.032 people are dead today, and the average interval between infection and death is 20 days, and the death rate is between 1 and 4%, that means that 20 days earlier, 29th of February, there were 100.000 to 400.000 people infected in Italy. Since the lockdown is in effect only since ten days, the exponential growth will have continued for at least the first ten days. The question is: Did the soft measures before the lockdown slow down the growth, that means bring down the growth rate, and if so, how much? From 27% to 25% or to 20% or even lower? And did the lockdown bring the growth rate really to 0% or did many infections still occur after the lockdown in the families and at the workplace? We simply do not now at this time, the numbers coming in from this weekend on will tell us — and unfortunately the further development of the death toll will tell us ten days later. If the soft measures taken until the lockdown was instigated ten days ago did not have a great effect, then the number of infected will have developed tenfold in this ten days: 1,27¹⁰ = 10,9. That would mean, there have been one to four million infected people in Italy on 10th of march, and at this time nobody knows how the further development of the spread in the last ten days unfolded. And if 1 to 4% of these people will die, the range is between 10.000 and 160.000 casualties in the next month or so. If the soft measures from before 10th of March showed a big effect, then the growth rate before the lockdown was diminished, the curve flattened, and less people will be infected now — so you hopefully see now, that washing your hands and keeping your distance saves lives, and possibly many lives. Italy is in a terrible situation right now, but it is far from over. And the same thing will happen to other countries, if not stringent measures are taken.
In the UK there are currently 177 deaths, in the US 154. Both countries have instigated some counter measures since a few days and hopefully diminished the exponential growth in these days significantly, even if this seems rather optimistic. And before that, the growth was almost completely unchecked and the death toll already around hundred in these countries. So both countries will at this moment have more then one million infected people each, even if their official numbers show only a fraction of that, for the UK under 1%…
Again: If the situation is like in the US or the UK now (or many other countries for that matter) — the death count is growing but officially only a few cases are reported — then you know, the virus is already widespread, in fact even you yourself might be an asymptomatic carrier right now — or you might be in incubation and get sick tomorrow. Anyway, if this situation is given, you should by all means try to get your elderly and vulnerable loved ones to isolate themselves and be very careful. The days before a lockdown are the most dangerous: The awareness of the population is still low, social distancing is not practiced consequently, there are many people around who spread the virus unknowingly — and three weeks later your health care system might be overwhelmed. So if you are not careful, your parents or grandparents might three weeks from now die lonely in a makeshift quarantine tent ,because there is no ventilator or ICU bed left. Don´t fall into the same trap as poor Italy please!
11. Strategies
My work is almost done here. Since three weeks I started to read more and more about the virus spread, and slowly I understood the deadly underlying mechanics. Most people around me were just reacting to the news, adjusting day by day, unable to really process what is happening. At a certain point I felt ahead of the news: Journalist and friends would wonder, what will happen the next days, will the spread grow further, when will it stop, etc. I felt almost like a fortune teller, because I could predict many things, like how many deaths will occur in Italy one week from now, how many official cases in Germany three days from now, that schools will have to close soon etc. I felt like Kepler, who could predict the movement of the planets, because he understood the simple mathematics governing their movements. When most people still thought this virus is basically a strong flu, I could predict the necessary lockdown of our European societies, and almost nobody would believe me, they thought it is all exaggeration, it will soon be over etc. And most people still underestimate the virus and are quite surprised by the harsh measures finally taken by many governments.
So in this article I try to explain the basic mechanics of this virus spread, as far as I could analyze it from the basic data available online. Now the question is, what do we do? How do we fight this? And this of course people and communities have to decide for themselves, hopefully a bit more informed day by day.
The method of achieving herd immunity by more or less controlled infection of large parts of the population seems to be not viable at the moment, which might change, as discussed above (chapter 08). If there is a well working drug or a vaccine soon, then the situation is completely changed anyway. This of course would be great, but we can not count on this, so we will probably have to follow other strategies.
At this time there seem to be two successful models in the fight against the Corona virus, and I highly recommend to research online about them, I will just outline this:
1) The Chinese model, which is based on a radical lockdown plus tracking of infected and quarantining them consequently.
2) The model of South Korea and Taiwan and others, which is focussing on very consequential testing, tracking, digital technology, a disciplined population etc.
And then there is the European and US-model: Stumble relatively unprepared and blind into the catastrophe, then shut everything down in panic and now try to cope somehow with the situation day by day…
It is sometimes said, China could win this fight only because of their centralized and authoritarian system, but South Korea, Taiwan and a few others show, that democracies can also succeed. But we will have to reduce the spread by minimizing contacts, be it voluntary and individually or be it enforced by official institutions, and we will have to quarantine infected, which means to take away certain liberties, and we will have to track contacts very strict, which may lead to stronger surveillance efforts. China seems to have ramped up their surveillance in this crisis a lot, and probably they will not make this undone after the crisis. The Asian societies, which seem to be ahead in the fight against the spread, also had a more prepared population: Since SARS they knew what it means to fight a pandemic and were much more careful, disciplined and sensible, and also the institutions were better prepared.
So can a western democratic society win this without loosing its soul?
I think we can, but we will have to balance the following factors, we have to balance five undesirable factors, and nobody can tell us what the best balance is:
1) personally changing the own behavior responsibly to minimize infections, selfdiszipline
2) social distancing, lockdowns etc. instigated by the governments
3) endangering the personal health and life of our fellow humans
4) endangering the economic and social life of society
5) tracking of our movements and contacts, loosening data security and data privacy
If we keep our societies in lockdown for too long, many people and businesses might go bankrupt. If we don´t act responsibly our governments might have to force certain restrictions on us. If we loosen the social distancing maybe we endanger some elderly people. How much of our personal data will we allow the administration to use in order to track efficiently all contacts, and how will we make sure that the surveillance is ended after the pandemic? I could go on very long like that, we have to find a viable balance, and there is no simple solution here. I hope that we succeed and don´t end up with a terrible outcome.
12. Epilogue
This virus seems to be so dangerous because of the combination of three factors:
1) the personal death rate is not too high, so people tend to underestimate it — if the death rate was like Ebola we probably would have acted much earlier and more consequently
2) the rapid exponential growth and the high contagiousness of the virus
3) the timeframe and latencies
So in the beginning people tend to underestimate the virus: „It is like the flu, don´t panic.“ Then the tests only show the number of the infected they found ten days ago, so the numbers are quite small. Then people start to die and suddenly the numbers jump up so fast, that even the small death rate of 1% leads to dramatic consequences. Societies go into lockdown, but the people continue dying for 20 days after the lockdown. So first everybody is underestimating the virus, then suddenly the catastrophe is there. And everything happens incredibly fast.
I hope I could explain the underlying mathematical mechanics of this outbreak, so that people retrospectively will understand what happened, and that they know better how to deal with the situation right now and in the future.
But the most important reason, the reason why I wrote this text with a great feeling of urgency and very fast (within two days), is this: There are many countries and regions in the world which have the worst impact still ahead of them. Hopefully by understanding the virus better they might be able to prepare and take the right measures before it is to late. I am not interested in the mathematics, I want to warn and potentially save my fellow human beings.
So please be warned: This thing is coming to you, and it is coming fast, and it will hit hard, and before you realize it, the situation will be terrible. So be careful everybody, do not take this lightly.
We will somehow come out on the other side. Hopefully we will not loose our humanity.
Take care and all the best
Daniel