As the German chancellor said today, by the end of the year 60-70% of the population will have been through a COVID-19 infection. Where does that number come from?

The basic mechanism is clear, and the magnitude is plausible: Let n be the average number of persons infected by one infected person. If n falls below 1, then the epidemy will run out. This will happen if an infected person mostly hits persons who are already immune.

The question is: Why just 60-70%, not 40-50 or 80-90%? Does it come from historic precedence? Or from some formula that takes into account the value of n (the value before saturation has set in)? What citation classics could serve as reference?

  • To be more specific, are you talking about COVID-19? Corona infection could be as simple as the common cold, as that is caused by a corona virus. As are MERS, SARS, many others. – JohnP Mar 11 '20 at 14:49
  • yes, edited for clarity – Gruber Hans Mar 11 '20 at 15:09
  • Good question, I wondered about it, too. I have heard the additional detail that the maximum percentage of infected population is 1-1/n, and apparently, n=3 is currently best guess for covid-19 (when nobody is immune yet; this is apparently called the basic reproduction rate R0). But I found all explanations lacking in clarity. They usually work like this: "once about 2/3 of the population are immune, n<1, so the infection dies out". But this is incomplete since the many infected will still infect many still healthy people. In my thinking I always end up at 100% infected. – WerKater Mar 11 '20 at 20:25
  • @WerKater the underlying modeling assumption is that people in the Infectious group don't remain infectious forever. They either recover or die. – DeltaIV Mar 17 '20 at 14:15

Those are rough estimates coming from estimates of the basic reproduction number R01, which for COVID-19 are between 2 and 32. R0 is a measure of how transferable a disease is, and it measures on average how many people an infectious individual will pass the disease to. 1-1/R0 is the fraction of the total population which needs to develop immunity, either through a vaccine (which currently doesn't exist for COVID-19) or because they got infected and recovered, developing immunity.

This can be intuitively understood in the following way: if 1 infectious individual infects on average 3 other susceptible individuals (R0=3), then, if 1-1/3=2/3 of the total population develop immunity, then 2 out of the 3 persons which would normally be infected won't be. This means that on average one infectious individual infects another one, before recovering. Thus the size of the disease doesn't grow, but it ends up in a so-called "endemic state".

Coming back to COVID-19 and considering the two extreme values for R0:

> R_0 <- c(2,3)
> (1-1/R_0)*100
[1] 50.00000 66.66667

we can see where the estimate you were referring to, comes from.

R0 is not to be confused with R, the effective reproduction number, which is the quantity we try to reduce through non-pharmacological interventions during an epidemic.


  • I understand this logic but it underlines the problem I and some others have with the originally quoted statement. Because, ultimately, everybody will have had the virus (in this model). It is just that the number of currently infected will never exceed 2/3 of the population. – WerKater Mar 17 '20 at 14:50
  • 1
    @WerKater which others? Anyway, your reasoning is flawed: not everyone gets in touch with everyone else, thus not everyone gets infected. As a matter of fact, herd immunity protects individuals which cannot be vaccinated (even more so, cannot survive being infected) because it greatly reduces the likelihood they get in contact with infectious individuals. See vk.ovg.ox.ac.uk/vk/herd-immunity – DeltaIV Mar 17 '20 at 17:22

Some Canadian experts said 35% to 70% will be infected:

According to a disease-transmission model developed by University of Toronto researchers, the virus’ overall attack rate in Canada could exceed 70 per cent. That number drops sharply, by about half, “if we add modest control,” said epidemiologist Dr. David Fisman, one of the model’s creators, but it will take “aggressive social distancing and large scale quarantines” to reduce it further, he said.

“That’s still a huge number of people ill, and critically ill people are a large fraction in this disease,” Fisman said in an email. “I’m not going to share more specific numbers because I think they will scare people to no particular end.”

In reality no one knows. I can tell you if they contain the spread no more people will be infected. If they don't contain the spread more people will be infected. Steps like Italy took today where only essential work can occur and all business closed except transportation, grocery stores and pharmacies are a desperate attempt at containment that may be too late. That said given recent numbers it appears to have worked for China.

The German Chancellor is wasting her time and ours spewing off meaningless numbers that will only serve to scare citizens of the nation she is supposed to lead. Something better would be her plan to make the homeless self-isolate for 14 days at home if they come into contact with someone who was positive or preemptively positive.

Today the WHO leader said if American governments (Federal, State, County, City, etc) do not act it could be "many, many millions" dead in the USA. Today's US government talk to borrow 40 billion dollars to spend on the pandemic is not a plan.

  • This doesn't answer the question and it's loaded with political opinion. – Carey Gregory May 17 '20 at 3:59

This is a rough estimate based on how contagious this virus is to provide a guess on when herd immunity can be reached.

Rough estimates indicate that herd immunity to Covid-19 would be reached when approximately 60% of the population has had the disease


The percentage needed for herd immunity depends on the virus. So, for measles, it is required that about 95% of the community be immune before herd immunity is effective for your local population.


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