ultimately, 60-70 percent of the population will have been infected - where does that number come from
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?
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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
www.bbc.com/news/science-environment-51892402
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.
www.globalhealthnow.org/2019-12/myth-about-herd-immunity
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.
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.
References
Milligan, Gregg N.; Barrett, Alan D. T. (2015). Vaccinology : an essential guide. Chichester, West Sussex: Wiley Blackwell. www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf
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