Today I saw the following screenshot of a spreadsheet that extrapolates the number of infections on a day by day basis in the UK from the 6th March to the end of April.
So, according to this, in the UK there will be almost 28 million people in the UK who have either recovered from the virus or who still have it by the end of April. The total UK population is around 65 million, so around half of us will have at some point have had the virus by this time.
However, this doesn't seem to me to be correct. According to a certain Dr. Stephen Gluckman -- an infectious diseases physician -- for other coronaviruses, immunity for most people is conferred after being infected once and having recovered (from here). So this current coronavirus, Covid-19, will likely be the same in this regard. And let's hope it is!
From what I've read, each infected person infects approximately, on average, 2.5 other people. But, this rate of infection won't be kept up indefinitely. Consider when half of the population has at some point been infected and recovered. If these people cannot be infected again, then an infected person will only infect half the number of people compared to the scenario where he is the only infected person. So, in other words, once half the population has been infected, an infected person will only infect half of 2.5 people, or in other words 1.25 people. Note that should this figure drop below 1 then the infection will die out since the virus will then be infecting fewer and fewer people as time goes by. When the figure drops below 1, even though a substantial proportion of people will have never been infected, the virus will nevertheless peter out. This phenomenon is labelled herd immunity.
In fact, I suspect that since a good proportion of the population will tend to avoid much contact with others over fears of the virus, that once around half of the population has had the virus and recovered, the rate of infection might well be around 1 rather than 1.25. So when around half of the UK population (or indeed world population) has had and recovered from the virus, this will represent the peak of the infection, and from then on it will gradually diminish. When will this occur? Well, not by the end of April since the person who compiled the spreadsheet assumed a constant exponential rate of 2.5. It'll be one or two months after that at a guess, perhaps around June or July?
I did some Googling after I wrote the condensed version of the above on facebook and came across this article. The article says that The UK’s chief scientific adviser, Sir Patrick Vallance, has given an estimate of 60% for herd immunity. More than my estimated 50%. How has he derived this figure? I guess by the following reasoning. If each person initially affects 2.5 others, then once 60% of the population have been infected and recovered from it, then we only have 40% of the original 2.5 figure remaining that have never been infected. 40% of 2.5 = 1. So, on average, once 60% of the population have been infected and recovered, each currently infected person will infect only 1 other person i.e we reach herd immunity with 60%.
It seems, though, that he's assuming the population will all behave the same, a supposition I would dispute. I still reckon herd immunity will kick in around 50% rather than 60%. Of course, these figures are parasitic on the initial 2.5 contagion rate being anything like correct.
27/03/2020 Update. I've heard the number that each infected person infects is now estimated to be slightly over 3, let's say 3.2. So this would mean 69% would have had to get the virus before herd immunity is reached. But I think it will be less than this, say 60%.
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