COVID-19 modeling estimates for India have been presented by a team of researchers affiliated with CDDEP, Johns Hopkins, and Princeton. The results described in https://cddep.org/wp-content/uploads/2020/03/covid19.indiasim.March23-2-4.pdf
Please explain all these curves predict a peaking behaviour. Exponential rise is understood, but why a decline, why peak. This factor has not been stated.
Could the authors or others throw some light?
You get a peak when not plotting the cumulative number of infected persons but the current number of infected persons. At the beginning, you have exponential growth as everybody is susceptible to infections, so every infected person infects on average a certain number of new persons > 1. This number is the basic reproduction number (often called R0). After some time, people will either die or heal. This is the number of "recovered" persons, and it increases with time, too, initially very slowly, but as the disease spreads, with increasing rate. Since the disease is over one way or another after about 4 weeks, everyone that was once infected will eventually "recover".
Because the total population is finite, this means the total number of actively infected persons must finally go to zero again. Actually, this will happen, before everybody has been infected, as the effective basic reproduction number decreases with increasing percentage of "recovered" people, who are immune against a new infection, at least for some time (and if they are dead, they are of course immune forever). So an infected person simply does not find enough persons to infect near the end of the pandemic.
On the other hand, if you plot the number of once-infected persons, not subtracting out those that "recover", then that quantity will approach a constant level at the end of the pandemic (1-1/R0 of the total population). It cannot decrease, because people are still counted in when they have already recovered.
that is perfect answer I so thought. I have modeled on the lines of this very argument. However R0 is controlled through lockdown. Therefore this buildup gets sustained much earlier.
I am uploading the short communication soon.
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