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Coronavirus Chronicles 2: The Curse of the Exponential
What will happen if we do nothing
Trigger Warning: What I show here can be extremely anxiety-inducing. My intention is not to stoke fear, pessimism or despair, but to offer a rational way of thinking about this epidemic.
Exponential processes can be deceiving. They start gradually so it looks like things are going to develop slowly, but all of a sudden things seem to explode and everything gets out of control. Our mind tends to assume that things change linearly and are quite unprepared to confront exponential processes. Unfortunately, epidemics are exponential phenomena until herd immunity or vaccination puts a brake on their development.
This is an exercise in mathematical modeling to answer a few basic questions about the coronavirus epidemic in the USA:
1. How long will it take until things get bad?
2. How many people are likely to get infected?
3. How many people are likely to die?
An important caveat: this model assumes that we do nothing to control the epidemic or that whatever we do has little effect on its spread. However, China and South Korea have been quite successful in curtailing the epidemic, so we know that this is possible.
Exponential progression in the number of cases
What I did is to take the number of reported coronavirus cases and deaths published in El País and used them for computer modeling using the scientific software program Prism 3 (GraphPad Software).
Figure 1 fits an exponential function [Y=Y0*exp(k*X)] to the number of cases of coronavirus in the USA reported until now. The goodness of fit is excellent, as shown by a high correlation coefficient (R2) of 0.9926. A perfect fit would have a value of 1. This means that the progression of the number of cases is really an exponential process. The parameters of the function, Y0 and k, do not have a straightforward interpretation, but the doubling time can be calculated as ln(2)/k. I got a value of 2.17 days, which is the time that it takes for the number of cases to double. So, not only we get an exponential progression, but the doubling time is alarmingly high.
