Understanding the effects of R0

In epidemiology, the R0 parameter represents the expected number of secondary cases produced by a single infected individual.  It varies through time, space, and among sick individuals.

This post’s objective is simply to show the large difference between R0 < 1 and R0 > 1, even when the actual values are numerically close.

With R0 < 1 (upper panel in the graph), following an incubation period (in the case of Covid-19, 14 days) the number of new cases inexorably drops (the faster the closer R0 is to zero).

With R0 > 1 (lower panel in the graph), the number of new cases increases until it reaches a peak, where the number of overall infected people is huge (for Covid-19 estimates vary between 20% and 70% of the total population) before it starts dropping. The greater R0 is with respect to 1, the higher the peak and the sooner it will arrive.

It is important to note the difference in scale between the two graphs. With R0 < 1, the drop from 20000 cases is very fast. On the other hand, with R0 > 1 the number of cases reaches the millions range very fast.

NB. The scenarios depicted in the graphs are only partially likely for the current pandemic. Many important (and unknown) factors, such as the contact networks between all of us, are not considered. Therefore, although there have been diseases with higher R0 values, it is important to keep in mind that the displayed progression would not match reality even though the actual R0 were equal to one of the values shown in the graphs.

(Translation by: Gabriele Fabozzi)