Basic reproduction number

The basic reproduction number ($R_0$) captures the idea of “on average, how many secondary infections does a single infection cause?” A number larger than 1 means that the infections are increasing and a number below 1 means that it is slowing down.

In classical mathematical epidemiological theories with homogeneous mixing, $R_0$ (or $R_t$) has a clear meaning and can be used to characterize how infectious a disease is. However, if we consider the contact network structure where the disease can spread, it is not necessarily a useful number to capture the nature of contagion nor how it is currently spreading. R0 is not a biological constant because the number of infections should depend on the characteristics of the contact network.

Another issue is that the number of secondary infections tends to have a heavy tail. In other words, many infections do not lead to secondary infections whereas a small number of infections leads to a large number of secondary infections. See Lloyd Smith2005superspreading.

See also: - hebert2020beyond: Beyond R0: heterogeneity in secondary infections and probabilistic epidemic forecasting - Liu2020measurability: Measurability of the epidemic reproduction number in data-driven contact networks