Exact solution of infection dynamics with gamma distribution of generation intervals

Abstract

Infectious disease outbreaks are expected to grow exponentially in time but their initial dynamics is less known. Here I derive analytical expressions for the infectious disease dynamics with a gamma distribution of generation intervals. Excluding the exponential distribution, the outbreak grows as a power law at short times. At long times the dynamics is exponential with a growth rate determined by the basic reproductive number and the parameters of the generation interval distribution. These analytical expressions can be deployed to do better estimates of infectious disease parameters.