Basic Reproduction Number in a Growing Population

Abstract

The basic reproduction number of a fast disease epidemic on a slowly growing network may increase to a maximum then decrease to its equilibrium value while the population increases, which is not displayed by classical homogeneous mixing disease models. In this paper, we show that, by properly keeping track of the dynamics of the per capita contact rate in the population due to population dynamics, classical homogeneous mixing models show similar non-monotonic dynamics in the basic reproduction number. This suggests that modeling the dynamics of the contact rate in classical disease models with population dynamics may be important to study disease dynamics in growing populations.