Disease invasion risk in a growing population

Journal of Mathematical Biology
Sanling YuanJunling Ma

Abstract

The spread of an infectious disease may depend on the population size. For simplicity, classic epidemic models assume homogeneous mixing, usually standard incidence or mass action. For standard incidence, the contact rate between any pair of individuals is inversely proportional to the population size, and so the basic reproduction number (and thus the initial exponential growth rate of the disease) is independent of the population size. For mass action, this contact rate remains constant, predicting that the basic reproduction number increases linearly with the population size, meaning that disease invasion is easiest when the population is largest. In this paper, we show that neither of these may be true on a slowly evolving contact network: the basic reproduction number of a short epidemic can reach its maximum while the population is still growing. The basic reproduction number is proportional to the spectral radius of a contact matrix, which is shown numerically to be well approximated by the average excess degree of the contact network. We base our analysis on modeling the dynamics of the average excess degree of a random contact network with constant population input, proportional deaths, and preferential attachment for ...Continue Reading

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