Disease dynamics and mean field models for clustered networks

Abstract

Social networks are clustered networks with short mean path length. In this work we analyze the disease dynamics in a class of this type of small-world networks composed of set of households and a set of workplaces. Individuals from each household are randomly assigned to workplaces. In both environments we assumed complete mixing and therefore we obtain highly clustered networks with short mean path lengths. Basic reproduction numbers were computed numerically and we show that at endemic equilibrium the average susceptible proportion <S/N> is different from the inverse of the basic reproduction number (R0-1). Therefore exist an exponent p≠1 for which <S/N>p=R0-1. Using this exponent we developed a mean field model which closely capture the disease dynamics in the network. Finally we outline how this model could be use to model vector-borne diseases in social networks.