Final attack ratio in SIR epidemic models for multigroup populations

Abstract

We analyse an SIR epidemic model in a closed population subdivided in n groups. Population mixing occurs at two levels: within each group, and uniformly in the population. We prove that, if within-group transmission rates are large enough and not all identical to each other, then the final attack ratio is lower than what would occur in a population mixing homogeneously with the average transmission rate. We also show that the opposite may hold for certain parameter values and explore numerically the parameter regions in which the final attack ratio is higher or lower than in the corresponding homogeneous model. Finally, we analyse simulations of the corresponding stochastic model with finite group size, studying how well final attack ratio is approximated by the deterministic outcome and its relations with exponential growth rate.