SIS epidemics with household structure: the self-consistent field method

Abstract

We consider a stochastic SIS infection model for a population partitioned into $m$ households assuming random mixing. We solve the model in the limit $m \to \infty$ by using the self-consistent field method of statistical physics. We derive a number of explicit results, and give numerical illustrations. We then do numerical simulations of the model for finite $m$ and without random mixing. We find in many of these cases that the self-consistent field method is a very good approximation.