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

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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 → ∞ 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.