Control of an epidemic spreading in a heterogeneously mixing population

A theoretical epidemic model for a heterogeneously mixing community is examined in the context of control by immunization of susceptibles and removal of infected people. Under certain assumptions an optimal control scheme is developed using the ideas of dynamic programming, and is found to have a particularly simple form for either method of control. Counterexamples are discussed to illustrate why the simplifying assumptions made cannot be relaxed. Applications of these results are considered with respect to the accuracy of the assumptions of the model.