Some results on optimal control applied to epidemics

Abstract This paper deals with a mathematical model for controlling an epidemic by the removal and isolation of infected people. The objective is taken to be to maximize the expected number of people removed at some terminal time. Some simple results are found for a deterministic model with a homogeneously mixing population by using the maximum principle. It is found that the optimal policy with the above objective function is to wait until a switching time and then attempt to remove as many infected people as possible. Next a stochastic model is discussed, and under certain assumptions similarresults are obtained. For the stochastic homogeneous mixing case the relationship between the switching times, the starting state of the epidemic, and the terminal time is explored.

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