An explicit optimal intervention policy for a deterministic epidemic model

Optimal policies involving the removal of susceptible individuals from the population at risk are derived for a deterministic epidemic model with a non-standard infection rate function. Denoting by y the number of infective individuals and by x the number of susceptible individuals in the population, we replace the classical Kermack–McKendrick infection rate function βxy (for some constant β) with βxy/(x+y). This modified model has been studied by various previous authors, including derivation of an optimal policy when intervention consists of isolation of infective individuals from the susceptible population. For the less tractable situation when intervention consists of removal of susceptible individuals, we show that the optimal policy is to intervene with maximal effort when y⩾Ax with x, y>0, and not to intervene otherwise, for some constant A∈[0, ∞] whose value depends upon the parameters of the model. Copyright © 2007 John Wiley & Sons, Ltd.