Optimal control of the simple stochastic epidemic with variable recovery rates

Abstract This paper derives the optimal control policy for the recovery of infectives in the simple stochastic epidemic. The control is effected by varying at any time the recovery rates of the infectives in a way which minimizes the expected social cost of the infectives and the expected cost of control until there are no more infectives. Dynamic programming can be used to determine easily the optimal control policy and to eliminate from consideration certain recovery rates. An analogy with maintenance theory is exploited in proving certain results.