Optimal intervention for epidemic models with general infection and removal rate functions

In this paper, known results on optimal intervention policies for the general stochastic epidemic model are extended to epidemic models with more general infection and removal rate functions. We consider first policies allowing for the isolation of any number of infectives from the susceptible population at any time, secondly policies allowing for the immunisation of the entire susceptible population at any time, and finally policies allowing for either of these interventions. In each case the costs of infection, isolation and immunisation are assumed to have a particular, rather simple, form. Sufficient conditions are given on the infection and removal rate functions of the model for the optimal policies to take the same simple form as in the case of the general stochastic epidemic model. More general costs are briefly discussed, and some numerical examples given. Finally, we discuss possible directions for further work.