Optimal control for stochastic model of epidemic infections

This paper discusses the development of a discrete stochastic model for SIR epidemic infection and calculation of the optimal control policy for the proposed model. Specifically, a Markov Decision Process based modeling approach is proposed as opposed to the traditional state space modeling. Proposed model consists of set of discrete states, actions, and transition probabilities. Selection of an optimality criterion is discussed for calculation of the optimal control policy. The behavior of the optimal policy and the tradeoffs involved in the selection of the optimality criterion are discussed through case study and graphical representations respectively. Furthermore, the concept of scaling the population size is introduced in order to tackle large scale problems.