Simple two dimensional models for the spread of a disease

A simple two dimensional stochastic model is proposed to model the spread of a disease amongst a fixed population. Two versions of this model are obtained which make assumptions corresponding to the assumptions made in the Greenwood and Reed-Frost Chain Binomial epidemic models. The epidemic is controlled by immunization so as to minimize the expected number of people infected. Some results, conjectures and counterexamples concerning the optimal policy are presented.