We develop a stochastic compartment model for disease populations consisting of susceptible (S), infected (I), recovered (R) and deceased (D) individuals. This model contains four parameters determining the rates of these transitions: S 0I, I0R, I0D and S 0R (vaccination). While all vaccination and death transitions are observed completely, the infected and recovered transitions are observed through sampling possibly with a delay between the transition and when the information can be used in a decision.