Epidemic modeling based on stochastic models is expressed by the analysis of underlying multi-state Markov process. In this paper, a model based on birth-death process which is a special case of continuous-time Markov process, is presented. By this approach, we model the dynamic of infection in the community. Then we present a system of first order differential equations that expresses the transmission probabilities from one state to other state after time t. Using investigation of the eigenvalues of the coefficient matrix of the system, we prove each solution of dynamical system attracts to a sink point, exponentially. Then, by examining these points, we estimate the number of expected infected individuals in a community in time t.

Markov model, transmission probability, dynamical system.