Calculation of transition probabilities in the birth and death Markov process in the epidemic model

Multi-state Markov models are an important tool in epidemiologic studies. One of the well-known multi-state Markov models is the birth–death model that describes the spread of a disease in the community. In this paper, we obtain transition probabilities of a birth and death Markov process based on the matrix method. One of the important subjects in the epidemic models is to obtain mathematical exception of the number of infected individuals after time t. For calculating this subject, we need to determine the transition probability matrix. We obtain this matrix by an analytic method. Finally, in an example we obtain the expected number of diseased individuals in the community.