(untitled) (European Journal of Pure and Applied Mathematics, 2019)
The study of infectious diseases represents one of the oldest and richest sectors of biomathematics. The transmission dynamics of these diseases are still a major problem in mathematical epidemiology. In this work, we propose a stochastic version of a SEIRS epidemiological model for infectious diseases evolving in a random environment for the propagation of infectious diseases. This random model takes into account the rates of immigration and mortality in each compartment and the spread of these diseases follows a four-state Makovian process. We first study the stability of the model and then estimate the marginal parameters of each disease state over time. Real measles data are applied to the model.