NUMERICAL SOLUTION OF STOCHASTIC EPIDEMIOLOGICAL MODEL: CASE OF SIR MODEL

In this paper we extend the SIR epidemic model, considered in [1], from a deterministic framework to a stochastic one, and we formulate it as a stochastic differential equation. We present a Picard iteration method of proving verification theorem for the existence and uniqueness of the solution in global behavior. As a side effect of this study, we move one the development of the numerical treatment to solve the considered problem using the Milstein’s scheme. A comparative numerical study is done using some values of the intensity of the stochastic environment around the endemic equilibrium.