A stochastic differential equation SIS epidemic model with two correlated Brownian motions

Abstract

In this paper, we introduce two perturbations in the classical deterministic susceptible-infected-susceptible epidemic model with two correlated Brownian motions. We consider two perturbations in the deterministic SIS model and formulate the original model as a stochastic differential equation with two correlated Brownian motions for the number of infected population, based on the previous work from Gray et al. (SIAM J Appl Math 71(3):876–902, 2011) and Hening and Nguyen (J Math Biol 77:135–163, 2017. https://doi.org/10.1007/s00285-017-1192-8 ). Conditions for the solution to become extinction and persistence are then stated, followed by computer simulation to illustrate the results.