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

Cai, Siyang and Cai, Yongmei and Mao, Xuerong (2019) A stochastic differential equation SIS epidemic model with two correlated Brownian motions. Nonlinear Dynamics, 97 (4). pp. 2175-2187. ISSN 0924-090X

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    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 (SDE) with two correlated Brownian Motions for the number of infected population, based on previous work from Gray et al. in 2011 and Hening’s work in 2017. Conditions for the solution to become extinction and persistence are then stated, followed by computer simulation to illustrate the results.