A higher order positivity preserving scheme for the strong approximations of a stochastic epidemic model

Abstract

By combining a predictor–corrector method with a Lamperti-type transformation, we propose a higher order, explicit, positivity preserving scheme for the stochastic susceptible-infected-susceptible (SIS) epidemic model that takes values in (0,N). The proposed scheme is able to preserve the domain (0,N) of the original SIS model and admits numerical approximations with the exponential integrability. These facts help us to recover the strong convergence rate of order 1.5 for the scheme. Moreover, the dynamic behaviors of numerical approximations are also investigated. It is shown that the numerical scheme is able to reproduce the extinction and persistence properties of the disease under certain assumptions. Numerical experiments are finally presented to verify the theoretical findings.