Explicit-implicit methods for stochastic susceptible-infected-recovered model

In this paper, we propose an explicit-implicit method to numerically solve the stochastic susceptible-infected-recovered (SIR) model driven by Brownian motion. We introduce a transformation to transform the stochastic SIR model into an auxiliary differential system without the diffusion term. Then we construct the explicit-implicit method for the auxiliary differential system and demonstrate that the convergence rate is 1.0. The inverse transformation of the explicit-implicit method is positivity preserving. This method yields a convergence rate of 1.0 for the stochastic SIR model. We confirm our theoretical results by a numerical example.