First order strong convergence of an explicit scheme for the stochastic SIS epidemic model

A novel explicit time-stepping scheme, called Lamperti smoothing truncation scheme, is devised in this paper to strongly approximate a stochastic SIS epidemic model, whose solution process takes values in a bounded domain and whose coefficients violate the global monotonicity condition. The proposed scheme is based on combining a Lamperti-type transformation with an explicit truncation method. The new scheme results in numerical approximations preserving the domain of the original SDEs and is proved to retain a mean-square convergence rate of order one. Numerical examples are finally reported to confirm our theoretical findings. (C) 2021 Elsevier B.V. All rights reserved.