Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model

This paper aims to establish a novel explicit method for the stochastic SIS epidemic model, which can preserve the bounded positive domain and asymptotic properties. The proposed new method is based on combining a logarithmic transformation with a truncated Euler-Maruyama method, and it has the first-order rate of convergence for the pth-moment with p>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p>0$$\end{document}. Moreover, without additional restriction conditions except those necessary to guarantee the extinction of the exact solution, the approximation of the extinction is achieved for the stochastic SIS model whose coefficients violate the global monotonicity condition. Some numerical experiments are given to illustrate the theoretical results and testify to the efficiency of our algorithm.