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The well-known stochastic SIS model characterized by highly nonlinear inepidemiology has a unique positive solution taking values in a bounded domainwith a series of dynamical behaviors. However, the approximation methods tomaintain the positivity and long-time behaviors for the stochastic SIS model,while very important, are also lacking. In this paper, based on a logarithmictransformation, we propose a novel explicit numerical method for a stochasticSIS epidemic model whose coefficients violate the global monotonicitycondition, which can preserve the positivity of the original stochastic SISmodel. And we show the strong convergence of the numerical method and derivethat the rate of convergence is of order one. Moreover, the extinction of theexact solution of stochastic SIS model is reproduced. Some numericalexperiments are given to illustrate the theoretical results and testify theefficiency of our algorithm.

First order strong convergence and extinction of positivity preserving  logarithmic truncated Euler-Maruyama method for the stochastic SIS epidemic  model