This article deals with the numerical positivity, boundedness, convergence, and dynamical behaviors for stochastic susceptible-infected-susceptible (SIS) model. To guarantee the biological significance of the split-step backward Euler method applied to the stochastic SIS model, the numerical positivity and boundedness are investigated by the truncated Wiener process. Motivated by the almost sure boundedness of exact and numerical solutions, the convergence is discussed by the fundamental convergence theorem with a local Lipschitz condition. Moreover, the numerical extinction and persistence are initially obtained by an exponential presentation of the stochastic stability function and strong law of the large number for martingales, which reproduces the existing theoretical results. Finally, numerical examples are given to validate our numerical results for the stochastic SIS model.

中文翻译：

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随机易感感染易感模型的分步向后欧拉方法与截断维纳过程的数值分析。

本文讨论随机易感-感染-易感 (SIS) 模型的数值正性、有界性、收敛性和动态行为。为了保证分步后向欧拉方法应用于随机SIS模型的生物学意义，通过截断维纳过程研究了数值正性和有界性。受精确解和数值解几乎确定有界性的启发，通过具有局部 Lipschitz 条件的基本收敛定理讨论了收敛性。此外，通过随机稳定函数和鞅大数强定律的指数表示，初步得到了数值消光和持久性，再现了现有的理论结果。最后，给出数值例子来验证随机 SIS 模型的数值结果。