In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a suitable transformed process. We prove the strong convergence of the proposed method, with order $1,$ and examine its stability properties. Since SDEs generally lack analytical solutions, numerical techniques are commonly employed. Hence, the research will seek numerical solutions for existing stochastic models by constructing suitable numerical schemes and comparing them with other schemes. The objective is to achieve a qualitative and efficient approach to solving the equations. Additionally, for models that have not yet been proposed for stochastic modeling using SDEs, the research will formulate them appropriately, conduct theoretical analysis of the model properties, and subsequently solve the corresponding SDEs.

翻译：本文针对易感-感染-易感（SIS）传染病模型的随机版本（由适当的随机微分方程SDE描述），通过对经适当变换后的过程应用半离散方法，构造了一种数值方法。我们证明了该方法具有阶数为$1$的强收敛性，并考察了其稳定性性质。由于随机微分方程通常缺乏解析解，数值技术被广泛采用。因此，本研究将通过构造合适的数值格式并将其与其他格式进行比较，为现有随机模型寻求数值解，旨在实现方程求解的定性与高效方法。此外，对于尚未提出采用随机微分方程进行随机建模的模型，本研究将对其进行适当公式化、模型性质的（理论分析），并进而求解相应的随机微分方程。