标题： 保持域和强收敛的随机SIS流行病模型显式格式 显示英文标题

标题： Domain preserving and strongly converging explicit scheme for the stochastic SIS epidemic model

摘要： 在本文中，我们通过使用半离散方法对适当的转换过程，构建了一个随机版本的易感感染易感（SIS）流行病模型的数值方法，该模型由适当的随机微分方程（SDE）表示。 我们证明了所提出方法的强收敛性，收敛阶为$1,$，并对其稳定性特性进行了研究。 由于SDE通常缺乏解析解，因此常采用数值技术。 因此，研究将通过构建合适的数值方案并与其他方案进行比较，寻求现有随机模型的数值解。 研究目标是实现一种定性和高效的方法来求解这些方程。 此外，对于尚未使用SDE进行随机建模的模型，研究将适当表述这些模型，进行模型特性的理论分析，并随后求解相应的SDE。 显示英文摘要

摘要： 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.