随机SIS传染病模型的保区域与强收敛显式格式
Domain preserving and strongly converging explicit scheme for the stochastic SIS epidemic model
AI总结：
本文针对随机SIS传染病模型，通过半离散方法构建了阶数为1且保区域的强收敛显式数值格式，并为其求解与理论分析提供了定性与高效的方法。
摘要：
本文针对易感者-感染者-易感者（SIS）传染病模型的随机版本，通过使用半离散方法处理一个合适的变换过程，构建了一种数值方法，该模型由合适的随机微分方程（SDE）表示。我们证明了所提方法具有阶数为1的强收敛性，并考察了其稳定性。由于SDE通常缺乏解析解，因此常采用数值技术。因此，本研究将通过构建合适的数值格式，寻求现有随机模型的数值解，并将其与其他格式进行比较。目标是实现求解方程的定性与高效的方法。此外，对于尚未使用SDE进行随机建模的模型，研究将对其进行适当表述，对模型性质进行理论分析，随后求解相应的SDE。
英文摘要：
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.
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