随机偏微分方程SEIRS流行病模型：适定性和长时间行为
Stochastic Partial Differential Equation SEIRS Epidemic Models: Well-posedness and Longtime Behavior
摘要：
流行病模型的研究在数学流行病学中占有重要地位。利用常微分方程、偏微分方程或随机微分方程对流行病模型进行了大量的研究。与这些研究相比，我们的工作分析了SEIRS（敏感-暴露-敏感）模型使用随机偏微分方程。具体而言，我们考虑了空间变量和时空白噪声对传染病模型的影响。在温和解的方法中，构造了一个压缩映射，利用不动点定理和因子分解方法证明了随机偏微分方程的适定性.我们还找到了持久性和灭绝性的充分条件来决定解的长期行为。希望本文的工作能为日益复杂的传染病模型及其相关数值模拟的研究提供一些新的思路。
英文摘要：
The study of epidemic models plays an important role in mathematical epidemiology. There are many researches on epidemic models using ordinary differential equations, partial differential equations or stochastic differential equations. In contrast to these researches, our work analyzes the SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) model using stochastic partial differential equations. Specifically, we consider the effects of spatial variables and space-time white noise on the epidemic model. In the means of mild solution, we construct a contraction mapping and prove the well-posedness for the stochastic partial differential equation using the fixed point argument and the factorization method. We also find sufficient conditions for permanence and extinction to determine the longtime behavior of the solution. We hope that this work can provide some new ideas for the study of increasingly complex epidemic models and related numerical simulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
