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The study of epidemic models plays an important role in mathematicalepidemiology. There are many researches on epidemic models using ordinarydifferential equations, partial differential equations or stochasticdifferential equations. In contrast to these researches, our work analyzes theSEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) model usingstochastic partial differential equations. Specifically, we consider theeffects 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 thewell-posedness for the stochastic partial differential equation using the fixedpoint argument and the factorization method. We also find sufficient conditionsfor permanence and extinction to determine the longtime behavior of thesolution. We hope that this work can provide some new ideas for the study ofincreasingly complex epidemic models and related numerical simulations.

Stochastic Partial Differential Equation SEIRS Epidemic Models: Well-posedness and Longtime Behavior