Modeling and analysis of COVID-19 epidemic: A stochastic reaction-diffusion framework with spatial heterogeneity and R-Wiener process

The research motivation of this paper stems from two aspects. From a practical perspective, viral evolution toward latent and asymptomatic characteristics, combined with population mobility and environmental perturbation, facilitate cryptic transmission and increases pandemic risk, imposing severe public health and economic burdens exemplified by COVID-19. Analysis of relevant models helps to address potential infectious disease threats. From a theoretical perspective, space-time white noise is not only suitable for partial differential equations but also can comprehensively reveal the impacts of noise intensity and dimension on disease transmission, whereas research on COVID-19 models perturbed by the R-Wiener process remains a gap. Therefore, this paper proposes a spatially heterogeneous stochastic reaction-diffusion SEIAR epidemic model and analyzes its dynamics. Specifically, the unique existence of the global non-negative strong solution is first established. Secondly, employing analytical tools suitable for the infinite-dimensional stochastic process, we obtain the p-th moment estimate and sublinear growth for the spatial integral of the total population. Thirdly, we derive the conditions for disease persistence and extinction through the temporal average value of compartments with viral. Finally, computer simulations are conducted to validate theoretical results and explore parameter influences. The obtained conclusions demonstrate that the sufficient condition for disease prevalence is most sensitive to the perturbation of susceptible compartment. More importantly, the noise intensity of diseased compartments exhibits a negative correlation with epidemic extinction.