{"title":"Wellposedness, equilibria, and patterns of an epidemic PDE model with spatiotemporally nonlocal memory","authors":"Guodong Liu , Hao Wang , Xiaoyan Zhang","doi":"10.1016/j.jde.2025.113491","DOIUrl":null,"url":null,"abstract":"<div><div>Spatiotemporal memory is incorporated to describe the movement of susceptible individuals in an epidemic reaction-diffusion model with vaccination. We propose equivalent quasilinear parabolic systems for the fully nonlinear PDE model to address global solvability. Theoretical analysis verifies that the solution remains bounded in a one-dimensional domain and can be extended to a three-dimensional domain by restricting the memory-driven diffusion rate. Furthermore, we discuss the existence and multiplicity of equilibria for the model with the zero memory-driven movement rate. Numerical findings reveal that spatiotemporal memory of susceptible individuals contributes to periodically reducing infection, given the formation of memory-driven temporal patterns.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113491"},"PeriodicalIF":2.4000,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625005182","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Spatiotemporal memory is incorporated to describe the movement of susceptible individuals in an epidemic reaction-diffusion model with vaccination. We propose equivalent quasilinear parabolic systems for the fully nonlinear PDE model to address global solvability. Theoretical analysis verifies that the solution remains bounded in a one-dimensional domain and can be extended to a three-dimensional domain by restricting the memory-driven diffusion rate. Furthermore, we discuss the existence and multiplicity of equilibria for the model with the zero memory-driven movement rate. Numerical findings reveal that spatiotemporal memory of susceptible individuals contributes to periodically reducing infection, given the formation of memory-driven temporal patterns.
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics