Wellposedness, equilibria, and patterns of an epidemic PDE model with spatiotemporally nonlocal memory

IF 2.4 2区 数学 Q1 MATHEMATICS
Guodong Liu , Hao Wang , Xiaoyan Zhang
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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.
具有时空非局部记忆的流行病PDE模型的适位性、平衡和模式
在具有疫苗接种的流行病反应-扩散模型中,将时空记忆用于描述易感个体的运动。为了解决全非线性PDE模型的全局可解性问题,我们提出了等价拟线性抛物方程组。理论分析证实了该解在一维区域内保持有界,并可以通过限制记忆驱动扩散速率将其扩展到三维区域。进一步,我们讨论了零记忆驱动运动速率模型的平衡态存在性和多重性。数值结果表明,考虑到记忆驱动的时间模式的形成,易感个体的时空记忆有助于周期性地减少感染。
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来源期刊
CiteScore
4.40
自引率
8.30%
发文量
543
审稿时长
9 months
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
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