一类含Logistic项SIS模型平衡解的稳定性及存在性
Stability and Existence of Equilibrium Solutions for a Class of SIS Model with Logistic Source
摘要: 近年来，越来越多的研究聚焦于各类反应–扩散型传染病模型，重点考察空间异质性与个体扩散对传染病传播动力学的联合影响。本文主要考虑一类含有Logistic项的反应扩散对流SIS模型解的性质。我们首先给出模型基本再生数的定义，其次证明了无病平衡解(DFE)的线性稳定性，最后证明了在高风险点的条件下地方病平衡解(EE)的存在性。
Abstract: In recent years, an increasing number of studies have focused on various types of reaction-diffusion epidemic models, emphasizing the combined effects of spatial heterogeneity and individual dispersal on the transmission dynamics of infectious diseases. This paper primarily considers the properties of solutions for a class of reaction-diffusion-advection SIS models with a logistic term. We first define the basic reproduction number of the model, then prove the linear stability of the disease-free equilibrium (DFE), and finally demonstrate the existence of an endemic equilibrium (EE) under conditions of high-risk sites.
文章引用：刘芳君. 一类含Logistic项SIS模型平衡解的稳定性及存在性[J]. 应用数学进展, 2025, 14(12): 147-154. https://doi.org/10.12677/aam.2025.1412494

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