{"title":"具有双自由边界的非局部扩散 SIR 流行病模型的动力学原理","authors":"Qianying Zhang , Mingxin Wang","doi":"10.1016/j.nonrwa.2024.104208","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study an SIR epidemic model with nonlocal diffusion and double free boundaries, which can be used to describe a class of biological phenomena: the depletion of native resources by all individuals, the infected individuals do not lose their fertility completely, the recovered individuals are immune and no longer infected, the infected and recovered individuals spread along the same free boundary. We first investigate the existence and uniqueness of global solution, long time behaviors and some sufficient conditions for spreading and vanishing. Then we estimate the spreading speed and derive that accelerated spreading could happen when the kernel function does not satisfy a threshold condition.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"81 ","pages":"Article 104208"},"PeriodicalIF":1.8000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamics for a nonlocal diffusive SIR epidemic model with double free boundaries\",\"authors\":\"Qianying Zhang , Mingxin Wang\",\"doi\":\"10.1016/j.nonrwa.2024.104208\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we study an SIR epidemic model with nonlocal diffusion and double free boundaries, which can be used to describe a class of biological phenomena: the depletion of native resources by all individuals, the infected individuals do not lose their fertility completely, the recovered individuals are immune and no longer infected, the infected and recovered individuals spread along the same free boundary. We first investigate the existence and uniqueness of global solution, long time behaviors and some sufficient conditions for spreading and vanishing. Then we estimate the spreading speed and derive that accelerated spreading could happen when the kernel function does not satisfy a threshold condition.</p></div>\",\"PeriodicalId\":49745,\"journal\":{\"name\":\"Nonlinear Analysis-Real World Applications\",\"volume\":\"81 \",\"pages\":\"Article 104208\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Real World Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1468121824001470\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824001470","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了一个具有非局部扩散和双重自由边界的 SIR 流行病模型，该模型可用于描述一类生物现象：所有个体的本地资源耗尽，受感染个体不会完全丧失生育能力，康复个体具有免疫力且不再受感染，受感染个体和康复个体沿同一自由边界扩散。我们首先研究了全局解的存在性和唯一性、长时间行为以及扩散和消失的一些充分条件。然后，我们估算了传播速度，并推导出当核函数不满足阈值条件时，可能会发生加速传播。
Dynamics for a nonlocal diffusive SIR epidemic model with double free boundaries
In this paper, we study an SIR epidemic model with nonlocal diffusion and double free boundaries, which can be used to describe a class of biological phenomena: the depletion of native resources by all individuals, the infected individuals do not lose their fertility completely, the recovered individuals are immune and no longer infected, the infected and recovered individuals spread along the same free boundary. We first investigate the existence and uniqueness of global solution, long time behaviors and some sufficient conditions for spreading and vanishing. Then we estimate the spreading speed and derive that accelerated spreading could happen when the kernel function does not satisfy a threshold condition.
期刊介绍：
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.
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