一类SEI传染病扩散模型及其移动边沿

数学物理学报 ›› 2015, Vol. 35 ›› Issue (3): 604-617.

一类SEI传染病扩散模型及其移动边沿

刘江¹, 朱林涛², 林支桂²

1. 江苏联合职业技术学院淮安生物工程分院江苏淮安 223200;
2. 扬州大学数学科学学院江苏扬州 225002

收稿日期:2014-04-21 修回日期:2015-01-07 出版日期:2015-06-25 发布日期:2015-06-25
作者简介:刘江, ljlh1031@163.com;朱林涛, 282184129@qq.com;林支桂, zglin68@hotmail.com
基金资助:
国家自然科学基金(11271197, 11371311) 和扬州大学高端人才支持计划资助

An SEI Epidemic Diffusive Model and Its Moving Front

Liu Jiang¹, Zhu Lintao², Lin Zhigui²

1. Jiangsu Union Technical Institute Huaian Biological Engineering Branch, Jiangsu Huaian 223200;
2. School of Mathematical Science, Yangzhou University, Jiangsu Yangzhou 225002

Received:2014-04-21 Revised:2015-01-07 Online:2015-06-25 Published:2015-06-25

摘要/Abstract

摘要：

该文研究一类SEI传染病模型, 其中病毒在潜伏期和感染期具有感染性. 首先研究固定区域上SEI偏微分方程组, 考虑平衡解的局部稳定性和全局稳定性. 然后重点研究相应的自由边界问题, 其中自由边界表示病毒的移动边沿. 给出了该问题解的全局存在性、唯一性, 讨论了自由边界的性质, 证明了病毒要么蔓延, 要么消退. 还给出了蔓延和消退的充分条件, 结果表明: 当有效接触率很小或平均潜伏期较短, 且初始染病区域小时, 疾病消退; 而当有效接触率大或平均潜伏期较长, 且初始染病区域大时, 疾病蔓延.

关键词: SEI模型, 反应扩散方程组, 稳定性, 自由边界

Abstract:

This paper is concerned about an SEI model, in which the disease is infectious in the latent period and the infected period. We first consider the PDE system in a fixed domain, the local and global stabilities of equilibriums are given. More attention has been given to the free boundary problem, which describes the moving front. Global existence and uniqueness of the solution are first given and then the properties of the free boundary are discussed. We prove that either the disease spreads or vanishes. Sufficient conditions for spreading or extinction are given. Our results show that when the contact rate is very small or average incubation period is short, and the initial infected domain is small enough, then the disease vanishes; and when the contact rate is big or the average incubation period is long, and the initial infected domain is sufficiently large, then the disease spreads.

Key words: SEI model, Reaction-diffusion equations, Stability, Free boundary

中图分类号:

O175.2

刘江, 朱林涛, 林支桂. 一类SEI传染病扩散模型及其移动边沿[J]. 数学物理学报, 2015, 35(3): 604-617.

Liu Jiang, Zhu Lintao, Lin Zhigui. An SEI Epidemic Diffusive Model and Its Moving Front[J]. Acta mathematica scientia,Series A, 2015, 35(3): 604-617.

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