一类SEI传染病扩散模型及其移动边沿

Abstract

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

CLC Number:

O175.2

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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An SEI Epidemic Diffusive Model and Its Moving Front

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