A spatial SEIRS reaction-diffusion model in heterogeneous environment

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Song, Pengfei¹  Lou, Yuan²  Xiao, Yanni¹ 

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

[2] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

关键词: SEIRS epidemic model;    Reaction-diffusion equation;    Basic reproduction number;    Persistence/extinction;    Endemic equilibrium;   

DOI  :  10.1016/j.jde.2019.05.022

来源: Elsevier

【 摘 要 】

We propose a susceptible-exposed-infected-recovered-susceptible (SEIRS) reaction-diffusion model, where the disease transmission and recovery rates can be spatially heterogeneous. The basic reproduction number (R-0) is connected with the principal eigenvalue of a linear cooperative elliptic system. Threshold-type results on the global dynamics in terms of R-0 are established. The monotonicity of R-0 with respect to the diffusion rates of the exposed and infected individuals, which does not hold in general, is established in several cases. Finally, the asymptotic profile of the endemic equilibrium is investigated when the diffusion rate of the susceptible individuals is small. Our results reveal the importance of the movement of the exposed and recovered individuals in disease dynamics, as opposed to most of previous works which solely focused on the movement of the susceptible and infected individuals. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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