A spatial SIS model in advective heterogeneous environments

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• 作者：Renhao Cui^a ; ^b ; ^{renhaocui@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Yuan Lou^a ; ^c ; ^{lou@math.ohio-state.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J55 ; 35B32
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：261
• 期：6
• 页码：3305-3343
• 全文大小：1000 K

文摘

We study the effects of diffusion and advection for a susceptible-infected-susceptible epidemic reaction–diffusion model in heterogeneous environments. The definition of the basic reproduction number R₀${\mathcal{R}}_0$ is given. If R₀<1${\mathcal{R}}_0<1$, the unique disease-free equilibrium (DFE) is globally asymptotically stable. Asymptotic behaviors of R₀${\mathcal{R}}_0$ for advection rate and mobility of the infected individuals (denoted by d_I$d_I$) are established, and the existence of the endemic equilibrium when R₀>1${\mathcal{R}}_0>1$ is studied. The effects of diffusion and advection rates on the stability of the DFE are further investigated. Among other things, we find that if the habitat is a low-risk domain, there may exist one critical value for the advection rate, under which the DFE changes its stability at least twice as d_I$d_I$ varies from zero to infinity, while the DFE is unstable for any d_I$d_I$ when the advection rate is larger than the critical value. These results are in strong contrast with the case of no advection, where the DFE changes its stability at most once as d_I$d_I$ varies from zero to infinity.