A sptial SIS model in advective heterogeneous environments

讲座内容：We study the dynamics ofa SIS epidemic model of reaction-diffusion- advection type. The persistence of infected and susceptible populations and the global stability of the disease free equilibrium are established when the basic reproduction number is greater than or less than or equal to one, respectively. We further consider the effects of diffusion and advection on asymptotic profiles of endemic equilibrium: When the advection rate is relatively large comparing to the diffusion rates of both populations, then two populations persist and concentrate at the downstream end. As the diffusion rate of the susceptible population tends to zero, the density of the infected population decays exponentially for positive advection rate but linearly when there is no advection. Our results suggest that advection can help speed up the elimination of disease. This talk is based on joint works with Renhao Cui and King-Yeung Lam.