Title: A Spatial SIS Model in Advective Heterogeneous Environments
Speaker: Renhao Cui (Harbin Normal University, China)
Abstract: 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 $\mathcal{R}_0$ is given. 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 futher 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 population 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 speed up the elimination of disease. This is joint work with King-Yeung Lam and Yuan Lou.
Seminar URL: https://research.math.osu.edu/pde/