Speaker: Shuwen Xue (Assistant Professor, Northern Illinois University)

 

Title: Multiplicity and asymptotic profiles of endemic equilibria of a cross-diffusive epidemic model

 

 

Abstract: Spatial heterogeneities in the environment and the movements of individuals play crucial roles in the spread of infectious diseases. In this talk, we focus on a cross-diffusive epidemic model that incorporates the repulsive movement of susceptible population away from infected population. We first show that the basic reproduction number alone cannot determine the existence of endemic equilibria (EEs) and the model may have multiple EEs when the repulsive movement rate is large. Next, we analyze the bifurcation curves of EEs. Specifically, we show that a large repulsive movement rate tends to induce backward bifurcation curves. This highlights the complex dynamics of the system under strong repulsive interactions. Finally, we investigate the asymptotic profiles of EEs as the repulsive movement rate is large or the random movement rates are small. Our findings indicate that a large tendency of susceptible people to avoid infected people can eliminate the disease if and only if the total population is below a threshold level.

 

 

Host: Wenxian Shen