Speaker: Prof. CUI Renhao,  Renmin University of China

Time: 2016-04-26,9:00-10:00

Place: Room 1518, School of Mathematical Sciences

Detail:  In this talk we shall be more interested in the effects of diffusion and advec-tion for a susceptible-infected-susceptible epidemic reaction-diffusion model inheterogeneous environments. The definition of the basic reproduction numberR1 is given. If R1 < 1, the unique disease-free equilibrium (dfe) is global-ly asymptotically stable. asymptotic behaviors of r1 for advection rate andmobility of the infected individuals (denoted by di ) are established, and theexistence of the endemic equilibrium when r1> 1 is studied. The effects ofdiffusion and advection rates on the stability of the DFE are further investi-gated. 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 DFEchanges its stability at least twice as dI varies from zero to infinity, while theDFE is unstable for any dI when the advection rate is larger than the criticalvalue. These results are in strong contrast with the case of no advection, wherethe DFE changes its stability at most once as dI varies from zero to infinity.

Organizer: School of Mathematical Sciences