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Dynamics and profiles of a PDE Cholera model with distinct dispersal rates

发布时间:2019-05-30 作者: 浏览次数:
Speaker: 王金良 DateTime: 2019年6月3日(周一)下午3:30--4:30
Brief Introduction to Speaker:

王金良,黑龙江大学教授。

Place: 六号楼二楼报告厅
Abstract:Spatial heterogeneity plays an important role in spread of infectious diseases, and hence, motivates and advocates diffusive models for disease dynamics. By analyzing a diffusive Cholera model with the bilinear incidence infection mechanism, heterogeneous parameters and distinct dispersal rates for the susceptible and infected hosts, we have investigated the asymptotical profiles of the endemic steady state as the dispersal rate of the susceptible or infected hosts approaches zero. Some arguments, such as, existence of global solution, uniform bounded of solution, asymptotic smoothness of semiflow and existence of global attractor are also addressed. We then identify the basic reproduction number $R_0$ for the model and prove its threshold role: if $R_0<1 $, the disease-free equilibrium is globally asymptotically stable; if $R_0>1$, the solution of the model is uniformly persistent and there exists a positive steady state. Finally, we demonstrate some biological implications on the t...