ASYMPTOTICAL ANALYSIS OF A REACTION- DIFFUSION EQUATIONS D-SIS EPIDEMIC MODEL

摘要

By monotone methods and invariant region theory, a reaction-diffusion equations D-SIS epidemic model with bilinear rate is studied. The existence and uniqueness of the solution of the model are proved. The basic reproductive number which determines whether the disease is extinct or not is found. The globally asymptotical stability of the disease-free equilibrium and the endemic equilibrium are obtained. Some results of the ordinary differential equations model are extended to the present partial differential equations model.