Spatial dynamics of a reaction-diffusion SIS epidemic model with mass-action-type nonlinearity

This work is devoted to investigate the global asymptotic stability of equilibriums for a reaction-diffusion susceptible-infected-susceptible(SIS)epidemic model with spatial heterogeneity and mass-action-type nonlinearity.By discretizing the spatial variables of the model,first,Lyapunov functions are constructed for the corresponding ordinary differential equations(ODEs)model of the original SIS PDEs model,and then the construction method is generalized to the PDEs model in which either the susceptible or the infectious individuals are spreading in spatial heterogeneity environment.For both the cases,we obtained the standard threshold dynamics results.