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In this paper, we consider reaction-diffusion epidemic models with massaction or standard incidence mechanism and study the impact of limitingpopulation movement on disease transmissions. We set either the dispersal rateof the susceptible or infected people to zero and study the correspondingdegenerate reaction-diffusion model. Our main approach to study the globaldynamics of these models is to construct delicate Lyapunov functions. Ourresults show that the consequences of limiting the movement of susceptible orinfected people depend on transmission mechanisms, model parameters, andpopulation size.

On degenerate reaction-diffusion epidemic models with mass action or standard incidence mechanism