  In this paper, we consider reaction-diffusion epidemic models with mass
action or standard incidence mechanism and study the impact of limiting
population movement on disease transmissions. We set either the dispersal rate
of the susceptible or infected people to zero and study the corresponding
degenerate reaction-diffusion model. Our main approach to study the global
dynamics of these models is to construct delicate Lyapunov functions. Our
results show that the consequences of limiting the movement of susceptible or
infected people depend on transmission mechanisms, model parameters, and
population size.
