  In this chapter, we consider a reaction-diffusion SVIR infection model with
dis-tributed delay and nonlinear incidence rate. The wellposedness of the
proposed model is proved. By means of Lyapunov functionals, we show that the
disease-free equilibrium state is globally asymptotically stable when the basic
reproduction number is less or equal than one, and that the disease endemic
equilibrium is globally asymptotically stable when the basic reproduction
number is greater than one. Numerical simulations are provided to illustrate
the obtained theoretical results.
