Dynamical analysis of a reaction–diffusion SEI epidemic model with nonlinear incidence rate.

In this paper, a reaction–diffusion SEI epidemic model with nonlinear incidence rate is proposed. The well-posedness of solutions is studied, including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions. The basic reproduction numbers are given in both heterogeneous and homogeneous environments. For spatially heterogeneous environment, by the comparison principle of the diffusion system, the infection-free steady state is proved to be globally asymptotically stable if R 0 < 1 , if R 0 > 1 , the system will be persistent and admit at least one positive steady state. For spatially homogenous environment, by constructing a Lyapunov function, the infection-free steady state is proved to be globally asymptotically stable if R 0 < 1 , and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if R 0 > 1. Finally, two examples are given via numerical simulations, and then some control strategies are also presented by the sensitive analysis. [ABSTRACT FROM AUTHOR]