Dynamics of a diffusive infection model with immune response

Firstly, in this paper, we analyze the globalstability for a new system with both immune response and two delays. By using the Lyapunov-LaSalle method, and by introducing the reproductive numbers R 0 and R 1 , we point out that the infection-free equilibrium E 0 is globally asymptotically stable, if R 0 ≤ 1 ; if R 1 ≤1 < R 0 , then the CTL -inactivated infectionequilibrium E1 is globally asymptotically stable; if R 1 > 1, then the CTL -activated equilibrium E 2 is globally asymptotically stable.Secondly, we investigate the discretization of the above system by making use of the non-standard finite difference scheme.That is, the global stability of equilibria is consistent when R 0 ≤ 1, or R 1 ≤ 1 < R 0 , however, if R 1 > 1, the global stability of the two kinds model is not consistent. Finally, we carry out numerical simulations to illustrate the theoretical results. AMS Subject Classification: 35C07, 35K55, 35K57, 92D25.