In this paper, we investigate the dynamical properties for a model of delay differential equations, which describes a virusimmune interaction in vivo. By analyzing corresponding characteristic equations, the local stability of the equilibria for infection-free, antibody-free, and antibody response and the existence of Hopf bifurcation with antibody response delay as a bifurcation parameter at the antibody-activated infection equilibrium are established, respectively. Global stability of the equilibria for infection-free, antibody-free, and antibody response, respectively, also are established by applying the Lyapunov functionals method. The numerical simulations are performed in order to illustrate the dynamical behavior of the model.

In this paper, a diffusive and delayed virus dynamics model with Crowley-Martin incidence function and CTL immune response is investigated. By constructing the Lyapunov functionals, the threshold conditions on the global stability of the infection-free, immune-free and interior equilibria are established if the space is assumed to be homogeneous. We show that the infection-free equilibrium is globally asymptotically stable if the basic reproductive number R 0 ≤ 1; the immune-free equilibrium is globally asymptotically stable if the immune reproduction number and the basic reproduction number satisfy R 1 ≤ 1 < R 0 ; the interior equilibrium is globally asymptotically stable if R 1 > 1.

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