Abstract 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 $R_{0}\leq1$ ; the immune-free equilibrium is globally asymptotically stable if the immune reproduction number and the basic reproduction number satisfy R 1 ≤ 1 < R 0 $R_{1}\leq1< R_{0}$ ; the interior equilibrium is globally asymptotically stable if R 1 > 1 $R_{1}>1$ .
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