Global stability of HIV infection model with CTL immune response and intracellular time delay

An HIV infection model with intracellular time delay and Cytotoxic T Lymphocyte （CTL） immune response was investigated. By using the next-generation matrix method， the basic reproduction number $R_{\mathrm{0}}$ without immunity was obtained， and the immune activation reproduction number $R_z$ was defined. By constructing Lyapunov functional， it was proved that， the infection-free equilibrium is globally asymptotically stable when $R_{\mathrm{0}}<\mathrm{1}$， the immune-free equilibrium is globally asymptotically stable when $R_z<\mathrm{1}<R_{\mathrm{0}}$， and the immune-activated equilibrium is globally asymptotically stable when $R_z>\mathrm{1}$.