具有CTL免疫反应和细胞内时滞的HIV感染模型的全局稳定性

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

摘要: 研究了一类具有细胞内时滞和细胞毒性T淋巴细胞（CTL）免疫反应的HIV感染模型。运用再生矩阵方法，得到无免疫再生数 $R_{0}$ ，并定义免疫激活再生数 $R_{z}$ 。通过构造Lyapunov泛函，证明了当 $R_{0} < 1$ 时，无感染平衡点是全局渐近稳定的；当 $R_{z} < 1 < R_{0}$ 时，无免疫平衡点是全局渐近稳定的；当 $R_{z} > 1$ 时，免疫激活平衡点是全局渐近稳定的。

Abstract: 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 $R_{0}$ 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 $R_{0} < 1$ ， the immune-free equilibrium is globally asymptotically stable when $R_{z} < 1 < R_{0}$ ， and the immune-activated equilibrium is globally asymptotically stable when $R_{z} > 1$ .