一类具有治愈率和非线性发生率的HIV感染模型的动力学特性

Dynamics of HIV Infection Model with Cure Rate and Nonlinear Incidence Rate

研究了一类具有治愈率和非线性发生率的HIV感染模型的动力学性质,给出了决定病毒消亡与否的基本再生数的数学表达式,利用特征方程和Hurwitz判据分析了模型平衡点的局部稳定性.通过构造Lyapunov函数,证明了当基本再生数<1时无病平衡点是全局渐近稳定性的,利用第二加性复合矩阵理论,证明了当基本再生数>1时感染平衡点是全局渐近稳定的.

The dynamics of HIV infection model with cure rate and nonlinear incidence rate is investigated. The explicit expression for the basic reproduction number of the model which determines whether the virus dies out or not is obtained. With characteristic equation and Hurwitz criterion, the local stability of the equilibria is analyzed. By constructing a proper Lyapunov function, the global stability of the infection-free equilibrium is derived when the basic reproduction number is less than unity. Using the second additive compound matrix theory, we prove that the endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than unity.