一类带有治疗及垂直传播的HIV/AIDS 模型的稳定性分析

摘要

讨论了一类带有治疗及垂直传播的HIV/AIDS 模型，找出了模型的无病平衡点以及地方病平衡点并研究了这两平衡点的稳定性。最终得出当基本再生数 R0<1时无病平衡是全局渐近稳定的，此时地方病平衡点不存在当 R0>1时地方病平衡点全局渐近稳定的。%This paper considers an HIV/AIDS epidemic model with treatment and vertical transmission. The equi-librium points of the model are found and their stability is investigated. The model exists two equilibria namely, the disease-free and endemic equilibrium. It is found that if the basic reproduction number R0<1 the disease free equilib-rium is globally asymptotically stable and in such a case the endemic equilibrium does not exist. Where as the unique infected equilibrium is globally asymptotically stable if R0>1.