具饱和发生率的被修正HIV传染病模型的全局稳定性

Global stability of a modified HIV infection model with saturation incidence

提出了一类具有饱和发生率的被修正HIV传染病模型。首先通过分析相应的特征方程,得到了无病平衡点E0(T0,0,0)和正平衡点E*(T*,I*,V*)的局部渐近稳定性。进一步构造Lyapunov函数和利用LaSalle不变集原理,证明了当基本再生数R0<1时,无病平衡点E0(T0,0,0)是全局渐近稳定的;利用第二加性复合矩阵,证明了当基本再生数R0>1时,正平衡点E*(T*,I*,V*)是全局渐近稳定的。最后通过数值模拟,验证了所得主要理论结果。

A modified HIV infection model with saturation incidence is studied. By analyzing characteristic equations , the local stability of an infection-free equilibrium , 0 , 0） and apositive equilibrium^ （T＊ , I＊ , V＊ ） is discussed. By using suitable Lyapunov functions and the LaSalle invariant principle , it is proved that if the basic reproductive number R0 〈1 , the infection-（T ,00） is globally asymptotically stable. I the basic reproductive number〉 1 , by means of the second additive compound matrix , the globally asymptotical stability of the positive equilibrium E＊ （T , I , V ） is obtained. Numerical simulations are carried out to simulations are carried out retical re-sults.