具有阶段结构和双线性发生率的HIV模型的稳定性分析

Stability Analysis of HIV Models with Stage Structure and Bilinear Incidence

摘要: 艾滋病是具有严重危害性的传染病之一。本文研究了一类具有阶段结构和双线性发生率的HIV传播模型，利用谱半径的方法计算得到疾病消亡或持续存在的阈值，即基本再生数R₀。进一步地，我们证明了当R₀<1时系统仅存在无病平衡点E⁰，并且由V函数法以及LaSalle不变原理得到了它的全局渐近稳定性；当R₀>1时系统新增一个全局渐近稳定的地方病平衡点E^*。在文章的最后我们进行了数值模拟来验证我们的理论结果。

Abstract: AIDS is one of the most harmful infectious diseases. In this paper, we study a class of HIV trans-mission models with stage structure and bilinear incidence. The spectral radius method is used to calculate the basic regeneration number R₀. Furthermore, we prove that the system has a unique disease-free equilibrium E⁰ when R₀<1 while its global asymptotic stability is obtained by the V-function method and the LaSalle invariant principle; and when R₀>1, the system adds an en-demic equilibrium E^* which is globally asymptotically stable. Numerical simulations are carried out to verify our theoretical results.