带有无细胞传播、细胞传播和体液免疫反应的HIV/AIDS模型的稳定性分析

Stability Analysis of HIV/AIDS Model with Non-Cell-Propagation, Cell-Propagation and Humoral Immune Response

摘要: 根据重要生物意义，我们研究了一类具有HIV感染经典细胞扩散与细胞之间传播以及具有治疗的HIV感染模型。本文我们首先讨论了解的正性和有界性。然后，给出了系统的平衡点和基本再生数 R₀ 。当 R₀<1 时，得到了系统无病平衡点的全局稳定性。当 R₁<1 时，得到了无体液免疫平衡点的稳定性，而当 R₁>1 时，得到了系统体液免疫平衡点的全局稳定性等结论。

Abstract: Based on vital biological meanings, we consider a class of HIV infection models with both cell-free virus spread and cell-to-cell transmission. First of all, we show that all the solution to our system is positive and bounded. Then, we give the basic reproduction number R₀ and we prove that if R₀<1 , the infection-free equilibrium is globally stable. And if R₁<1 , the endemic equilibrium with humoral immunity is locally asymptotically stable, if R₁>1 , the endemic equilibrium with humoral immunity is globally stable.