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

作者: 阿斯亚•吾斯曼 , 夏米西努尔•阿布都热合曼 :新疆大学,数学与系统科学学院,新疆 乌鲁木齐;

关键词: 药物疗法细胞与细胞之间的传递体液免疫Lyapunov函数全局稳定性Drug Therapy Cell-to-Cell Transmission Humoral Immune Lyapunov Function Global Stability

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.

文章引用: 阿斯亚•吾斯曼 , 夏米西努尔•阿布都热合曼 (2016) 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。 应用数学进展, 5, 523-535. doi: 10.12677/AAM.2016.53063

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