一类基于游离病毒感染和细胞-细胞传播的宿主体内HIV-1感染动力学模型  

A with-in Host HIV-1 Infection Dynamics Model Based on Virus-to-cell Infection and Cell-to-cell Transmission

作　　者：徐瑞 周凯娟 白宁 Xu Rui;Zhou Kaijuan;Bai Ning(Complex Systems Research Center,Shanxi University,Taiyuan 030006;Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention,Shanxi University,Taiyuan 030006;School of Mathematics Science,Shanxi University,Taiyuan 030006)

机构地区：[1]山西大学复杂系统研究所,太原030006 [2]山西省疾病防控的数学技术与大数据分析重点实验室,太原030006 [3]山西大学数学科学学院,太原030006

出　　处：《数学物理学报（A辑）》2024年第3期771-782,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(12271317,11871316)。

摘　　要：该文考虑一类具有细胞-细胞传播、胞内时滞、饱和CTL免疫反应和免疫损害的HIV-1感染动力学模型.通过计算得到了免疫未激活和免疫激活再生率.通过分析特征方程根的分布,讨论了可行平衡点的局部渐近稳定性.通过构造适当的Lyapunov泛函并应用LaSalle不变性原理,证明了模型的全局动力学由免疫未激活和免疫激活再生率决定:如果免疫未激活再生率小于1,则病毒未感染平衡点是全局渐近稳定的;如果免疫未激活再生率大于1且免疫激活再生率小于1,则免疫未激活感染平衡点是全局渐近稳定的;如果免疫激活再生率大于1,则慢性感染平衡点是全局渐近稳定的.此外,通过数值模拟说明了免疫损害和细胞-细胞传播对模型动力学的影响.In this paper,we consider an HIV-1 infection model with cell-to-cell transmission,intracellular delay,saturated CTL immune response and immune impairment.By calculation,we get immunity-inactivated and immunity-activated reproduction ratios.By analyzing the characteristic equations,the local stability of each of feasible equilibria is established.By means of suitable Lyapunov functional and LaSalle's invariance principle,it is proved that the global asymptotic stability of each of feasible equilibria is determined by immunity-inactivated and immunity-activated reproduction ratios:If the immunity-inactivated reproduction ratio is less than unity,the infection-free equilibrium is globally asymptotically stable;if the immunity-inactivated reproduction ratio is greater than unity and the immunity-activated reproduction ratio is less than unity,the immunity-inactivated infection equilibrium is globally asymptotically stable;if the immunity-activated reproduction ratio is greater than unity,the chronic infection equilibrium is globally asymptotically stable.In addition,numerical simulation is carried out to illustrate the effects of immune impairment and cell-to-cell transmission on dynamics of the model.

关 键 词：HIV-1感染 细胞-细胞传播 胞内时滞 饱和CTL免疫反应 免疫损害 稳定性 

分 类 号：O175.23[理学—数学]