一类具有细胞-细胞传播和免疫损害的HIV-1感染动力学模型  

Dynamics of a type HIV-1 infection model with cell-to-cell transmission and immune impairment

作　　者：徐瑞 宫云英 任华荣 XU Rui;GONG Yun-ying;REN Hua-rong(Institute of Complex Systems,Shanxi Univ.,Taiyuan 030006,China;Shanxi Provincial Key Laboratory of Mathematical Technology and Big Data Analysis for Disease Prevention and Control,Taiyuan 030006,China;School of Mathematical Sci.,Shanxi Univ.,Taiyuan 030006,China)

机构地区：[1]山西大学复杂系统研究所,山西太原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,山西太原030006 [3]山西大学数学科学学院,山西太原030006

出　　处：《高校应用数学学报（A辑）》2024年第2期163-174,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12271317;11871316)。

摘　　要：基于病毒-细胞感染和细胞-细胞传播两种机制,研究一类具有胞内时滞,CTL免疫反应和免疫损害的HIV-1感染动力学模型.通过计算得到了病毒感染基本再生率.通过分析特征方程根的分布,讨论了模型的病毒未感染平衡点和慢性感染平衡点的局部稳定性.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性态由病毒感染基本再生率完全确定:若基本再生率小于1,则病毒未感染平衡点全局渐近稳定;若基本再生率大于1,则慢性感染平衡点全局渐近稳定.进一步,通过数值模拟说明了理论结果,并对参数进行了敏感性分析,确定了参数对病毒感染基本再生率的影响程度.Based on the two mechanisms of virus-to-cell infection and cell-to-cell transmissions,a dynamic model of HIV-1 infection with the intracellular delay,CTL immune response and immune impairment is studied.The basic reproduction ratio of virus infection is calculated.By analyzing the distribution of roots of the corresponding characteristic equations,the local stability of the infection-free and chronic-infection equilibria of the model is discussed.By constructing appropriate Lyapunov functionals and using LaSalle's invariance principle,it is proved that the global dynamics of the model can be completely determined by the basic reproduction ratio of virus infection:if the basic reproduction ratio of virus infection is less than unity,the infection-free equilibrium is globally asymptotically stable;If the basic reproduction ratio of virus infection is greater than unity,the chronic-infection equilibrium is globally asymptotically stable.Furthermore,numerical simulations are carried out to illustrate the theoretical results,the sensitivity analysis is performed to determined the the degree of influence of the basic reproduction ratio of virus infection on parameters.

关 键 词：HIV-1感染 细胞-细胞传播 胞内时滞 免疫损害 稳定性 

分 类 号：O175[理学—数学]