一类具有Hill型感染率的HIV模型的动力学分析  

Dynamic analysis of a HIV model with Hill type infection rate

作　　者：李永凤 黄嵩 朱城志 Li Yongfeng;Huang Song;Zhu Chengzhi(College of Mathematics and Information Science,Zhengzhou University of Light Industry,Zhengzhou 450002,China)

机构地区：[1]郑州轻工业大学数学与信息科学学院,郑州450002

出　　处：《河南师范大学学报（自然科学版）》2022年第5期29-35,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11901541);河南省科技攻关项目(202102310631);河南省高等学校重点科研项目(19A110036).

摘　　要：首先考虑了一类具有Hill感染率的HIV模型,给出了平衡点的具体表达式,分析了系统解的正性和有界性,并得到了无病平衡点局部和全局稳定的条件,以及正平衡点局部稳定的条件.然后考虑了对应的时滞系统,给出了平衡点稳定的充分条件,并讨论了正平衡点处的分支现象.最后借助计算机数值模拟验证了结论的正确性.Firstly, a class of HIV model with Hill type infection rate is considered, the exact forms of equilibria are obtained, the positivity and boundedness of solution are analyzed, and the condition for local and global stability of the infection-free equilibrium are obtained, the conditions for local stability of the positive equilibrium are also given. Secondly, the corresponding delay system is taken into consideration, the sufficient conditions for stability of equilibria are provided, and the bifurcation of the positive equilibrium is discussed. Finally, the correctness of the conclusions are verified by computer numerical simulition.

关 键 词：HIV模型 时滞 Hill型感染率 平衡点 稳定性 

分 类 号：O175.2[理学—数学]