具有治疗和免疫时滞的乙肝病毒模型的稳定性  

Stability of a Delayed Hepatitis B Virus Infection Model with Drug Treatment and Immune Responses

作　　者：沈佳星 刘贤宁[1] SHEN Jiaxing;LIU Xianning(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2022年第7期55-64,共10页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12071382).

摘　　要：建立并分析了具有治疗和免疫时滞的乙肝病毒动力学模型.首先,证明了解的正性和有界性.其次,讨论了模型平衡点的存在唯一性,并计算了基本再生数和免疫再生数.再次,通过LaSalle不变集原理和构造Lyapunov泛函得到无病平衡点和无免疫平衡点的稳定性;同时分别得到地方病平衡点局部渐近稳定以及产生Hopf分支的条件.最后,通过数值模拟验证了理论结果.In this paper,a dynamical model of hepatitis B virus,which incorporates both treatment and immune response,has been presented and analyzed.Firstly,the positivity and boundedness of the solutions have been proved.Secondly,the existence and uniqueness of the equilibrium of the model has been discussed,and the basic reproduction number and immune reproduction number have been calculated.Thirdly,the stability of disease-free equilibrium and immune free equilibrium have been obtained by Lasalle's invariance principle and Lyapunov functional;the conditions of locally asymptotically stable of endemic equilibrium and Hopf bifurcation have been obtained respectively.Finally,the theoretical results are verified by numerical simulations.

关 键 词：药物治疗 时滞 Lyapunov稳定 HOPF分支 全局稳定性 

分 类 号：O193[理学—数学]