一类具有DAAs治疗和多尺度年龄结构的时滞丙肝模型  

A time-delayed HCV model with DAAs treatment and multi-scale age structure

作　　者：康玉娇 张太雷[1] 马怡婷 KANG Yujiao;ZHANG Tailei;MA Yiting(School of Sciences,Chang′an University,Xi′an,Shaanxi 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《石河子大学学报（自然科学版）》2023年第5期622-632,共11页Journal of Shihezi University(Natural Science)

基　　金：陕西省自然科学基础研究计划项目(2022JM-023)。

摘　　要：为了研究DAAs治疗对丙肝的传播机理的影响,建立了一类具有时滞的多尺度年龄结构的丙肝模型,给出了模型的基本再生数。通过构造Lyapunov泛函和LaSalle不变集原理,证明了当R_(0)^(*)<1时,无病平衡点全局渐近稳定;当R_(1)^(*)<1<R_(0)^(*)且满足一定的条件时,细胞免疫激发平衡点全局渐近稳定。最后进行数值模拟,结果表明在一定程度内加强DAAs的治疗效果会抑制细胞免疫反应,并且免疫时滞会影响细胞免疫激发平衡点的稳定性,在实际治疗中将通过优化组合药物和用量来达到消除丙肝的目的。In order to study the effect of DAAs treatment on the transmission mechanism of hepatitis C,a class of HCV model with time-delays and multi-scale age structure is established,and the basic reproductive number of the model is given.By constructing Lya-punov functional and LaSalle invariant set principle,it is proved that the disease-free equilibrium point is globally asymptotically stable when R_(0)^(*)<1;the equilibrium point of cellular immunity is globally asymptotically stable when R_(1)^(*)<1<R_(0)^(*);when R_(0)^(*)>1,the equilibri-um point of cellular immune excitation is globally asymptotically stable under certain conditions.Finally,numerical simulations are car-ried out.The results show that strengthening the therapeutic effect of DAAs to a certain extent will inhibit the cellular immune re-sponse,and the immune delay will affect the stability of the equilibrium point of cellular immune excitation.In the actual treatment,the objective of eliminating hepatitis C will be achieved by optimizing the combination of drugs and dosage.

关 键 词：时滞 丙型肝炎 DAAs治疗 稳定性 数值模拟 

分 类 号：O175.1[理学—数学]