一类带有特异性免疫细胞钟形增殖率的慢性病毒感染模型的全局动力学性态（英文）  

Global Dynamics of a Chronic Virus Infection Model with Bell-shaped Proliferation Rate of Specific Immune Cells

作　　者：李佳[1] 李建全[1] 李益群[1] LI Jia;LI Jian-quan;LI Yi-qun(School of Science, Air Force Engineering University, Xi'an 710051)

机构地区：[1]空军工程大学理学院,西安710051

出　　处：《工程数学学报》2017年第4期424-436,共13页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11371369)

摘　　要：特异性免疫应答对控制宿主体内的病毒感染起着非常重要的作用.本文提出并研究了一类具有特异性免疫细胞钟形增殖率的慢性病毒感染模型.这里免疫细胞的钟形增殖意指当病毒载量足够大时其繁殖率会降低.病毒对免疫应答的损害也在本文的模型中被考虑.在找到该模型免疫应答基本再生数的同时,完整分析了其局部动力学行为.为了确定其全局动力学性态,应用中心流型理论对一些临界情形进行了分析,并通过构造适当的Dulac函数排除了该模型周期解的存在性.本文得到的结果显示在一定条件下模型会出现后向分支,这意味着模型的动力学性质会因初始状态的不同而改变.最后的数值模拟说明最终的单调和持续震荡对病毒种群和免疫应答都是有可能发生的.The specific immune response plays a very important role in controlling the viralinfection within host.A chronic virus infection model with bell-shaped proliferationrate of specific immune cells is proposed and investigated in this paper,wherethe bell-shaped expansion implies that the proliferation rate of immune cells coulddecrease when the virus load is sufficiently large.The impairment of virus onimmune response is also incorporated in the model.For the model,the net reproductionnumber of the immune response with virus impairment is found,and thelocal dynamical behaviors are demonstrated completely.In order to determine theglobal dynamics,the center manifold theory is applied for some critical situations,and we also construct the suitable Dulac function to rule out the existence of periodicsolutions.The obtained results in this paper show that the backward bifurcationmay occur under certain conditions,which reflects the dependence of dynamics ofthe model on the initial conditions.Finally,the numerical simulation also suggeststhat both eventual monotonicity and sustained oscillation of viral population andimmune response are possible for the model.

关 键 词：慢性病毒感染模型 免疫应答 净再生数 动力学性态 后向分支 

分 类 号：O175.1[理学—数学]