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）

发布时间：2018-07-05 12:58

  本文选题：慢性病毒感染模型 + 免疫应答　； 参考：《工程数学学报》2017年04期

【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.
[Abstract]:Specific immune responses play an important role in controlling viral infection in the host. In this paper, a class of chronic virus infection models with specific immune cell bell-shaped proliferation rate was proposed and studied. Here the bell-shaped proliferation of immune cells means that when the viral load is large enough, its reproduction rate decreases. Virus damage to the immune response is also considered in this model. At the same time, the local dynamic behavior of the model was analyzed. In order to determine its global dynamic behavior, some critical cases are analyzed by using the central flow regime theory, and the existence of periodic solutions of the model is excluded by constructing appropriate Dulac functions. The results obtained in this paper show that the model will have backward bifurcation under certain conditions, which means that the dynamic properties of the model will change with the initial state. The final numerical simulation shows that the final monotone and sustained oscillation are possible for both virus population and immune response.
【作者单位】： 空军工程大学理学院;
【基金】：The National Natural Science Foundation of China(11371369)
【分类号】：O175
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本文编号：2100282