本文選題：慢性病毒感染模型 + 免疫應答　； 參考：《工程數學學報》2017年04期

【摘要】：特異性免疫應答對控制宿主體內的病毒感染起著非常重要的作用.本文提出并研究了一類具有特異性免疫細胞鐘形增殖率的慢性病毒感染模型.這里免疫細胞的鐘形增殖意指當病毒載量足夠大時其繁殖率會降低.病毒對免疫應答的損害也在本文的模型中被考慮.在找到該模型免疫應答基本再生數的同時,完整分析了其局部動力學行為.為了確定其全局動力學性態(tài),應用中心流型理論對一些臨界情形進行了分析,并通過構造適當的Dulac函數排除了該模型周期解的存在性.本文得到的結果顯示在一定條件下模型會出現(xiàn)后向分支,這意味著模型的動力學性質會因初始狀態(tài)的不同而改變.最后的數值模擬說明最終的單調和持續(xù)震蕩對病毒種群和免疫應答都是有可能發(fā)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.
【作者單位】： 空軍工程大學理學院;
【基金】：The National Natural Science Foundation of China(11371369)
【分類號】：O175
，

本文編號：2100282