本文選題：慢性病毒感染模型 + 免疫應(yīng)答��； 參考：《工程數(shù)學(xué)學(xué)報(bào)》2017年04期

【摘要】：特異性免疫應(yīng)答對(duì)控制宿主體內(nèi)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(xì)胞鐘形增殖率的慢性病毒感染模型.這里免疫細(xì)胞的鐘形增殖意指當(dāng)病毒載量足夠大時(shí)其繁殖率會(huì)降低.病毒對(duì)免疫應(yīng)答的損害也在本文的模型中被考慮.在找到該模型免疫應(yīng)答基本再生數(shù)的同時(shí),完整分析了其局部動(dòng)力學(xué)行為.為了確定其全局動(dòng)力學(xué)性態(tài),應(yīng)用中心流型理論對(duì)一些臨界情形進(jìn)行了分析,并通過構(gòu)造適當(dāng)?shù)腄ulac函數(shù)排除了該模型周期解的存在性.本文得到的結(jié)果顯示在一定條件下模型會(huì)出現(xiàn)后向分支,這意味著模型的動(dòng)力學(xué)性質(zhì)會(huì)因初始狀態(tài)的不同而改變.最后的數(shù)值模擬說明最終的單調(diào)和持續(xù)震蕩對(duì)病毒種群和免疫應(yīng)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(xué)理學(xué)院;
【基金】：The National Natural Science Foundation of China(11371369)
【分類號(hào)】：O175
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本文編號(hào)：2100282