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  本文選題：腫瘤免疫系統(tǒng)　切入點：時滯　出處：《哈爾濱工業(yè)大學》2015年碩士論文

【摘要】：腫瘤免疫治療是生物醫(yī)學領域的一個重要的分支。早在八十年代初,生物數(shù)學家對腫瘤免疫機制產生了濃烈的興趣并進行了廣泛的實驗和深入的研究。主要研究不同免疫環(huán)境下,先天性免疫和適應性免疫保護生物體的動力學機制。隨著生物數(shù)學科學的發(fā)展,Kuznetsov提出了經典的腫瘤免疫模型——Kuznetsov模型。近二十年,對此腫瘤免疫時滯系統(tǒng)的穩(wěn)定性和Hopf分支性質研究已在腫瘤醫(yī)學治療得到廣泛應用。人體內的效應細胞對于潛伏的腫瘤細胞的攻擊有一定的時間延遲(時滯),這一復雜的免疫過程可以用時滯免疫系統(tǒng)加以描述和刻畫。分支分析方法是研究帶有時滯參數(shù)的系統(tǒng)動力學性質主要采用的方法和途徑。所謂分支,就是一類具參數(shù)的動力學系統(tǒng),當參數(shù)在臨界值附近發(fā)生微小變動的的情況下,系統(tǒng)的動力學性質發(fā)生改變的現(xiàn)象。局部Hopf分支是微分方程動力系統(tǒng)分支研究中較常見的分支類型,它的產生對應于系統(tǒng)的線性化方程的特征方程有一對純虛根的情形,主要研究系統(tǒng)隨參數(shù)改變情況下平衡點處的穩(wěn)定性情況和出現(xiàn)周期解的現(xiàn)象。本文主要研究了一類腫瘤免疫時滯模型的穩(wěn)定性和Hopf分支性質。首先引入了一類具時滯反饋的腫瘤免疫模型,分析了模型的平衡點的存在性及其穩(wěn)定性。然后定性地研究了Hopf分支性質。最后運用MATLAB軟件進行相應的數(shù)值模擬,分析驗證了在一段時期內,隨著時間的增長,腫瘤細胞與免疫細胞在生物體競爭波動存在的這一生物現(xiàn)象。
[Abstract]:Tumor immunotherapy is an important branch of biomedicine. As early as the early 1980s, Biological mathematicians have developed a strong interest in tumor immune mechanisms and conducted extensive experiments and in-depth studies. With the development of biological mathematics science, Kuznetsov put forward a classical tumor immune model, Kuznetsov model. Studies on the stability of tumor immune delay systems and the properties of Hopf branching have been widely used in the medical treatment of cancer. There is a time delay in the response of effector cells to latent tumor cells in the human body. A complex immune process can be described and characterized by a time-delay immune system. Bifurcation analysis is the main method and approach to study the dynamical properties of a system with time-delay parameters. Is a kind of dynamic system with parameters, when the parameters change slightly near the critical value, Local Hopf bifurcation is one of the most common bifurcation types in the study of dynamical system bifurcation of differential equations. It produces a pair of pure imaginary roots corresponding to the characteristic equations of the linear equations of the system. In this paper, the stability and Hopf bifurcation of a class of tumor immune delay models are studied. Delayed feedback tumor immune model, The existence and stability of equilibrium point of the model are analyzed, and the properties of Hopf bifurcation are studied qualitatively. Finally, the corresponding numerical simulation is carried out by using MATLAB software. This biological phenomenon in which tumor cells and immune cells compete in biological fluctuations.
【學位授予單位】：哈爾濱工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O175

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本文編號：1653597