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

【摘要】：腫瘤免疫治療是生物醫(yī)學(xué)領(lǐng)域的一個(gè)重要的分支。早在八十年代初,生物數(shù)學(xué)家對腫瘤免疫機(jī)制產(chǎn)生了濃烈的興趣并進(jìn)行了廣泛的實(shí)驗(yàn)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(yīng)性免疫保護(hù)生物體的動(dòng)力學(xué)機(jī)制。隨著生物數(shù)學(xué)科學(xué)的發(fā)展,Kuznetsov提出了經(jīng)典的腫瘤免疫模型——Kuznetsov模型。近二十年,對此腫瘤免疫時(shí)滯系統(tǒng)的穩(wěn)定性和Hopf分支性質(zhì)研究已在腫瘤醫(yī)學(xué)治療得到廣泛應(yīng)用。人體內(nèi)的效應(yīng)細(xì)胞對于潛伏的腫瘤細(xì)胞的攻擊有一定的時(shí)間延遲(時(shí)滯),這一復(fù)雜的免疫過程可以用時(shí)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(shí)滯參數(shù)的系統(tǒng)動(dòng)力學(xué)性質(zhì)主要采用的方法和途徑。所謂分支,就是一類具參數(shù)的動(dòng)力學(xué)系統(tǒng),當(dāng)參數(shù)在臨界值附近發(fā)生微小變動(dòng)的的情況下,系統(tǒng)的動(dòng)力學(xué)性質(zhì)發(fā)生改變的現(xiàn)象。局部Hopf分支是微分方程動(dòng)力系統(tǒng)分支研究中較常見的分支類型,它的產(chǎn)生對應(yīng)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(diǎn)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(shí)滯模型的穩(wěn)定性和Hopf分支性質(zhì)。首先引入了一類具時(shí)滯反饋的腫瘤免疫模型,分析了模型的平衡點(diǎn)的存在性及其穩(wěn)定性。然后定性地研究了Hopf分支性質(zhì)。最后運(yùn)用MATLAB軟件進(jìn)行相應(yīng)的數(shù)值模擬,分析驗(yàn)證了在一段時(shí)期內(nèi),隨著時(shí)間的增長,腫瘤細(xì)胞與免疫細(xì)胞在生物體競爭波動(dòng)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(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O175

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