本文選題：雙線性 + 標(biāo)準(zhǔn)型�。� 參考：《北方工業(yè)大學(xué)》2011年碩士論文

【摘要】：我國(guó)1985年首次發(fā)現(xiàn)艾滋病后,艾滋病以傳播迅速、無(wú)法治療而震驚全國(guó).當(dāng)前,人類正面臨著艾滋病長(zhǎng)期而嚴(yán)峻的威脅.因此,建立能反映艾滋病特性的數(shù)學(xué)模型.通過(guò)對(duì)模型的分析,揭示其流行規(guī)律,預(yù)測(cè)其發(fā)展趨勢(shì),分析疾病流行的原因,尋求預(yù)防和控制的策略是非常必要的. 本文建立了一類多因素HIV傳染病動(dòng)力學(xué)模型,建立了三種模型：雙線性模型；標(biāo)準(zhǔn)型模型；SP模型.并進(jìn)行了理論性研究.在建立數(shù)學(xué)模型時(shí),主要參考了馬知恩,James M. Hyman等人的文章.在證明過(guò)程中,主要利用了M矩陣?yán)碚?LaSalle不變?cè)?Liapunov函數(shù)進(jìn)行證明,得到了無(wú)病平衡點(diǎn)的穩(wěn)定性定理.所得結(jié)果推廣、豐富了已有文獻(xiàn)中的相關(guān)結(jié)論. 首先,介紹了研究傳染病的重要意義、HIV/AIDS的研究現(xiàn)狀、預(yù)備知識(shí)、本文的研究?jī)?nèi)容與結(jié)構(gòu)安排. 其次,建立了雙線性HIV模型.求出了基本再生數(shù),證明了無(wú)病平衡點(diǎn)的局部漸近穩(wěn)定性與全局漸近穩(wěn)定性. 再次,建立了標(biāo)準(zhǔn)型HIV模型.求出了基本再生數(shù),證明了無(wú)病平衡點(diǎn)的局部漸近穩(wěn)定性與全局漸近穩(wěn)定性；給出了一些持續(xù)生存的概念和結(jié)論,證明了系統(tǒng)的一致持續(xù)生存性. 最后,建立了SP模型.求出了基本再生數(shù)R0,證明了當(dāng)R01時(shí),無(wú)病平衡點(diǎn)是局部漸近穩(wěn)定的和全局漸近穩(wěn)定的；當(dāng)R01時(shí),無(wú)病平衡點(diǎn)是不穩(wěn)定的.
[Abstract]:After our country first discovered AIDS in 1985, AIDS shocked the whole country because of its rapid spread and untreatable. At present, human beings are facing the long-term and severe threat of AIDS. Therefore, the establishment of mathematical models can reflect the characteristics of AIDS. Through the analysis of the model, it is very necessary to reveal its epidemic law, forecast its developing trend, analyze the cause of disease epidemic, and seek the strategy of prevention and control. In this paper, a class of multi-factor HIV epidemic dynamics model is established, and three models are established: bilinear model, standard model and SP model. And carried on the theoretical research. In establishing the mathematical model, we mainly refer to the paper by James M. Hyman et al. In the process of proving, we mainly use M-matrix theory and LaSalle invariant principle to prove the stability theorem of disease-free equilibrium. The generalization of the results enriches the relevant conclusions in the previous literature. Firstly, this paper introduces the significance of HIV / AIDS research, the preparatory knowledge, the content and structure of this study. Secondly, a bilinear HIV model is established. The basic reproducing numbers are obtained and the local asymptotic stability and global asymptotic stability of disease-free equilibrium are proved. Thirdly, the standard HIV model is established. The local asymptotic stability and global asymptotic stability of disease-free equilibrium are proved, and some concepts and conclusions of persistent existence are given, and the uniform persistence of the system is proved. Finally, the SP model is established. The basic reproducing number R _ 0 is obtained and it is proved that the disease-free equilibrium is locally asymptotically stable and globally asymptotically stable when R _ 01, and that the disease-free equilibrium is unstable at R _ 01.
【學(xué)位授予單位】：北方工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2011
【分類號(hào)】：R311;O242.1

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

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本文編號(hào)：1961300