本文關(guān)鍵詞：具有時(shí)滯的SEIR的肺結(jié)核模型研究　出處：《西安科技大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 時(shí)滯 肺結(jié)核 基本再生數(shù) 穩(wěn)定性 持續(xù)性

【摘要】：本文考慮肺結(jié)核在潛伏期和染病期都具有傳染性，建立了幾類具有不同傳染率的SEIR肺結(jié)核傳播時(shí)滯微分方程模型.綜合運(yùn)用微分方程理論等方法對(duì)模型的無(wú)病平衡點(diǎn)的全局漸近穩(wěn)定性、地方平衡點(diǎn)的局部穩(wěn)定性及疾病的持續(xù)性做了系統(tǒng)的研究.得到了決定疾病絕滅與否的基本再生數(shù). 首先，建立了一類具有雙線性傳染率的SEIR肺結(jié)核模型.利用不動(dòng)點(diǎn)理論、微分方程穩(wěn)定性理論及LaSalle不變集原理研究了模型的平衡點(diǎn)的存在性、穩(wěn)定性及系統(tǒng)的持續(xù)性.當(dāng)時(shí)，無(wú)病平衡點(diǎn)全局漸近穩(wěn)定，疾病將消除；當(dāng)時(shí)無(wú)病平衡點(diǎn)不穩(wěn)定，惟一的地方病平衡點(diǎn)全局穩(wěn)定且系統(tǒng)是持續(xù)的. 再次，建立了一類具有型傳染率的肺結(jié)核模型.通過(guò)線性化方法和Hurwitz判別法及LaSalle不變集原理研究了模型的無(wú)病平衡點(diǎn)的全局漸近穩(wěn)定性及地方病平衡點(diǎn)的局部漸近穩(wěn)定性，得到了依賴于時(shí)滯的基本再生數(shù)，，并討論了模型在時(shí)的持續(xù)性. 最后，建立了一類具有垂直傳染和預(yù)防接種的肺結(jié)核模型.討論了地方病平衡點(diǎn)的存在惟一性、穩(wěn)定性及模型的持續(xù)性.通過(guò)分析模型的基本再生數(shù)并提出了合理的預(yù)防和控制措施，最后通過(guò)數(shù)值模擬驗(yàn)證所得的理論結(jié)果.為肺結(jié)核傳播的控制和預(yù)防提供理論依據(jù)和數(shù)量基礎(chǔ).
[Abstract]:In this paper, we consider that tuberculosis is infectious in both incubation period and infection stage. In this paper, several kinds of delay differential equation models of SEIR tuberculosis transmission with different infection rates are established, and the global asymptotic stability of the disease-free equilibrium point of the model is obtained by using the differential equation theory and other methods. The local stability of the local equilibrium point and the persistence of the disease are systematically studied, and the basic regeneration numbers which determine the extinction or extinction of the disease are obtained. Firstly, a class of SEIR pulmonary tuberculosis model with bilinear infection rate is established, and the fixed point theory is used. The stability theory of differential equations and the LaSalle invariant set principle are used to study the existence, stability and persistence of the equilibrium point of the model. At that time, the disease-free equilibrium point is globally asymptotically stable and the disease will be eliminated. At that time, the disease-free equilibrium was unstable, the only endemic equilibrium was globally stable and the system was persistent. Again. A class of pulmonary tuberculosis models with type infection rate is established. The global asymptotic stability and ground of disease-free equilibrium of the model are studied by means of linearization method, Hurwitz criterion and LaSalle invariant set principle. The local asymptotic stability of the equilibrium point of square disease. The basic reproducing numbers dependent on time delay are obtained, and the persistence of the model in time is discussed. Finally, a class of pulmonary tuberculosis models with vertical transmission and vaccination are established, and the existence and uniqueness of endemic equilibrium are discussed. Stability and sustainability of the model. By analyzing the basic regeneration number of the model, reasonable prevention and control measures are proposed. Finally, the theoretical results are verified by numerical simulation, which provide theoretical basis and quantitative basis for the control and prevention of tuberculosis transmission.
【學(xué)位授予單位】：西安科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：O175;R311

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