本文關(guān)鍵詞：一類帶時(shí)滯且具有預(yù)防接種免疫力的SIR傳染病模型的穩(wěn)定性與Hopf分岔分析　出處：《天津大學(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 無病平衡點(diǎn) 地方病平衡點(diǎn) 穩(wěn)定性 Hopf分岔

【摘要】：本文所研究的問題是一類帶時(shí)滯且具有預(yù)防接種免疫力的SIR傳染病模型的穩(wěn)定性及Hopf分岔情況. 全文的內(nèi)容分為兩部分：首先是建模的過程,其次是分析該模型無病平衡點(diǎn)和地方病平衡點(diǎn)的穩(wěn)定性和Hopf分岔的情況. 在建模過程中,我們充分考慮了一定的種群增長(zhǎng)、疾病的傳染速度、預(yù)防接種、自然死亡、因病死亡、治愈情況、疾病潛伏期等多種因素,使得我們所建模型能更貼切地反應(yīng)本文所研究問題的真實(shí)情況. 本文所建模型為： 建模后,全文關(guān)心的問題是潛伏期對(duì)模型穩(wěn)定性和分岔的影響,所利用的知識(shí)和方法有：穩(wěn)定性和分岔理論、特征值法、中心流形、規(guī)范型方法. 最后,通過嚴(yán)密的論證,得出了： (1)模型無病平衡點(diǎn)和地方病平衡點(diǎn)存在的條件； (2)模型無病平衡點(diǎn)的穩(wěn)定性和Hopf分岔的情況； (3)模型地方病平衡點(diǎn)的穩(wěn)定性和Hopf分岔的情況； (4)模型地方病平衡點(diǎn)的Hopf分岔周期解的穩(wěn)定性和分岔方向的計(jì)算公式.
[Abstract]:The problem studied in this paper is the stability and Hopf bifurcation of a class of SIR infectious disease models with time delay and immunity from inoculation. The content of this paper is divided into two parts: first, the process of modeling, and secondly, the stability of the disease-free equilibrium and endemic equilibrium and the Hopf bifurcation of the model are analyzed. In the process of modeling, we fully considered a certain number of factors, such as population growth, disease transmission rate, vaccination, natural death, disease death, cure situation, disease incubation period and so on. The model can reflect the real situation of the problem studied in this paper. The models in this paper are as follows: After modeling, the effect of incubation period on the stability and bifurcation of the model is concerned. The knowledge and methods are as follows: stability and bifurcation theory, eigenvalue method, center manifold, canonical form method. Finally, through rigorous argumentation, it is concluded that: 1) the conditions for the existence of disease-free equilibrium and endemic equilibrium in the model; (2) the stability of the disease-free equilibrium point and the Hopf bifurcation of the model; (3) the stability of the endemic equilibrium point and the Hopf bifurcation of the model; 4) the stability and bifurcation direction of the Hopf bifurcation periodic solution of the endemic equilibrium point of the model.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：R311;R181.3

【參考文獻(xiàn)】

相關(guān)期刊論文 前6條

1 原三領(lǐng),蔣里強(qiáng);一類具有非線性飽和傳染力的傳染病模型[J];工程數(shù)學(xué)學(xué)報(bào);2001年04期

2 徐文雄,張仲華;具有預(yù)防接種免疫力的雙線性傳染率SIR流行病模型全局穩(wěn)定性[J];大學(xué)數(shù)學(xué);2003年06期

3 靳禎,馬知恩;具有連續(xù)和脈沖預(yù)防接種的SIRS傳染病模型[J];華北工學(xué)院學(xué)報(bào);2003年04期

4 桂占吉;一類非自治SIS傳染病模型的持續(xù)性[J];海南師范學(xué)院學(xué)報(bào)(自然科學(xué)版);2000年02期

5 趙仕杰;袁朝暉;;一類時(shí)滯SIR傳染病模型的穩(wěn)定性與Hopf分岔分析[J];經(jīng)濟(jì)數(shù)學(xué);2010年03期

6 徐文雄,張仲華;年齡結(jié)構(gòu)SIR流行病傳播數(shù)學(xué)模型漸近分析[J];西安交通大學(xué)學(xué)報(bào);2003年10期

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