發(fā)布時間：2018-10-15 19:11

【摘要】： 本論文對具有年齡結(jié)構(gòu)的傳染病模型進(jìn)行了研究。 建立傳染病模型的主要目的是利用模型對影響疾病傳播的生物學(xué)和社會學(xué)機(jī)理作清晰描述,然后通過模型的研究來揭示疾病流行規(guī)律,預(yù)測流行趨勢,為發(fā)現(xiàn)、預(yù)防和控制疾病的流行提供根據(jù)和策略。 本文針對不同的傳染病的傳播特點,建立了三類具有年齡結(jié)構(gòu)的傳染病模型,分別是：具有年齡和隔離措施的SEIQR模型,具有年齡結(jié)構(gòu)的手足口病模型和具有年齡結(jié)構(gòu)和常數(shù)遷移率的SIR模型。 這三類模型都是偏微分方程組,本文使用傳染病動力學(xué)中的有關(guān)方法和實變函數(shù)論中的有關(guān)理論對模型進(jìn)行了分析,得到了模型無病平衡態(tài)和地方病平衡態(tài)的存在性和穩(wěn)定性條件,并且證明了在基本再生數(shù)小于1時,無病平衡態(tài)是局部漸近穩(wěn)定(或全局漸近穩(wěn)定)的,當(dāng)基本再生數(shù)大于1時,地方病平衡態(tài)在一定條件下局部漸近穩(wěn)定(或模型在地方病平衡態(tài)處的線性化系統(tǒng)的特征方程無非負(fù)實根)。 最后,在上述理論結(jié)果的基礎(chǔ)上,對這些偏微分方程組的解進(jìn)行數(shù)值模擬,給出了模型的差分格式,然后對模型的差分格式進(jìn)行了Matlab編程。最后,對模型中易感者和染病者的發(fā)展趨勢進(jìn)行了模擬。在進(jìn)行計算機(jī)試驗的過程中,通過改變各個參數(shù)的數(shù)值,尋找對傳染病發(fā)展影響較大的因素,為以后的生活實踐提供了很好的依據(jù)。 試驗結(jié)果表明,傳染病模型的兩個平衡態(tài)是和基本再生數(shù)息息相關(guān)的。而基本再生數(shù)又依賴于模型中的參數(shù),于是,我們可以通過對某些參數(shù)的控制,來控制傳染病的傳播。 本文的創(chuàng)新點體現(xiàn)在將傳染病動力學(xué)中的有關(guān)方法成功地應(yīng)用于具有年齡結(jié)構(gòu)的傳染病模型中,而且對模型的地方病平衡態(tài)進(jìn)行了比較深入的分析。
[Abstract]:In this paper, the infectious disease model with age structure is studied. The main purpose of establishing infectious disease model is to clearly describe the biological and sociological mechanism of disease transmission by using the model, and then to reveal the epidemic law and predict the epidemic trend through the study of the model. The prevention and control of disease prevalence provides the basis and strategy. In this paper, according to the transmission characteristics of different infectious diseases, three kinds of infectious disease models with age structure are established, which are SEIQR model with age and isolation measures. Hand-foot-mouth disease model with age structure and SIR model with age structure and constant mobility. These three models are all partial differential equations. In this paper, the models are analyzed by using the relevant methods in infectious disease dynamics and the theory of real variable function theory. The existence and stability conditions of disease-free equilibrium state and endemic equilibrium state are obtained, and it is proved that the disease-free equilibrium state is locally asymptotically stable (or globally asymptotically stable) when the basic regeneration number is less than 1. When the basic regeneration number is greater than 1, the endemic equilibrium state is locally asymptotically stable under certain conditions (or the characteristic equations of the linearized system of the model at the endemic equilibrium state are all negative real roots). Finally, on the basis of the above theoretical results, the solutions of these partial differential equations are numerically simulated, the difference scheme of the model is given, and the difference scheme of the model is programmed by Matlab. Finally, the development trend of susceptible and infected people in the model was simulated. In the course of computer experiment, by changing the values of each parameter, the factors which have great influence on the development of infectious diseases are found, which provides a good basis for the later life practice. The experimental results show that the two equilibrium states of the infectious disease model are closely related to the basic regeneration number. The basic reproduction number depends on the parameters in the model, so we can control the spread of infectious diseases by controlling some parameters. The innovation of this paper lies in the successful application of the relevant methods in the dynamics of infectious diseases to the epidemic model with age structure and the analysis of the endemic equilibrium state of the model.
【學(xué)位授予單位】：北京林業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2010
【分類號】：R181.3

【引證文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 彭華勤;多個斑塊間傳播的傳染病模型的研究[D];廣州大學(xué);2012年

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本文編號：2273551