本文選題：流行病模型 + 階段結(jié)構(gòu)��； 參考：《西南師范大學(xué)》2005年碩士論文

【摘要】：本文主要討論了離散的階段結(jié)構(gòu)傳染病模型。 第一章建立并研究了離散的單種群階段結(jié)構(gòu)模型,討論了平衡點(diǎn)的存在性和穩(wěn)定性,證明了種群的持續(xù)生存。對(duì)于Beverton-Holt形式的出生率,證明了其正平衡點(diǎn)的漸近穩(wěn)定性,計(jì)算機(jī)模擬表明當(dāng)不考慮時(shí)滯時(shí),正平衡點(diǎn)是全局漸近穩(wěn)定的;對(duì)于Ricker形式的出生率,作出了其在幾種參數(shù)條件下的分支圖,倍周期分支會(huì)出現(xiàn),然后產(chǎn)生混沌,和一般的Logistic模型的分支圖相比,分支圖變得更為復(fù)雜,時(shí)滯和階段結(jié)構(gòu)會(huì)延緩混沌的出現(xiàn)。 本文第二章建立并研究了離散的階段結(jié)構(gòu)成年病模型。得到了疾病的基本再生數(shù)R_0,其計(jì)算過(guò)程比一般的微分方程模型更為復(fù)雜,這是因?yàn)榇藭r(shí)無(wú)病空間上的吸引子可以是平衡點(diǎn),也可以是周期解或者奇怪吸引子。對(duì)于Beverton-Holt形式出生率的離散階段結(jié)構(gòu)成年病模型,當(dāng)恢復(fù)率為零時(shí)證明了無(wú)病平衡點(diǎn)的全局穩(wěn)定性。我們還可以發(fā)現(xiàn)基本再生數(shù)R_0關(guān)于系統(tǒng)內(nèi)所有的參數(shù)單調(diào)。對(duì)于Ricker形式的出生率,我們發(fā)現(xiàn)隨著自然增長(zhǎng)率的變化疾病的存在和消除可能會(huì)交替出現(xiàn)。此種計(jì)算基本再生數(shù)的方法可以被其它的一些離散模型所用。 本文第三章研究了離散的階段結(jié)構(gòu)時(shí)滯傳染病模型。運(yùn)用第二章尋求基本再生數(shù)的方法對(duì)兩種出生函數(shù)分別進(jìn)行了研究,得出了基本再生數(shù),可以看到,時(shí)滯模型比非時(shí)滯模型得性態(tài)更為復(fù)雜.發(fā)現(xiàn)隨著自然增長(zhǎng)率的變化疾病的存在和消除仍然可能會(huì)交替出現(xiàn)。
[Abstract]:In this paper, the discrete structural infectious disease model is discussed. In chapter 1, the discrete single-population structure model is established and studied. The existence and stability of the equilibrium point are discussed, and the persistence of the population is proved. For the birth rate of Beverton-Holt form, the asymptotic stability of the positive equilibrium point is proved. The computer simulation shows that the positive equilibrium point is globally asymptotically stable when time delay is not considered, and for the birth rate in Ricker form, the positive equilibrium point is globally asymptotically stable. In this paper, the bifurcation graph under several parameter conditions is given, the double periodic bifurcation will appear, and then chaos will occur. Compared with the general branching graph of Logistic model, the branching graph becomes more complex, and the delay and phase structure will delay the emergence of chaos. In chapter 2, discrete structural adult disease models are established and studied. The basic regenerative number R _ S _ 0 of the disease is obtained, and the calculation process is more complicated than the ordinary differential equation model. This is because the attractor in the disease-free space can be an equilibrium point, a periodic solution or a strange attractor. The global stability of disease-free equilibrium point is proved when the recovery rate is 00:00 for the discrete stage structured adult disease model of Beverton-Holt form birth rate. We can also find that the basic reproduction number R _ S _ 0 is monotone for all the parameters in the system. For the birth rate in the form of Ricker, we find that the existence and elimination of diseases may alternate with the change of natural growth rate. This method can be used in other discrete models. In the third chapter, we study the discrete stage structural time-delay infectious disease model. In the second chapter, we study the two kinds of birth function by using the method of searching for the basic reproducing number, and get the basic reproducing number. It can be seen that the delay model is more complex than the non-delay model. It is found that the existence and elimination of diseases may alternate with the change of natural growth rate.
【學(xué)位授予單位】：西南師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2005
【分類號(hào)】：R181.3

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 金瑜,張勇,王穩(wěn)地;一類具有階段結(jié)構(gòu)的傳染病模型[J];西南師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2003年06期

2 劉賢寧;一個(gè)離散單種群擴(kuò)散模型的全局漸近穩(wěn)定性[J];西南師范大學(xué)學(xué)報(bào)(自然科學(xué)版);1998年06期

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本文編號(hào)：1813558