發(fā)布時間：2018-06-06 22:49

  本文選題：流動人口 + 肺結(jié)核模型　； 參考：《北京建筑大學(xué)》2017年碩士論文

【摘要】：地區(qū)經(jīng)濟發(fā)展的差異,使得大量流動人口進入經(jīng)濟發(fā)達地區(qū)。流動人口帶來巨大經(jīng)濟效益的同時,也給傳染病的防治帶來一定挑戰(zhàn)。本文基于流動人口這一因素,在肺結(jié)核傳播機制的基礎(chǔ)上建立了四個帶有流動人口的肺結(jié)核模型:1.建立了帶有外來流入人口和快慢反應(yīng)的肺結(jié)核模型,通過計算得出無病平衡點和地方病平衡點的存在性,利用Hurwitz判據(jù)證明了平衡點處的局部漸近穩(wěn)定性,利用Lyapunov函數(shù)、LaSalle不變集原理證明了特殊條件下平衡點的全局漸近穩(wěn)定性。通過數(shù)值模擬表明對于高低流入人口地區(qū),外來流入潛伏者和快慢反應(yīng)參數(shù)存在不同影響。2.建立了帶有流動人口和本地人口交叉感染的肺結(jié)核動力學(xué)模型,通過理論分析和數(shù)值模擬得,當(dāng)一類群體不存在交叉感染時,另類群體中的交叉感染并不會對系統(tǒng)的再生數(shù)產(chǎn)生影響,當(dāng)兩類群體都存在交叉感染時,任一交叉感染的增加都會提高系統(tǒng)的基本再生數(shù),這時控制每類群體中的基本再生數(shù)小于1,并不能達到消除疾病的目的,必須控制整個系統(tǒng)的基本再生數(shù)。因此在制定控制措施時,合理的控制交叉感染尤為重要。3.建立了帶有兩地區(qū)間人口流動的肺結(jié)核動力學(xué)模型,通過計算得到系統(tǒng)基本再生數(shù),并證明基本再生數(shù)R(29)1時,無病平衡點不穩(wěn)定,基本再生數(shù)R(27)1時,無病平衡點是局部漸進穩(wěn)定的。通過模型分析得出系統(tǒng)的兩個邊界平衡點并求出邊界平衡點的穩(wěn)定性不只受發(fā)病區(qū)再生數(shù)的影響,還與平衡點及另一地區(qū)再生數(shù)有關(guān)。4.以流入廣東省的人口數(shù)和肺結(jié)核發(fā)病數(shù)作為依據(jù),將流入人口5萬以上的22個省份通過聚類分析分成兩類,建立了包含兩類不同來源人口分段的SEIR肺結(jié)核數(shù)學(xué)模型,計算疾病的有效再生數(shù)。在此基礎(chǔ)上建立了最優(yōu)免疫規(guī)劃模型,通過求解得到廣東本省人口,第I類及第II類移入廣東地區(qū)的人口最優(yōu)免疫接種比例,確定了肺結(jié)核防控的最優(yōu)控制方案,并通過數(shù)值模擬驗證分析結(jié)果的可靠性。
[Abstract]:The difference in regional economic development makes a large number of floating population into the economically developed areas. While the floating population brings huge economic benefits, it also brings some challenges to the prevention and control of infectious diseases. Based on the factors of floating population, this paper establishes four tuberculosis models with floating population on the basis of the mechanism of tuberculosis transmission: 1. The tuberculosis model with the influx of population and the fast and slow reaction is obtained. By calculating the existence of the disease free equilibrium point and the existence of the endemic equilibrium point, the Hurwitz criterion is used to prove the local asymptotic stability at the equilibrium point. The global asymptotic stability of the equilibrium point under special conditions is proved by the Lyapunov function and the LaSalle invariant set principle. The over numerical simulation shows that there are different effects on the influx of latent and slow response parameters for high and low inflow areas..2. has established a pulmonary tuberculosis dynamic model with the cross infection of the floating population and the local population. Through theoretical analysis and numerical simulation, when a group of groups does not exist cross infection, the intersecting of alternative groups Infection does not affect the number of regeneration of the system. When there are cross infections in the two groups, the increase of any cross infection will increase the basic regeneration number of the system. At this time, the basic regeneration number of each group is less than 1, and the basic regeneration number of the whole system must be controlled. Therefore, the system must be controlled. When controlling the control measures, the rational control of cross infection is particularly important for.3. to establish a pulmonary tuberculosis dynamic model with the population flow in two regions. The basic regeneration number of the system is obtained by calculation, and it is proved that when the basic regeneration number is R (29) 1, the disease free equilibrium point is unstable and the basic regeneration number is R (27) 1, and the disease free equilibrium point is locally asymptotically stable. The model analysis shows that the stability of the two boundary equilibrium points and finding the equilibrium point of the boundary is not only affected by the number of regeneration in the incidence area, but also related to the equilibrium point and the number of the other regions in the region of.4. to flow into the population of Guangdong and the number of tuberculosis, and the 22 provinces which are over 50 thousand of the population are divided into two by cluster analysis. A mathematical model of SEIR tuberculosis containing two different sources of population was established to calculate the effective regeneration number of the disease. On this basis, the optimal immune programming model was established. By solving the optimal immunization ratio of population, class I and class II, the optimal immunization ratio of the population in Guangdong province was obtained, and the optimal prevention and control of tuberculosis was determined. The reliability of the analysis results is verified by numerical simulation.
【學(xué)位授予單位】：北京建筑大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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相關(guān)期刊論文 前3條

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本文編號：1988423