带有流动人口肺结核模型的研究

发布时间：2018-06-06 22:49

本文选题：流动人口 + 肺结核模型　；参考：《北京建筑大学》2017年硕士论文

【摘要】：地区经济发展的差异,使得大量流动人口进入经济发达地区。流动人口带来巨大经济效益的同时,也给传染病的防治带来一定挑战。本文基于流动人口这一因素,在肺结核传播机制的基础上建立了四个带有流动人口的肺结核模型:1.建立了带有外来流入人口和快慢反应的肺结核模型,通过计算得出无病平衡点和地方病平衡点的存在性,利用Hurwitz判据证明了平衡点处的局部渐近稳定性,利用Lyapunov函数、LaSalle不变集原理证明了特殊条件下平衡点的全局渐近稳定性。通过数值模拟表明对于高低流入人口地区,外来流入潜伏者和快慢反应参数存在不同影响。2.建立了带有流动人口和本地人口交叉感染的肺结核动力学模型,通过理论分析和数值模拟得,当一类群体不存在交叉感染时,另类群体中的交叉感染并不会对系统的再生数产生影响,当两类群体都存在交叉感染时,任一交叉感染的增加都会提高系统的基本再生数,这时控制每类群体中的基本再生数小于1,并不能达到消除疾病的目的,必须控制整个系统的基本再生数。因此在制定控制措施时,合理的控制交叉感染尤为重要。3.建立了带有两地区间人口流动的肺结核动力学模型,通过计算得到系统基本再生数,并证明基本再生数R(29)1时,无病平衡点不稳定,基本再生数R(27)1时,无病平衡点是局部渐进稳定的。通过模型分析得出系统的两个边界平衡点并求出边界平衡点的稳定性不只受发病区再生数的影响,还与平衡点及另一地区再生数有关。4.以流入广东省的人口数和肺结核发病数作为依据,将流入人口5万以上的22个省份通过聚类分析分成两类,建立了包含两类不同来源人口分段的SEIR肺结核数学模型,计算疾病的有效再生数。在此基础上建立了最优免疫规划模型,通过求解得到广东本省人口,第I类及第II类移入广东地区的人口最优免疫接种比例,确定了肺结核防控的最优控制方案,并通过数值模拟验证分析结果的可靠性。
[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.
【学位授予单位】：北京建筑大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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