几类甲型H1N1流感SEIRS斑块模型的定性研究

发布时间：2018-04-11 11:13

本文选题：SIR + 仓室模型　；参考：《西安科技大学》2012年硕士论文

【摘要】：本文以经典的SIR仓室模型为基础，考虑疾病具有潜伏期、人员在不同区域流动等因素，建立了几类甲型H1N1流感传播的SEIRS传染病模型.利用矩阵谱半径定义基本再生数并得到了几类模型的基本再生数，证明了基本再生数决定的模型的动力学性态，如平衡点的存在性和稳定性等.所得结果能够为疾病的预防和控制提供理论依据和数量基础. 首先，建立了一类具有两个彼此独立斑块的SEIRS模型，利用矩阵谱半径来定义模型的基本再生数，得到了该模型的基本再生数R0的表达式，并证明了当R01时无病平衡点0的不稳定性及当R01时无病平衡点是全局渐近稳定性.通过分析基本再生数的表达式发现当参数c（国家和政府采取的保护措施）的值越大，基本再生数越小，疾病越容易控制.最后通过数值模拟也验证了该理论结果. 其次，建立了一类具有两个斑块且只有一个斑块迁移的SEIRS模型.得到了决定疾病消亡与否的基本再生数R0.证明了当R01时无病平衡点0的不稳定性以及当R01时无病平衡点0的全局渐近稳定性.数值模拟结果显示：当R01时，第二个斑块的染病者曲线很快地收敛于零，而第一个斑块的染病者曲线则是先逐渐上升达到某一峰值然后再逐渐下降最终趋于零.接着考虑两个斑块具有相同或者不同迁移率的SEIRS模型并得到基本再生数的理论表达式.数值模拟结果显示：当R01时，两个斑块的染病者人数均趋近于一个常数，表明该疾病将会在此地流行而成为地方病；当R01时，两个斑块的染病者人数最终均趋近于零，，表明该疾病将会逐渐消亡. 最后，推广两个斑块上的SEIRS模型到n个斑块，利用矩阵谱半径的方法定义并得到了具有n个斑块的SEIRS模型基本再生数的一般表达式，讨论了该模型的平衡点存在性和稳定性.
[Abstract]:Based on the classical SIR chamber model and considering the latent period of the disease and the movement of personnel in different regions, several SEIRS infectious disease models of A / H1N1 influenza transmission were established in this paper.The fundamental reproducing number is defined by using the matrix spectral radius and the basic reproducing numbers of several kinds of models are obtained. The dynamical behavior of the model determined by the basic reproduction number is proved, such as the existence and stability of the equilibrium point, etc.The results can provide theoretical basis and quantitative basis for disease prevention and control.Firstly, a class of SEIRS model with two independent patches is established. The basic reproduction number of the model is defined by using the matrix spectral radius, and the expression of the basic reproduction number R _ 0 of the model is obtained.The instability of the disease-free equilibrium 0 at R01 and the global asymptotic stability of the disease-free equilibrium at R01 are proved.By analyzing the expression of basic reproduction number, it is found that when the value of parameter c (protection measures taken by state and government) is larger, the number of basic regeneration is smaller, and the disease is easier to control.Finally, the theoretical results are verified by numerical simulation.Secondly, a SEIRS model with two patches and only one patch migration is established.The basic regeneration number R0.The instability of the disease-free equilibrium 0 at R01 and the global asymptotic stability of the disease-free equilibrium 0 at R01 are proved.The numerical simulation results show that when R01, the second patch curve converges to zero quickly, while the first patch curve rises to a certain peak at first and then decreases gradually to zero.Then the SEIRS model of two patches with the same or different mobility is considered and the theoretical expression of the basic regeneration number is obtained.The numerical simulation results show that when R01, the number of people infected with both plaques approaches a constant, indicating that the disease will become endemic in this area, and when R01, the number of infected people of both plaques eventually approaches zero.This suggests that the disease will die out.Finally, we generalize the SEIRS model on two patches to n patches, define and obtain the general expression of the basic regeneration number of the SEIRS model with n patches by using the method of matrix spectral radius, and discuss the existence and stability of the equilibrium point of the model.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：O175;R311

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