西尼罗河病毒扩散的周期性和空间特征研究
发布时间：2018-12-13 01:26
【摘要】：传染病严重威胁人们的健康,并对社会的稳定和经济的发展产生重要影响.一直以来,人们与传染病做着不屈不挠的斗争.西尼罗河病毒是一种虫媒传染病,可以感染人、马、鸟、蚊子和其它动物,蚊子是其主要传播媒介.本文主要研究描述西尼罗河病毒传播的传染病数学模型.首先在前人工作的基础上简化模型并研究其行波解.然后考虑到环境的周期性和空间的非均质性对病毒传播的影响,我们进一步研究周期反应扩散问题和非均质空间上的反应扩散问题,通过定性分析和数值模拟给出病毒发展趋势的预测.论文具体包括六个部分.第一章简要介绍了传染病的历史及其模型的发展和研究的现状,然后引入了西尼罗河病毒模型及相关数学问题.第二章在Wonham和Lewis西尼罗河病毒模型的基础上利用蚊子和鸟的关系简化模型并研究其行波解.第三章考虑了环境的周期性变化这一实际现象,我们研究具周期条件的反应扩散问题.利用上下解方法及其迭代序列得到周期解的存在性.第四章考虑蚊子和鸟所在空间位置的不同特征,我们研究非均质空间的西尼罗河病毒模型,讨论无病平衡点和染病平衡点的存在性,唯一性以及全局稳定性.第五章我们使用Matlab软件对上述的部分结论进行数值模拟,用图像和数值结果来检验已得的理论结果.第六章对整篇文章进行总结并给出将来需要研究的问题.
[Abstract]:Infectious diseases seriously threaten people's health and have an important impact on social stability and economic development. For a long time, people have been making indomitable struggle against infectious diseases. West Nile virus (WNV) is an insect-borne disease that infects humans, horses, birds, mosquitoes and other animals. In this paper, a mathematical model describing the transmission of West Nile virus (WNV) is studied. Firstly, the model is simplified on the basis of previous work and its traveling wave solution is studied. Then, considering the effects of environmental periodicity and spatial heterogeneity on virus transmission, we further study the problem of periodic reaction-diffusion and the problem of reaction-diffusion in heterogeneous spaces. The trend of virus development is predicted by qualitative analysis and numerical simulation. The thesis includes six parts. The first chapter briefly introduces the history of infectious diseases, the development of models and research status, and then introduces the West Nile virus model and related mathematical problems. In chapter 2, based on the Wonham and Lewis West Nile virus models, the relationship between mosquitoes and birds is simplified and the traveling wave solutions are studied. In chapter 3, we consider the phenomenon of periodic change of environment, and we study the problem of reaction diffusion with periodic conditions. The existence of periodic solutions is obtained by using the upper and lower solution method and its iterative sequence. In chapter 4, we study the West Nile virus model in heterogeneous space, and discuss the existence, uniqueness and global stability of disease-free equilibrium and disease-free equilibrium. In chapter 5, we use Matlab software to simulate some of the above conclusions, and use the image and numerical results to verify the obtained theoretical results. Chapter 6 summarizes the whole article and gives some problems that need to be studied in the future.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
，
本文编号：2375610
[Abstract]:Infectious diseases seriously threaten people's health and have an important impact on social stability and economic development. For a long time, people have been making indomitable struggle against infectious diseases. West Nile virus (WNV) is an insect-borne disease that infects humans, horses, birds, mosquitoes and other animals. In this paper, a mathematical model describing the transmission of West Nile virus (WNV) is studied. Firstly, the model is simplified on the basis of previous work and its traveling wave solution is studied. Then, considering the effects of environmental periodicity and spatial heterogeneity on virus transmission, we further study the problem of periodic reaction-diffusion and the problem of reaction-diffusion in heterogeneous spaces. The trend of virus development is predicted by qualitative analysis and numerical simulation. The thesis includes six parts. The first chapter briefly introduces the history of infectious diseases, the development of models and research status, and then introduces the West Nile virus model and related mathematical problems. In chapter 2, based on the Wonham and Lewis West Nile virus models, the relationship between mosquitoes and birds is simplified and the traveling wave solutions are studied. In chapter 3, we consider the phenomenon of periodic change of environment, and we study the problem of reaction diffusion with periodic conditions. The existence of periodic solutions is obtained by using the upper and lower solution method and its iterative sequence. In chapter 4, we study the West Nile virus model in heterogeneous space, and discuss the existence, uniqueness and global stability of disease-free equilibrium and disease-free equilibrium. In chapter 5, we use Matlab software to simulate some of the above conclusions, and use the image and numerical results to verify the obtained theoretical results. Chapter 6 summarizes the whole article and gives some problems that need to be studied in the future.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
，
本文编号：2375610
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