西尼罗河病毒的建模与研究

发布时间：2018-06-21 02:07

本文选题：西尼罗河病毒 + 基本再生数　；参考：《中北大学》2017年硕士论文

【摘要】：传染病一直以来给人类的生产生活造成极大的威胁,有效的防治传染病是当今世界着手解决的一个重大问题。研究并建立合理的传染病模型是十分重要的。本文主要研究了一种在许多国家流行但在中国还没有发现的传染病:西尼罗河病毒(WNV)。西尼罗河病毒是一种虫媒病毒,WNV的传染源大部分是处于病毒血症期的带有毒性的动物和WNV的自然贮藏宿主,主要是鸟类。通过蚊虫叮咬把病毒传给叮咬对象,在此过程中也会传染给人类,但是人类是偶然宿主。鸟在传播中起着宿主作用,蚊子起着媒介作用,它们之间进行循环传播。WNV对中国人群来说是一种全新的致病病毒,人群缺乏对该病毒的免疫力,一旦感染爆发,会造成严重的后果。因此对WNV的研究是十分必要的。第一章,主要介绍了WNV的研究意义、国内外研究现状以及本文的研究工作。第二章,因为带有logistic增长的种群是比较符合实际情况的,因此本文考虑鸟类和蚊子都为logistic增长的情况,依据此建立模型,并对模型分析,获得了基本再生数R_0,证明了当R_01时,无病平衡点时全局渐进稳定的,当R_01,而且满足不同条件时,得到正平衡点的存在性,并对模型进行数值模拟,验证了理论结果的正确性。第三章,考虑到蚊虫的爆发具有季节性,夏秋季节是蚊虫繁殖时期,蚊虫叮咬率高。在此基础上建立传染率为周期函数的传染病模型,获得了基本再生数,得到无病平衡点的全局稳定性以及正平衡点的存在性。最后在R_01和R_01的情况下对模型进行数值模拟,得到了比较好的结果。第四章,WNV是一种人畜共患病,也会感染人,但是人不会反传给蚊子。据此,本文建立了有偶然宿主的WNV传染病模型,并对模型进行了进一步分析,得到了模型的基本再生数,当基本再生数小于1时,无病平衡点是全局稳定的,当基本再生数大于1时,分析了正平衡点的稳定性,数值模拟验证了理论结果的正确性。第五章,总结以及对未来工作的展望。
[Abstract]:Infectious diseases have always posed a great threat to the production and life of human beings. Effective prevention and treatment of infectious diseases is a major problem to be solved in the world today. It is very important to study and establish a reasonable infectious disease model. In this paper, a new infectious disease, West Nile virus (WNV), which is prevalent in many countries but has not yet been found in China, is studied. West Nile virus (WNV) is a kind of insect-borne virus (WNV). Most of the sources of WNV are viremia animals and natural storage hosts of WNV, mainly birds. Passing the virus through mosquito bites can also spread to humans in the process, but humans are accidental hosts. Birds play a host role in the transmission, mosquitoes act as a vector, and they circulate between them. WNV is a completely new pathogenic virus for Chinese people, who lack immunity to the virus, and once the infection erupts, There are serious consequences. Therefore, the study of WNV is very necessary. The first chapter introduces the significance of WNV research, domestic and international research status and research work in this paper. In the second chapter, because the population with logistic growth is more in line with the actual situation, this paper considers the increase of both birds and mosquitoes as logistic, establishes the model according to this, and analyzes the model, and obtains the basic regenerative number R0, which proves that when R01, The existence of positive equilibrium is obtained when R01 is satisfied and the existence of positive equilibrium is obtained. Numerical simulation of the model is carried out to verify the correctness of the theoretical results. In the third chapter, considering the seasonal outbreak of mosquitoes, the summer and autumn seasons are the breeding period of mosquitoes, and the mosquito bite rate is high. On this basis, the infectious disease model with infection rate as periodic function is established, and the basic reproducing number is obtained. The global stability of disease-free equilibrium and the existence of positive equilibrium point are obtained. Finally, the numerical simulation of the model is carried out in the case of R _ S _ 1 and R _ S _ 01, and a good result is obtained. Chapter 4: WNV is a zoonotic disease that infects humans, but not mosquitoes. Based on this, a WNV infectious disease model with accidental host is established, and the model is further analyzed. The basic reproduction number of the model is obtained. When the basic regeneration number is less than 1, the disease-free equilibrium point is globally stable. The stability of the positive equilibrium point is analyzed when the basic reproduction number is greater than 1, and the correctness of the theoretical results is verified by numerical simulation. Chapter five, summary and prospect of future work.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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