两类含有绝育蚊子的疟疾传播模型的定性分析

发布时间：2018-04-11 18:03

本文选题：绝育蚊子 + 常数投放　；参考：《华中师范大学》2017年硕士论文

【摘要】：疟疾是世界上最常见也是最严重的热带传染病之一,对人类生活带来了极大的危害.为控制疟疾的传播,科学家们作出了大量的研究.世界卫生组织和很多国家对疟疾也高度重视,均采取了相应措施以对抗疟疾.本文建立了两个含有绝育蚊子的疟疾传播模型,对疟疾模型作出定性分析并得到相关结论.最后根据所得出的结论提出了相应的控制策略.本文共分为四章,第一章的引言部分介绍了疟疾的发病原理和传播机制以及科学家们为对抗疟疾所采取的相关措施.预备知识部分介绍了本文所涉及到的传染病动力学的相关概念和定理.本章最后介绍了疟疾动力学模型的发展进程并提出了本文的基本模型.第二章我们研究了绝育蚊子常数投放的疟疾传染病模型.首先在第一节中研究了仅含有绝育蚊子和野生蚊子的二维动力学模型,通过对模型进行定性分析,寻找到绝育蚊子的投放阈值b0,当绝育蚊子投放量b大于或等于b0,野生蚊子最终消失;当b小于b0时,野生蚊子与绝育蚊子共存.接着本章研究了既含有人口项又含有蚊虫项的八维疟疾模型,通过对无病平衡点局部稳定性的分析,我们得出当基本再生数R0小于1时,无病平衡点局部渐进稳定;当基本再生数R0大于1时,地方病平衡点存在.通过令R0=1寻找到小于b0的更具有实际意义的投放阈值b*.数值模拟显示结论与实际相符,数值模拟过程中我们发现当R0小于1时,地方病平衡点依旧存在,因此系统在R0=1处可能存在后向分支,则第四节中对后向分支的存在性作出了理论性证明.本章结论显示投放绝育蚊子对控制疟疾传播有显著作用.考虑到有些地区野生蚊子数量相对较少,从经济学角度来讲,常数投放的成本较大,因此第三章我们研究了绝育蚊子成比例投放的疟疾传染病模型,相应的此时野生蚊子输入项中我们考虑Allee效应.具体的分析计算过程与常数投放类似,通过数值模拟,验证所得结论与实际相符.绝育蚊子对疟疾控制作用显著,而且根据不同地区蚊子的数量情况,采取不同的投放措施也是必要的.绝育蚊子投放成本相对较大,因此我们要在控制疟疾的同时尽可能降低成本.在第四章中,我们对本文的主要结论作出总结并提出了未来还需要继续研究努力的目标。
[Abstract]:Malaria is the most common in the world is one of the most serious infectious disease, bring great harm to human life. In order to control the spread of malaria, scientists have made a lot of research. The WHO and many countries attach great importance to malaria, have taken corresponding measures to fight malaria. This paper established two containing sterilization the malaria mosquito propagation model, make a qualitative analysis on the malaria model and relevant conclusions. Finally according to the conclusion put forward the corresponding control strategy. This paper is divided into four chapters, the first chapter of the introduction introduces the principle and the spread of malaria incidence mechanism and scientists have taken relevant measures to fight malaria. Preparation the knowledge part introduces the related concepts of the dynamics of infectious diseases are involved in this paper and the theorem. This chapter introduces the development process and the dynamic model of malaria The basic model of this paper. In the second chapter, we study the malaria epidemic model on the mosquito. Constant sterilization in the first section of a two-dimensional dynamic model containing only the sterilization of mosquitoes and wild mosquitoes, through qualitative analysis of the model, find the mosquito on the threshold of B0 sterilization, sterilization when B is greater than the amount of mosquitoes or equal to B0, wild mosquitoes eventually disappear; when B is less than B0, wild mosquitoes and mosquito sterilization coexist. Then this chapter studies the population contains both containing the eight dimensional model of the malaria mosquito, through the analysis of the local stability of the disease-free equilibrium, we conclude that when the basic reproduction number R0 is less than 1. The disease-free equilibrium point is locally asymptotically stable; when the basic reproduction number R0 is greater than 1, the endemic equilibrium exists. By R0=1 to less than B0 has more practical significance on the threshold of b*. numerical simulation shows the conclusion and practical With numerical simulation we found that when R0 is less than 1, the endemic equilibrium still exist, so the system may exist in R0=1 to the branch, is the fourth section of the backward bifurcation existence made theoretically. The conclusion of this chapter shows on the sterilization mosquito has a significant effect on the spread of malaria control. Considering the number of wild mosquitoes in some areas is relatively small, from the perspective of economics, constant delivery cost is larger, so the third chapter we study the malaria epidemic model into the mosquito sterilization delivery ratio, the corresponding input in this wild mosquitoes. We consider the effect of Allee specific analysis and calculation process and constant release similar numerical simulation is given to verify the conclusion is consistent with the reality. The sterilization on malaria control mosquitoes significantly, and according to the number of mosquitoes in different regions, different measures will also launch Yes, the cost of sterilization is relatively large. Therefore, we need to control malaria at the same time and reduce costs as much as possible. In the fourth chapter, we summarize the main conclusions of this paper and put forward the goals that we need to continue to study in the future.

【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

【参考文献】