投放有免疫力的蚊子对疟疾病控制的影响

发布时间：2018-04-14 17:43

本文选题：传染病动力学 + 种群动力学　；参考：《西南大学》2009年硕士论文

【摘要】： 本文主要从数学上研究用不能传播疟疾的蚊子来代替野生蚊子种群的可能性.用不同的方式引入对疟疾有免疫力的蚊子,建立相应的疟疾传染模型.随后,讨论它们的无病平衡点的存在性和稳定性.全文共分为三章. 在第一章中,简述了疟疾的发病、传播原理和主要防护措施,进一步给出了传染病动力学、种群动力学和脉冲微分方程的相关理论和本文的主要工作. 在第二章中,我们主要考虑一次性投放转基因蚊子到自然环境中后的模型.基于随机配对理论和种群竞争模型,我们建立了蚊子部分的竞争模型,再综合上人类的部分就得到了整个疟疾病传染病模型.在假设两种蚊子能够共存的情况下,运用下一代矩阵法(The Next GenerationMatrix Method)找到疾病模型对应的基本再生数.通过比较投放前模型和投放后新系统的基本再生数,我们发现无论两种蚊子竞争有多激烈,改良基因蚊子的引入都对传染起到了阻碍作用,非常利于疾病控制的.接下来,通过对蚊子部分的系统进行动力学分析得到其稳定共存的条件后,我们发现这样的结果只通过长期进化实现.因此一次性投放并不是最理想的方法.因此便引出了第三章中定期投放的方法. 在第三章中,我们希望仿效控制害虫时用到的定期投放天敌的生物防治法.于是,假设我们定期向野生蚊子种群投放改良基因后对疾病有免疫力的蚊子.同时,在上一章的基础上,我们引入了脉冲微分方程来描述这一过程建立了新的模型.首先,在不考虑疾病的情况下,运用脉冲微分方程比较定理和Brouwer不动点定理等分析了蚊子的二维脉冲竞争模型的持久性和灭绝性.随后,我们得到了一物种灭绝而另一物种趋近于稳定状态的条件.我们的结果显示了适当的脉冲扰动可破坏系统的长时间的性态.接下来,运用Floquet乘子理论对整个疟疾病传染系统在一个特殊的无病周期解处的稳定性进行了分析,得到了其局部稳定的条件. 通过本文,说明了在控制疟疾病的问题上,长期定时投放野生蚊的竞争者-改良基因后获得免疫力的蚊子,的方法比一次性投放天敌的方法更有效。
[Abstract]:This paper mainly studies the possibility of using mosquitoes unable to spread malaria in order to replace the species of wild mosquito . In different ways , the mosquito that has immunity to malaria is introduced , and the corresponding malaria transmission model is established . Then , the existence and stability of their disease - free equilibrium points are discussed . The whole text is divided into three chapters .

In the first chapter , the pathogenesis , transmission principle and main protective measures of malaria are briefly described , and the related theories of infectious diseases dynamics , population dynamics and impulsive differential equations and the main work of this paper are also given .

In chapter 2 , we mainly consider the model of single - step delivery of transgenic mosquitoes to the natural environment . Based on the random pairing theory and population competition model , we have established the competition model of the mosquito portion , and then integrated the human part to find the basic regeneration number corresponding to the disease model . After comparing the pre - launch model and the basic regeneration number of the new system , we find that whether the two kinds of mosquitoes are able to coexist , we find that the result is only realized by long - term evolution . Therefore , the one - time delivery is not the most ideal method . Therefore , the method of the third chapter is led out .

In chapter 3 , we hope to emulate the biological control method of the natural enemy on the regular basis of controlling pests . So , we have introduced the pulse differential equation to describe the persistence and extinction of the two - dimensional pulse competition model of the mosquito . At the same time , we have obtained a new model of the two - dimensional pulse competition model of the mosquito on the basis of the previous chapter . First , we analyze the stability of the whole malaria transmission system in a special disease - free period by using the Floquet multiplier theory , and get the local stability condition .

In this paper , we describe the method of using the competitor - modified gene of wild mosquito for long - term timing to control malaria , and the method is more effective than the one - time throwing natural enemy .

【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2009
【分类号】：R311;O175

【引证文献】