带绝育蚊子的年龄结构疟疾传播模型的分析与研究
发布时间：2018-08-23 14:06
【摘要】：疟疾是危害人类健康的第五大传染性疾病,通过雌蚊子的叮咬在人群中传播.目前,全世界约一半的人口有患疟疾的风险,其中五岁以下的儿童是高发人群,并且在所有的死亡病例中约三分之二是该年龄段的人群.对于这种蚊媒性疾病,比较好的控制方法就是控制蚊子的数量,传统的使用杀虫剂灭蚊的方法不仅污染环境,而且效果有限,在这种情况下,绝育蚊子出现.绝育蚊子可以影响野生蚊子之间的交配从而降低野生蚊子的密度.本文建立了带绝育蚊子的年龄结构疟疾传播模型,将人口分为学龄前儿童(0～5岁)和剩余人群(5岁以上)两类,旨在研究绝育蚊子对疟疾传播的影响并且分析以何种方式投放绝育蚊子既可以控制疾病又不会造成浪费.本文由五章组成,第一章介绍了疟疾的研究背景、目的、现状和本文研究内容,其中研究背景包括疟疾相关介绍、世界疟疾疫情和中国疟疾疫情三部分.第二章给出了一些本文需要用到的基本知识.第三章建立并研究了绝育蚊子常数投放且蚊子之间的交配率为常数的年龄结构模型.通过第二代矩阵法求得了模型的基本再生数R0,R0由两部分组成:由学龄前儿童引起的疾病的传播R1和由剩余人群引起的疾病的传播R2,通过数值模拟得出在一定范围内,这两部分都会随着绝育蚊子的投放k的增大而减小,但k对R2的影响更大一些;利用R0证明了无病平衡点的稳定性;利用数值模拟得出在一定的范围内,绝育蚊子的投放数量越多,达到平衡点时患病者的数量越少;最后,我们求得了一个绝育蚊子的投放区间,在这个区间里,在一定的条件下,野生蚊子仍然存在,但疾病消失.考虑到绝育蚊子的培养耗时耗力耗钱,若野生蚊子的数量很少,常数投放绝育蚊子会造成浪费,并且此时野生蚊子之间会出现交配困难,故第四章建立了一个绝育蚊子的投放与野生蚊子的数量成正比例比值为k且交配考虑Allee效应的年龄结构模型.利用第二代矩阵的方法求得了基本再生数,得出在一定的范围内,k越大,基本再生数的值越小;通过数值模拟得出k越大,达到平衡点时患病者的数量越少;通过分析得出不同年龄阶段的人群对疟疾传播的影响程度不同,并给定了一个比例区间,在这个区间里,在一定的条件下,野生蚊子仍然存在,但疾病消失.第五章总结了全文的主要结论,并作了研究展望.
[Abstract]:Malaria is the fifth most contagious disease in human health and is transmitted through the bite of female mosquitoes. Currently, about half of the world's population is at risk of malaria, with children under the age of five having a high risk, and about 2/3 of all deaths in this age group. For this mosquito-borne disease, the better control method is to control the number of mosquitoes. The traditional method of using insecticides to kill mosquitoes not only pollutes the environment, but also has limited effect. In this case, the sterilization of mosquitoes appears. Mosquito sterilization can affect the mating of wild mosquitoes and thus reduce the density of wild mosquitoes. An age-structured malaria transmission model with sterilized mosquitoes was established in this paper. The population was divided into two groups: preschool children (0 ~ 5 years old) and the rest of the population (over 5 years old). The aim is to study the effects of mosquito sterilization on malaria transmission and to analyze the ways in which sterilizing mosquitoes can control disease without causing waste. This paper is composed of five chapters. The first chapter introduces the research background, objectives, present situation and research contents of malaria. The research background includes three parts: malaria related introduction, world malaria epidemic situation and China malaria epidemic situation. The second chapter gives some basic knowledge which need to be used in this paper. In chapter 3, an age structure model with constant delivery of sterilized mosquitoes and constant mating rate between mosquitoes is established and studied. By using the second generation matrix method, the basic regeneration number R0 / R0 of the model is obtained, which consists of two parts: the spread of disease R1 caused by preschool children and the spread of disease R2 caused by the remaining population. The numerical simulation shows that the number of R0 and R0 is within a certain range. Both of these parts decrease with the increase of mosquito sterilisation k, but k has a greater effect on R2; using R0 to prove the stability of disease-free equilibrium; using numerical simulation to show that the stability of disease-free equilibrium is within a certain range. The more the number of mosquito sterilization, the less the number of infected people at the equilibrium point. Finally, we found an interval of mosquito sterilization, in which wild mosquitoes still exist under certain conditions, but the disease disappears. Considering that the breeding of mosquito sterilization is time-consuming and costly, if the number of wild mosquitoes is small, constant delivery of sterilized mosquitoes is wasteful and mating difficulties occur between wild mosquitoes, In chapter 4, a model of age structure of sterilizing mosquitoes with the ratio of K to the number of wild mosquitoes and mating considering Allee effect is established. By using the second generation matrix method, the basic reproduction number is obtained, and the value of the basic regeneration number is smaller with the increase of k in a certain range, and the number of patients with disease becomes less when the number of patients reaches the equilibrium point by numerical simulation. Through analysis, it is concluded that different age groups have different influence on malaria transmission, and a proportion interval is given. In this interval, wild mosquitoes still exist under certain conditions, but the disease disappears. The fifth chapter summarizes the main conclusions of the paper and makes a research prospect.
【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
本文编号：2199299
[Abstract]:Malaria is the fifth most contagious disease in human health and is transmitted through the bite of female mosquitoes. Currently, about half of the world's population is at risk of malaria, with children under the age of five having a high risk, and about 2/3 of all deaths in this age group. For this mosquito-borne disease, the better control method is to control the number of mosquitoes. The traditional method of using insecticides to kill mosquitoes not only pollutes the environment, but also has limited effect. In this case, the sterilization of mosquitoes appears. Mosquito sterilization can affect the mating of wild mosquitoes and thus reduce the density of wild mosquitoes. An age-structured malaria transmission model with sterilized mosquitoes was established in this paper. The population was divided into two groups: preschool children (0 ~ 5 years old) and the rest of the population (over 5 years old). The aim is to study the effects of mosquito sterilization on malaria transmission and to analyze the ways in which sterilizing mosquitoes can control disease without causing waste. This paper is composed of five chapters. The first chapter introduces the research background, objectives, present situation and research contents of malaria. The research background includes three parts: malaria related introduction, world malaria epidemic situation and China malaria epidemic situation. The second chapter gives some basic knowledge which need to be used in this paper. In chapter 3, an age structure model with constant delivery of sterilized mosquitoes and constant mating rate between mosquitoes is established and studied. By using the second generation matrix method, the basic regeneration number R0 / R0 of the model is obtained, which consists of two parts: the spread of disease R1 caused by preschool children and the spread of disease R2 caused by the remaining population. The numerical simulation shows that the number of R0 and R0 is within a certain range. Both of these parts decrease with the increase of mosquito sterilisation k, but k has a greater effect on R2; using R0 to prove the stability of disease-free equilibrium; using numerical simulation to show that the stability of disease-free equilibrium is within a certain range. The more the number of mosquito sterilization, the less the number of infected people at the equilibrium point. Finally, we found an interval of mosquito sterilization, in which wild mosquitoes still exist under certain conditions, but the disease disappears. Considering that the breeding of mosquito sterilization is time-consuming and costly, if the number of wild mosquitoes is small, constant delivery of sterilized mosquitoes is wasteful and mating difficulties occur between wild mosquitoes, In chapter 4, a model of age structure of sterilizing mosquitoes with the ratio of K to the number of wild mosquitoes and mating considering Allee effect is established. By using the second generation matrix method, the basic reproduction number is obtained, and the value of the basic regeneration number is smaller with the increase of k in a certain range, and the number of patients with disease becomes less when the number of patients reaches the equilibrium point by numerical simulation. Through analysis, it is concluded that different age groups have different influence on malaria transmission, and a proportion interval is given. In this interval, wild mosquitoes still exist under certain conditions, but the disease disappears. The fifth chapter summarizes the main conclusions of the paper and makes a research prospect.
【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】
相关期刊论文 前8条
1 李永军;刘起勇;奚志勇;;应用沃尔巴克氏体通过种群替换阻断蚊媒病的传播[J];中国媒介生物学及控制杂志;2015年01期
2 Jia Li;;具有发育阶段结构的野生与不育蚊子交互作用的数学模型（英文）[J];上海师范大学学报(自然科学版);2014年05期
3 郑小英;刘起勇;奚志勇;;基于沃尔巴克氏体的蚊媒和蚊媒病控制的生物安全性[J];中国媒介生物学及控制杂志;2014年02期
4 潘晓玲;刘起勇;奚志勇;;基于昆虫共生菌沃尔巴克氏体的蚊媒和蚊媒病控制研究进展[J];中国媒介生物学及控制杂志;2014年01期
5 丁俊;;疟疾流行现状研究进展[J];中国公共卫生;2012年05期
6 高春玉,柴光军,韩光红,杨小为,刘莉,蒋正杰;1950～2001年我国疟疾发病趋势分析[J];中国公共卫生;2003年06期
7 吴湛勇;制造不传播疾病的转基因蚊子[J];世界科学;2001年11期
8 商永珍;;疟疾的临床表现及联合用药[J];中国社区医师;1993年06期
，本文编号：2199299
本文链接：https://www.wllwen.com/kejilunwen/yysx/2199299.html
