【摘要】：瘧疾是危害人類健康的第五大傳染性疾病,通過雌蚊子的叮咬在人群中傳播.目前,全世界約一半的人口有患瘧疾的風(fēng)險(xiǎn),其中五歲以下的兒童是高發(fā)人群,并且在所有的死亡病例中約三分之二是該年齡段的人群.對(duì)于這種蚊媒性疾病,比較好的控制方法就是控制蚊子的數(shù)量,傳統(tǒng)的使用殺蟲劑滅蚊的方法不僅污染環(huán)境,而且效果有限,在這種情況下,絕育蚊子出現(xiàn).絕育蚊子可以影響野生蚊子之間的交配從而降低野生蚊子的密度.本文建立了帶絕育蚊子的年齡結(jié)構(gòu)瘧疾傳播模型,將人口分為學(xué)齡前兒童(0～5歲)和剩余人群(5歲以上)兩類,旨在研究絕育蚊子對(duì)瘧疾傳播的影響并且分析以何種方式投放絕育蚊子既可以控制疾病又不會(huì)造成浪費(fèi).本文由五章組成,第一章介紹了瘧疾的研究背景、目的、現(xiàn)狀和本文研究?jī)?nèi)容,其中研究背景包括瘧疾相關(guān)介紹、世界瘧疾疫情和中國瘧疾疫情三部分.第二章給出了一些本文需要用到的基本知識(shí).第三章建立并研究了絕育蚊子常數(shù)投放且蚊子之間的交配率為常數(shù)的年齡結(jié)構(gòu)模型.通過第二代矩陣法求得了模型的基本再生數(shù)R0,R0由兩部分組成:由學(xué)齡前兒童引起的疾病的傳播R1和由剩余人群引起的疾病的傳播R2,通過數(shù)值模擬得出在一定范圍內(nèi),這兩部分都會(huì)隨著絕育蚊子的投放k的增大而減小,但k對(duì)R2的影響更大一些;利用R0證明了無病平衡點(diǎn)的穩(wěn)定性;利用數(shù)值模擬得出在一定的范圍內(nèi),絕育蚊子的投放數(shù)量越多,達(dá)到平衡點(diǎn)時(shí)患病者的數(shù)量越少;最后,我們求得了一個(gè)絕育蚊子的投放區(qū)間,在這個(gè)區(qū)間里,在一定的條件下,野生蚊子仍然存在,但疾病消失.考慮到絕育蚊子的培養(yǎng)耗時(shí)耗力耗錢,若野生蚊子的數(shù)量很少,常數(shù)投放絕育蚊子會(huì)造成浪費(fèi),并且此時(shí)野生蚊子之間會(huì)出現(xiàn)交配困難,故第四章建立了一個(gè)絕育蚊子的投放與野生蚊子的數(shù)量成正比例比值為k且交配考慮Allee效應(yīng)的年齡結(jié)構(gòu)模型.利用第二代矩陣的方法求得了基本再生數(shù),得出在一定的范圍內(nèi),k越大,基本再生數(shù)的值越小;通過數(shù)值模擬得出k越大,達(dá)到平衡點(diǎn)時(shí)患病者的數(shù)量越少;通過分析得出不同年齡階段的人群對(duì)瘧疾傳播的影響程度不同,并給定了一個(gè)比例區(qū)間,在這個(gè)區(qū)間里,在一定的條件下,野生蚊子仍然存在,但疾病消失.第五章總結(jié)了全文的主要結(jié)論,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.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

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