本文選題：絕育蚊子 + 常數(shù)投放��； 參考：《華中師范大學》2017年碩士論文

【摘要】：瘧疾是世界上最常見也是最嚴重的熱帶傳染病之一,對人類生活帶來了極大的危害.為控制瘧疾的傳播,科學家們作出了大量的研究.世界衛(wèi)生組織和很多國家對瘧疾也高度重視,均采取了相應措施以對抗瘧疾.本文建立了兩個含有絕育蚊子的瘧疾傳播模型,對瘧疾模型作出定性分析并得到相關結論.最后根據(jù)所得出的結論提出了相應的控制策略.本文共分為四章,第一章的引言部分介紹了瘧疾的發(fā)病原理和傳播機制以及科學家們?yōu)閷汞懠菜扇〉南嚓P措施.預備知識部分介紹了本文所涉及到的傳染病動力學的相關概念和定理.本章最后介紹了瘧疾動力學模型的發(fā)展進程并提出了本文的基本模型.第二章我們研究了絕育蚊子常數(shù)投放的瘧疾傳染病模型.首先在第一節(jié)中研究了僅含有絕育蚊子和野生蚊子的二維動力學模型,通過對模型進行定性分析,尋找到絕育蚊子的投放閾值b0,當絕育蚊子投放量b大于或等于b0,野生蚊子最終消失;當b小于b0時,野生蚊子與絕育蚊子共存.接著本章研究了既含有人口項又含有蚊蟲項的八維瘧疾模型,通過對無病平衡點局部穩(wěn)定性的分析,我們得出當基本再生數(shù)R0小于1時,無病平衡點局部漸進穩(wěn)定;當基本再生數(shù)R0大于1時,地方病平衡點存在.通過令R0=1尋找到小于b0的更具有實際意義的投放閾值b*.數(shù)值模擬顯示結論與實際相符,數(shù)值模擬過程中我們發(fā)現(xiàn)當R0小于1時,地方病平衡點依舊存在,因此系統(tǒng)在R0=1處可能存在后向分支,則第四節(jié)中對后向分支的存在性作出了理論性證明.本章結論顯示投放絕育蚊子對控制瘧疾傳播有顯著作用.考慮到有些地區(qū)野生蚊子數(shù)量相對較少,從經(jīng)濟學角度來講,常數(shù)投放的成本較大,因此第三章我們研究了絕育蚊子成比例投放的瘧疾傳染病模型,相應的此時野生蚊子輸入項中我們考慮Allee效應.具體的分析計算過程與常數(shù)投放類似,通過數(shù)值模擬,驗證所得結論與實際相符.絕育蚊子對瘧疾控制作用顯著,而且根據(jù)不同地區(qū)蚊子的數(shù)量情況,采取不同的投放措施也是必要的.絕育蚊子投放成本相對較大,因此我們要在控制瘧疾的同時盡可能降低成本.在第四章中,我們對本文的主要結論作出總結并提出了未來還需要繼續(xù)研究努力的目標。
[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.

【學位授予單位】：華中師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

【參考文獻】

相關期刊論文 前1條

1 王一凡;;青蒿素與瘧疾防治[J];百科知識;2011年21期

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本文編號：1737082