本文選題：傳染病動力學(xué) + 種群動力學(xué)　； 參考：《西南大學(xué)》2009年碩士論文

【摘要】： 本文主要從數(shù)學(xué)上研究用不能傳播瘧疾的蚊子來代替野生蚊子種群的可能性.用不同的方式引入對瘧疾有免疫力的蚊子,建立相應(yīng)的瘧疾傳染模型.隨后,討論它們的無病平衡點的存在性和穩(wěn)定性.全文共分為三章. 在第一章中,簡述了瘧疾的發(fā)病、傳播原理和主要防護措施,進一步給出了傳染病動力學(xué)、種群動力學(xué)和脈沖微分方程的相關(guān)理論和本文的主要工作. 在第二章中,我們主要考慮一次性投放轉(zhuǎn)基因蚊子到自然環(huán)境中后的模型.基于隨機配對理論和種群競爭模型,我們建立了蚊子部分的競爭模型,再綜合上人類的部分就得到了整個瘧疾病傳染病模型.在假設(shè)兩種蚊子能夠共存的情況下,運用下一代矩陣法(The Next GenerationMatrix Method)找到疾病模型對應(yīng)的基本再生數(shù).通過比較投放前模型和投放后新系統(tǒng)的基本再生數(shù),我們發(fā)現(xiàn)無論兩種蚊子競爭有多激烈,改良基因蚊子的引入都對傳染起到了阻礙作用,非常利于疾病控制的.接下來,通過對蚊子部分的系統(tǒng)進行動力學(xué)分析得到其穩(wěn)定共存的條件后,我們發(fā)現(xiàn)這樣的結(jié)果只通過長期進化實現(xiàn).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,我們希望仿效控制害蟲時用到的定期投放天敵的生物防治法.于是,假設(shè)我們定期向野生蚊子種群投放改良基因后對疾病有免疫力的蚊子.同時,在上一章的基礎(chǔ)上,我們引入了脈沖微分方程來描述這一過程建立了新的模型.首先,在不考慮疾病的情況下,運用脈沖微分方程比較定理和Brouwer不動點定理等分析了蚊子的二維脈沖競爭模型的持久性和滅絕性.隨后,我們得到了一物種滅絕而另一物種趨近于穩(wěn)定狀態(tài)的條件.我們的結(jié)果顯示了適當(dāng)?shù)拿}沖擾動可破壞系統(tǒng)的長時間的性態(tài).接下來,運用Floquet乘子理論對整個瘧疾病傳染系統(tǒng)在一個特殊的無病周期解處的穩(wěn)定性進行了分析,得到了其局部穩(wěn)定的條件. 通過本文,說明了在控制瘧疾病的問題上,長期定時投放野生蚊的競爭者-改良基因后獲得免疫力的蚊子,的方法比一次性投放天敵的方法更有效。
[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 .

【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2009
【分類號】：R311;O175

【引證文獻】

相關(guān)期刊論文 前1條

1 劉瑞田;;基本消滅瘧疾后主動開展瘧疾疫情監(jiān)測的必要性與措施[J];社區(qū)醫(yī)學(xué)雜志;2012年13期

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本文編號：1750404