【摘要】：傳染病嚴(yán)重威脅人們的健康,并對(duì)社會(huì)的穩(wěn)定和經(jīng)濟(jì)的發(fā)展產(chǎn)生重要影響.一直以來(lái),人們與傳染病做著不屈不撓的斗爭(zhēng).西尼羅河病毒是一種蟲媒傳染病,可以感染人、馬、鳥、蚊子和其它動(dòng)物,蚊子是其主要傳播媒介.本文主要研究描述西尼羅河病毒傳播的傳染病數(shù)學(xué)模型.首先在前人工作的基礎(chǔ)上簡(jiǎn)化模型并研究其行波解.然后考慮到環(huán)境的周期性和空間的非均質(zhì)性對(duì)病毒傳播的影響,我們進(jìn)一步研究周期反應(yīng)擴(kuò)散問題和非均質(zhì)空間上的反應(yīng)擴(kuò)散問題,通過定性分析和數(shù)值模擬給出病毒發(fā)展趨勢(shì)的預(yù)測(cè).論文具體包括六個(gè)部分.第一章簡(jiǎn)要介紹了傳染病的歷史及其模型的發(fā)展和研究的現(xiàn)狀,然后引入了西尼羅河病毒模型及相關(guān)數(shù)學(xué)問題.第二章在Wonham和Lewis西尼羅河病毒模型的基礎(chǔ)上利用蚊子和鳥的關(guān)系簡(jiǎn)化模型并研究其行波解.第三章考慮了環(huán)境的周期性變化這一實(shí)際現(xiàn)象,我們研究具周期條件的反應(yīng)擴(kuò)散問題.利用上下解方法及其迭代序列得到周期解的存在性.第四章考慮蚊子和鳥所在空間位置的不同特征,我們研究非均質(zhì)空間的西尼羅河病毒模型,討論無(wú)病平衡點(diǎn)和染病平衡點(diǎn)的存在性,唯一性以及全局穩(wěn)定性.第五章我們使用Matlab軟件對(duì)上述的部分結(jié)論進(jìn)行數(shù)值模擬,用圖像和數(shù)值結(jié)果來(lái)檢驗(yàn)已得的理論結(jié)果.第六章對(duì)整篇文章進(jìn)行總結(jié)并給出將來(lái)需要研究的問題.
[Abstract]:Infectious diseases seriously threaten people's health and have an important impact on social stability and economic development. For a long time, people have been making indomitable struggle against infectious diseases. West Nile virus (WNV) is an insect-borne disease that infects humans, horses, birds, mosquitoes and other animals. In this paper, a mathematical model describing the transmission of West Nile virus (WNV) is studied. Firstly, the model is simplified on the basis of previous work and its traveling wave solution is studied. Then, considering the effects of environmental periodicity and spatial heterogeneity on virus transmission, we further study the problem of periodic reaction-diffusion and the problem of reaction-diffusion in heterogeneous spaces. The trend of virus development is predicted by qualitative analysis and numerical simulation. The thesis includes six parts. The first chapter briefly introduces the history of infectious diseases, the development of models and research status, and then introduces the West Nile virus model and related mathematical problems. In chapter 2, based on the Wonham and Lewis West Nile virus models, the relationship between mosquitoes and birds is simplified and the traveling wave solutions are studied. In chapter 3, we consider the phenomenon of periodic change of environment, and we study the problem of reaction diffusion with periodic conditions. The existence of periodic solutions is obtained by using the upper and lower solution method and its iterative sequence. In chapter 4, we study the West Nile virus model in heterogeneous space, and discuss the existence, uniqueness and global stability of disease-free equilibrium and disease-free equilibrium. In chapter 5, we use Matlab software to simulate some of the above conclusions, and use the image and numerical results to verify the obtained theoretical results. Chapter 6 summarizes the whole article and gives some problems that need to be studied in the future.
【學(xué)位授予單位】：揚(yáng)州大學(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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本文編號(hào)：2375610