本文選題：西尼羅河病毒 + 基本再生數(shù)��； 參考：《中北大學》2017年碩士論文

【摘要】：傳染病一直以來給人類的生產生活造成極大的威脅,有效的防治傳染病是當今世界著手解決的一個重大問題。研究并建立合理的傳染病模型是十分重要的。本文主要研究了一種在許多國家流行但在中國還沒有發(fā)現(xiàn)的傳染病:西尼羅河病毒(WNV)。西尼羅河病毒是一種蟲媒病毒,WNV的傳染源大部分是處于病毒血癥期的帶有毒性的動物和WNV的自然貯藏宿主,主要是鳥類。通過蚊蟲叮咬把病毒傳給叮咬對象,在此過程中也會傳染給人類,但是人類是偶然宿主。鳥在傳播中起著宿主作用,蚊子起著媒介作用,它們之間進行循環(huán)傳播。WNV對中國人群來說是一種全新的致病病毒,人群缺乏對該病毒的免疫力,一旦感染爆發(fā),會造成嚴重的后果。因此對WNV的研究是十分必要的。第一章,主要介紹了WNV的研究意義、國內外研究現(xiàn)狀以及本文的研究工作。第二章,因為帶有l(wèi)ogistic增長的種群是比較符合實際情況的,因此本文考慮鳥類和蚊子都為logistic增長的情況,依據此建立模型,并對模型分析,獲得了基本再生數(shù)R_0,證明了當R_01時,無病平衡點時全局漸進穩(wěn)定的,當R_01,而且滿足不同條件時,得到正平衡點的存在性,并對模型進行數(shù)值模擬,驗證了理論結果的正確性。第三章,考慮到蚊蟲的爆發(fā)具有季節(jié)性,夏秋季節(jié)是蚊蟲繁殖時期,蚊蟲叮咬率高。在此基礎上建立傳染率為周期函數(shù)的傳染病模型,獲得了基本再生數(shù),得到無病平衡點的全局穩(wěn)定性以及正平衡點的存在性。最后在R_01和R_01的情況下對模型進行數(shù)值模擬,得到了比較好的結果。第四章,WNV是一種人畜共患病,也會感染人,但是人不會反傳給蚊子。據此,本文建立了有偶然宿主的WNV傳染病模型,并對模型進行了進一步分析,得到了模型的基本再生數(shù),當基本再生數(shù)小于1時,無病平衡點是全局穩(wěn)定的,當基本再生數(shù)大于1時,分析了正平衡點的穩(wěn)定性,數(shù)值模擬驗證了理論結果的正確性。第五章,總結以及對未來工作的展望。
[Abstract]:Infectious diseases have always posed a great threat to the production and life of human beings. Effective prevention and treatment of infectious diseases is a major problem to be solved in the world today. It is very important to study and establish a reasonable infectious disease model. In this paper, a new infectious disease, West Nile virus (WNV), which is prevalent in many countries but has not yet been found in China, is studied. West Nile virus (WNV) is a kind of insect-borne virus (WNV). Most of the sources of WNV are viremia animals and natural storage hosts of WNV, mainly birds. Passing the virus through mosquito bites can also spread to humans in the process, but humans are accidental hosts. Birds play a host role in the transmission, mosquitoes act as a vector, and they circulate between them. WNV is a completely new pathogenic virus for Chinese people, who lack immunity to the virus, and once the infection erupts, There are serious consequences. Therefore, the study of WNV is very necessary. The first chapter introduces the significance of WNV research, domestic and international research status and research work in this paper. In the second chapter, because the population with logistic growth is more in line with the actual situation, this paper considers the increase of both birds and mosquitoes as logistic, establishes the model according to this, and analyzes the model, and obtains the basic regenerative number R0, which proves that when R01, The existence of positive equilibrium is obtained when R01 is satisfied and the existence of positive equilibrium is obtained. Numerical simulation of the model is carried out to verify the correctness of the theoretical results. In the third chapter, considering the seasonal outbreak of mosquitoes, the summer and autumn seasons are the breeding period of mosquitoes, and the mosquito bite rate is high. On this basis, the infectious disease model with infection rate as periodic function is established, and the basic reproducing number is obtained. The global stability of disease-free equilibrium and the existence of positive equilibrium point are obtained. Finally, the numerical simulation of the model is carried out in the case of R _ S _ 1 and R _ S _ 01, and a good result is obtained. Chapter 4: WNV is a zoonotic disease that infects humans, but not mosquitoes. Based on this, a WNV infectious disease model with accidental host is established, and the model is further analyzed. The basic reproduction number of the model is obtained. When the basic regeneration number is less than 1, the disease-free equilibrium point is globally stable. The stability of the positive equilibrium point is analyzed when the basic reproduction number is greater than 1, and the correctness of the theoretical results is verified by numerical simulation. Chapter five, summary and prospect of future work.
【學位授予單位】：中北大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

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