本文選題：登革熱模型　切入點：類年齡結構　出處：《信陽師范學院》2017年碩士論文

【摘要】：首先,根據登革熱在人群感染治療和預防接種等特點,我們建立了一類帶有感染和疫苗接種時間的登革熱傳播模型.運用無窮維特征方程理論、疾病持續(xù)生存理論和構造合適的Lyapunov泛函等方法,全局分析了這類模型動力學性質,得到了控制疾病傳播的基本再生數,而且當基本再生數小于1時,無病平衡態(tài)是全局漸近穩(wěn)定的;當基本再生數大于1時,系統(tǒng)疾病是持續(xù)生存并且地方病平衡態(tài)是全局漸近穩(wěn)定的.其次,根據傳播登革熱的伊蚊生理結構特點,蚊卵發(fā)育時間對疾病的影響,我們建立了一類蚊蟲階段結構的登革熱動力學模型.數學建模分析了這類系統(tǒng)平衡態(tài)的存在性,得到控制疾病傳播的基本再生數,無病平衡態(tài)的全局穩(wěn)定性.特別地,我們研究了帶有類年齡結構的伊蚊種群模型動力學性質,得到了控制伊蚊種群的階段結構成長發(fā)育的閾值條件:當閾值R01時,系統(tǒng)中的地方平衡態(tài)是全局漸近穩(wěn)定的;當閾值R01時,系統(tǒng)中的正平衡態(tài)是全局漸近穩(wěn)定的.最后,結合登革熱感染、預防接種和伊蚊卵持續(xù)時間對疾病傳播的特點,我們進一步討論了控制登革熱傳播的具體措施.
[Abstract]:First of all, according to the characteristics of dengue fever infection treatment and vaccination in the population, we establish a dengue transmission model with infection and vaccination time. Based on the theory of disease persistence and the method of constructing suitable Lyapunov functional, the dynamic properties of this kind of model are analyzed globally, and the basic regenerative number of disease transmission is obtained, and when the basic regeneration number is less than 1, The disease-free equilibrium state is globally asymptotically stable, and when the basic regeneration number is greater than 1, the disease is persistent and the endemic equilibrium state is globally asymptotically stable. Based on the effect of mosquito egg development time on disease, a dynamic model of dengue fever with mosquito stage structure was established. The existence of equilibrium state of this system was analyzed, and the basic regeneration number of disease transmission was obtained. The global stability of disease-free equilibrium state. In particular, we study the dynamic properties of Aedes mosquito population model with age-like structure, and obtain the threshold conditions for controlling the growth and development of Aedes mosquito population in different stages: when the threshold is R01, The local equilibrium state in the system is globally asymptotically stable, and the positive equilibrium state in the system is globally asymptotically stable when the threshold is R01. Finally, combined with the characteristics of dengue fever infection, inoculation and the duration of Aedes mosquito eggs, We further discussed specific measures to control the spread of dengue fever.
【學位授予單位】：信陽師范學院
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

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相關期刊論文 前1條

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本文編號：1691197