带有类年龄结构的登革热动力学建模与研究

发布时间：2018-03-31 14:49

本文选题：登革热模型　切入点：类年龄结构　出处：《信阳师范学院》2017年硕士论文

【摘要】：首先,根据登革热在人群感染治疗和预防接种等特点,我们建立了一类带有感染和疫苗接种时间的登革热传播模型.运用无穷维特征方程理论、疾病持续生存理论和构造合适的Lyapunov泛函等方法,全局分析了这类模型动力学性质,得到了控制疾病传播的基本再生数,而且当基本再生数小于1时,无病平衡态是全局渐近稳定的;当基本再生数大于1时,系统疾病是持续生存并且地方病平衡态是全局渐近稳定的.其次,根据传播登革热的伊蚊生理结构特点,蚊卵发育时间对疾病的影响,我们建立了一类蚊虫阶段结构的登革热动力学模型.数学建模分析了这类系统平衡态的存在性,得到控制疾病传播的基本再生数,无病平衡态的全局稳定性.特别地,我们研究了带有类年龄结构的伊蚊种群模型动力学性质,得到了控制伊蚊种群的阶段结构成长发育的阈值条件:当阈值R01时,系统中的地方平衡态是全局渐近稳定的;当阈值R01时,系统中的正平衡态是全局渐近稳定的.最后,结合登革热感染、预防接种和伊蚊卵持续时间对疾病传播的特点,我们进一步讨论了控制登革热传播的具体措施.
[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.
【学位授予单位】：信阳师范学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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