媒介传染病动力学行为研究

发布时间：2018-06-18 15:46

本文选题：登革热模型 + 免疫接种和W　；参考：《新疆大学》2017年硕士论文

【摘要】：近年来,关于如何控制媒介传染病的研究受到了国内外学者的广泛关注.本文主要针对几类具有疫苗接种控制策略和具有Wolbachia控制的媒介传染病动力学模型展开了深入细致的研究,分别讨论了疫苗接种和媒介控制对疾病的消除和流行的影响.主要内容可以概述如下:1.第一部分(对应第二节),建立了媒介具有孵化期时滞和新生儿具有免疫接种的登革热病毒在人和蚊虫之间传播的数学模型,主要讨论该传染病模型的解的非负性与有界性,无病平衡点和地方病平衡点的存在性,无病平衡点的全局吸引性等动力学行为.进一步,通过采用庞特里亚金最大原理等方法,得到了该疾病的最优控制策略.最后,数值模拟验证了理论结果的正确性和免疫接种的可行性.2.第二部分(对应第三节),建立了一类媒介具有孵化期时滞和易感者具有免疫接种的登革热数学模型,通过采用常微分方程比较原理,线性近似和庞特里亚金最大值原理等方法,建立了判定模型无病平衡解的全局吸引性与地方病平衡解的存在性的判别准则,以及该疾病的最优控制策略,并讨论模型参数的敏感性以及后向分支的存在性.数值模拟验证了理论结果的正确性和控制方法的有效性.3.第三部分(对应第四节),考虑到蚊虫的数量呈明显的季节波动性,提出具有季节波动影响和Wolbachia媒介控制的登革热病毒在人与蚊子之间传播的动力学模型,建立了模型无病周期解稳定及地方病周期解存在的判别准则.数值模拟验证了理论结果的正确性和控制策略的可行性.理论结果和数值模拟均显示Wolbachia媒介控制能够有效的遏制登革热病毒的蔓延.4.第四部分(对应第五节),建立了具有季节影响和脉冲投放Wolbachia病毒蚊子的登革热病毒在人和蚊虫之间传播的动力学模型,考虑了脉冲控制对登革热病毒传播的影响,确定了疾病消除和持久分充分条件.
[Abstract]:In recent years, the research on how to control vector infectious diseases has been widely concerned by scholars at home and abroad. In this paper, the effects of vaccination and vector control on the elimination and prevalence of the disease were discussed in detail, focusing on several kinds of vaccination control strategies and Wolbachia controlled vector infectious disease dynamics models. The main content can be summarized as follows: 1. In the first part (corresponding to section II), a mathematical model for the transmission of dengue virus between humans and mosquitoes with incubation delay and immunization is established. The non-negative and boundedness of the solution of the epidemic model are discussed. The existence of disease-free equilibrium and endemic equilibrium, the global attractiveness of disease-free equilibrium and so on. Furthermore, the optimal control strategy of the disease is obtained by using Ponteriagin maximum principle and other methods. Finally, the numerical simulation verifies the correctness of the theoretical results and the feasibility of immunization. In the second part (corresponding to the third section), a mathematical model of dengue fever with incubation delay and immune inoculation is established. By means of comparison principle of ordinary differential equation, linear approximation and Ponterriaquin maximum principle, etc. The criteria for determining the global attractiveness of the disease-free equilibrium solution and the existence of the endemic equilibrium solution, and the optimal control strategy for the disease are established. The sensitivity of the model parameters and the existence of backward bifurcation are discussed. Numerical simulation verifies the correctness of the theoretical results and the effectiveness of the control method. Part III (corresponding to section IV), taking into account the apparent seasonal volatility of mosquito populations, a dynamic model for the transmission of dengue virus between humans and mosquitoes with seasonal fluctuations and with Wolbachia vector control, The criteria for the stability of disease-free periodic solutions and the existence of endemic periodic solutions are established. Numerical simulation verifies the correctness of the theoretical results and the feasibility of the control strategy. Both theoretical results and numerical simulations show that Wolbachia vector control can effectively contain the spread of dengue virus. 4. Part IV (corresponding to section V), a kinetic model for the transmission of dengue virus between humans and mosquitoes with seasonal effects and pulsed delivery of Wolbachia virus mosquitoes is established, taking into account the effect of pulse control on the transmission of dengue virus. Sufficient conditions for disease elimination and persistence were determined.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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