铜绿假脓单胞菌群体感应对免疫反应影响的定性研究
发布时间：2018-11-02 06:53
【摘要】：基于铜绿假脓单胞菌群体感应机理及群体感应信号分子具有免疫调控功能这一生物学行为,本文研究了几类铜绿假脓单胞菌群体感应对免疫反应影响的数学模型的动力学行为,主要讨论了模型平衡点的存在性、稳定性及分歧行为。第一章主要介绍了铜绿假脓单胞菌及群体感应相关背景知识,铜绿假脓单胞菌群体感应数学模型的研究进展及相关的理论基础。第二章建立了一类数学模型描述群体感应信号分子的免疫调控机理,分析了模型平衡点的存在性及其渐近稳定性,并通过数值模拟验证了理论结果的准确性。有趣的是,我们发现当0 1?(29)1,?(27)1,(35)(29)0时,存在双稳现象。为进一步研究双稳态下平衡点的性质,通过构造李雅普诺夫函数,对双稳态下无菌平衡点和正平衡点的吸引域进行估计,并运用Matlab的工具箱GLOPTIPOLY及SeDuMi对双稳态下的吸引域进行仿真分析。此外,运用MatCont分析了模型可能存在的分歧现象,得到了单参数分歧图、双参数分歧图。本文的第三章主要研究了一类群体感应信号分子调控细菌与免疫系统间竞争的数学模型,利用Lyapunov方法证明了无菌平衡点的稳定性;分析了正平衡点的存在条件及稳定性,并证明了正平衡点前后向分歧的存在性,利用MatCont,通过数值模拟进一步探测模型复杂的动力学行为,得到系统存在的三种动力学性态,包括前、后向分歧以及双稳态现象。
[Abstract]:Based on the population sensing mechanism of Pseudomonas aeruginosa and the biological behavior of population sensing signaling molecules with immunomodulatory function, the dynamic behaviors of several mathematical models of Pseudomonas aeruginosa group somatosensory response to immune response were studied in this paper. The existence, stability and bifurcation behavior of equilibrium point are discussed. The first chapter mainly introduces the background knowledge of Pseudomonas aeruginosa and its population induction, the research progress of mathematical model of Pseudomonas aeruginosa population induction and the related theoretical basis. In chapter 2, a kind of mathematical model is established to describe the immune regulation mechanism of population sensing signal molecules. The existence and asymptotic stability of the equilibrium point of the model are analyzed, and the accuracy of the theoretical results is verified by numerical simulation. Interestingly, we find that there is bistability when 0? (29) 1? (27) 1, (35) (29) 0. In order to further study the properties of equilibrium point in bistable state, the attractive regions of aseptic equilibrium point and positive equilibrium point in bistable state are estimated by constructing Lyapunov function. Matlab toolbox GLOPTIPOLY and SeDuMi are used to simulate the attraction region in bistable state. In addition, the possible bifurcation phenomena of the model are analyzed by using MatCont, and the single parameter bifurcation graph and the double parameter bifurcation graph are obtained. In the third chapter, a mathematical model of competition between bacteria and immune system is studied, and the stability of aseptic equilibrium point is proved by Lyapunov method. The existence condition and stability of the positive equilibrium point are analyzed, and the existence of the forward and backward bifurcation of the positive equilibrium point is proved. The complex dynamic behavior of the model is further detected by MatCont, numerical simulation, and three dynamic states of the system are obtained. It includes forward, backward bifurcation and bistable phenomena.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：R378.991
本文编号：2305266
[Abstract]:Based on the population sensing mechanism of Pseudomonas aeruginosa and the biological behavior of population sensing signaling molecules with immunomodulatory function, the dynamic behaviors of several mathematical models of Pseudomonas aeruginosa group somatosensory response to immune response were studied in this paper. The existence, stability and bifurcation behavior of equilibrium point are discussed. The first chapter mainly introduces the background knowledge of Pseudomonas aeruginosa and its population induction, the research progress of mathematical model of Pseudomonas aeruginosa population induction and the related theoretical basis. In chapter 2, a kind of mathematical model is established to describe the immune regulation mechanism of population sensing signal molecules. The existence and asymptotic stability of the equilibrium point of the model are analyzed, and the accuracy of the theoretical results is verified by numerical simulation. Interestingly, we find that there is bistability when 0? (29) 1? (27) 1, (35) (29) 0. In order to further study the properties of equilibrium point in bistable state, the attractive regions of aseptic equilibrium point and positive equilibrium point in bistable state are estimated by constructing Lyapunov function. Matlab toolbox GLOPTIPOLY and SeDuMi are used to simulate the attraction region in bistable state. In addition, the possible bifurcation phenomena of the model are analyzed by using MatCont, and the single parameter bifurcation graph and the double parameter bifurcation graph are obtained. In the third chapter, a mathematical model of competition between bacteria and immune system is studied, and the stability of aseptic equilibrium point is proved by Lyapunov method. The existence condition and stability of the positive equilibrium point are analyzed, and the existence of the forward and backward bifurcation of the positive equilibrium point is proved. The complex dynamic behavior of the model is further detected by MatCont, numerical simulation, and three dynamic states of the system are obtained. It includes forward, backward bifurcation and bistable phenomena.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：R378.991
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