Qualitative Study On Pseudomonas Aeruginosa Quorum Sensing Influence On Immune Response

In this paper,based on pseudomonas aeruginosa quorum sensing mechanism and biological fact for immunomodulatory of pseudomonas aeruginosa quorum sensing signal molecule.Dynamics for some kinds of mathematical model are studied to describe the influence on immune response of pseudomonas aeruginosa quorum sensing,furthermore,the existence and stability of equilibria and bifurcation analysis are discussed.Background about pseudomonas aeruginosa and quorum sensing,progress of mathematical model about pseudomonas aeruginosa quorum sensing,and some basic theories are introduced in Chapter 1.In chapter 2,a mathematical model is proposed to describe the immune modulation of quorum sensing signal molecules.The existence and the asymptotic stability of equilibrium are throughly analyzed,and numerical simulations are performed to illustrate and to validate the accuracy of the theoretical results.More interestingly,it is found that the present model system experiences bi-stable phenomena for suitable choice of the parameter values when0 1?(29)1,?(27)1,(35)(29)0.In order to further study the properties of the equilibrium of bistability,a new method is adopted to construct a Lyapunov function,and the domain of the attraction is estimated for the bacteria-free equilibrium and a positive equilibrium which are stable under the same condition.With the help of Matlab package: GLOPTIPOLY and Se Du Mi,simulation analysis of the domain of attractions on bi-stability is shown in details.In addition,with the help of Mat Cont,the possible bifurcation of the present model is carried out and obtaining the one-parameter bifurcation and double parameter bifurcation diagram.In Chapter 3,a mathematical model is proposed to investigate the modulation of quorum sensing signal molecule on the competition between bacteria and immune system.The stability of bacteria-free equilibrium are discussed by using Lyapunov methods.And also,we study the existence and asymptotic stability of positive equilibrium and find the modulation leads to a backward bifurcation.By numerical simulations within Mat Cont,it is found that themodel also exhibits some other complicated dynamical behaviors,which include three patterns of dynamical behavior including forward bifurcation,backward bifurcation and the bi-stable phenomenon.