Analysis Of Dynamical Models About Within-host Mycobacterium Tuberculosis

In this thesis,based on the affecting process and immune response of mycobac-terium tuberculosis,we establish a model about mycobacterium tuberculosis,in which intracellular proliferation and extracellular proliferation are both considered,as well as another within-host mycobacterium tuberculosis dynamical model with a discrete time delay.Besides,the dynamical properties and biological meanings of each model are discussed.In Chapter 1,we introduce the epidemic of tuberculosis,the background of my-cobacterium tuberculosis and the current research status of the mycobacterium tubercu-losis dynamical models at home and abroad.Meanwhile some basic theory are briefly stated.In Chapter 2,we study a model about mycobacterium tuberculosis,in which gen-erally infection incidence rate,intracellular proliferation and extracellular proliferation are considered.For the model,both the reproductive numbers of the bacteria and the immune system are computed.Then we use the reproductive numbers to study the ex-istence and stability of the non-immune equilibrium.Besides,we get the sufficient and necessary conditions of the backward bifurcation at disease-free equilibrium,which are closely related with the incidence function and the burst-size of mycobacterium tuber-culosis produced by intracellular proliferation.Finally,some numerical simulations are presented to illustrate the conclusions.In Chapter 3,we propose a within-host mycobacterium tuberculosis infection mod-el and analyze its stability,in which a discrete delay and CTL immune saturated inci-dence rate are contained.First of all,the nonnegativity and boundedness of solutions are proved and the reproductive numbers of the bacteria and the immune system are comput-ed.Secondly,the existence and stability of the equilibrium point are analyzed.Finally,by constructing suitable Lyapunov functional,we get the conditions for the global stabil-ity of the infection-free equilibrium point,the immune-free equilibrium and the positive equilibrium.In the last chapter,the basic results of this paper are briefly reviewed.Then we introduce the biological meaning and practical value of the model.Finally,we discuss some shortages of this paper and problems which need to be studied further.