Study For Tuberculosis Models With Reinfection And Constant Immigration

In traditional Tuberculosis models,the host population is divided into the following four classes: susceptible, exposed, infectious and treated individuals.With Tuberculosis developing and being known about deeply, Tuberculosis has some following new characteristics: the appearing of reinfection, untreaed rate and drug-resistant strains ,and that exposed individuals can also be infectious.Combining with these new characteristics,the paper mainly proposes two Tuberculosis models on the basis of traditional Tuberculosis models.Meanwhile, combined with these new characteristics, Tuberculosis models of one-strain and two-strains are developed.In chapter 2,with the imoportant influence of reinfection, untreaed rate,and partle immuned rate ,an untread Tuberculosis model with reinfection is developed.By proposing this model,the basic reproductive number R0 is obtained,and when R0 < 1,the multipie endemic equilibria may exists in the system.Meanwhile,untreaed rate is an important factor for today Tuberculosis prevalence.In chapter 3,on the basis of the dynamical system on a Tuberculosis spread model, the paper mainly discusses the dynamical behavior of a Tuberculosis spread model with constant immigration.The local and global asymptotically stability of the endemic equilibrium on this model is studied. It is proved by using the hurwitz criterion and the compound matrix theory. Sufficient conditions for the local and global asymptotically stability of the endemic equilibrium on this model are obtained.In chapter 4, combined with these new characteristics, Tuberculosis models of one-strain and two-strains are developed.