The Study On Epidemic Models With Recruitment Rate And Nonlinear Incidence Rate

In this paper, we mainly study the dynamics of some classes of epidemical model with anonlinear birth in population. The article includes three chapters.The preface is in chapter1, we introduce the research background of this article, the maintask and some important preliminaries.In Chapter2, epidemic models involving a vertical transmission ware studied. There aretwo part in this chapter: In the first part, a pulse vaccination SEIQR epidemic model withvertical transmission and nonlinear incidence rate was studied. Using the discrete dynamicalsystem determined by the stroboscopic map, we obtained the exact disease-free periodic solution.We obtained two threshold value R1and R2. We show that the disease-free periodic solution ofthis system is globally attractive when R1<1by the theory of delayed diferential equations andthe comparison theorem for impulsive diferential equations. The system is permanent underR2>1. In the second part, A SEIQR epidemic model with vertical transmission and nonlinearincidence rate was studied. We obtained the threshold value R0to determine the dynamicsqualities of the epidemic model by directly using the next generation method. The locallyasymptotically stable of equilibriam was verified by Routh-Hurwitz criterion. We discussed theglobally asymptotically stable of the disease-free equilibrium when R≤1by constructing aLyapunov function.In Chapter3, an SIRS epidemic model with partial vaccination input and nonlinear inci-dence rate was studied. We obtained the threshold value R0about disease infection whether ornot. The locally asymptotically stable of disease-free equilibrium was verified by Routh-Hurwitzcriterion. We the possibility of Hopf bifurcation of the endemic equilibrium when R0>1. Weobtained the globally asymptotically stable of the disease-free equilibrium when R0<1. In theend, the persistence of our system was verified.