The Study For A Dynamic Epidemical Models Theoretics And Numerical Simulation

In the paper, we studied the global dynamics of an SEI epidemic model with generalcontact rate that incorporates constant recruitment and have infectious force in the latentperiod and infected period.By means of Lyapunov function and LaSalle s invariant set the-orem, we proved the global asymptotical stable results of the disease-free equilibrium. Thelocal asymptotical stable results of the epidemic equilibrium was proved by using the Hurwitzcriterion and the global asymptotical stable results of its by means of Poincare`?Bendixsonproperty. In addition, we we studied the global dynamics of an SEIR epidemic model with thebilinear incidence rate that incorporates constant recruitment in which the latent and immunestate were also infective. By means of Lyapunov function and LaSalle s invariant set theorem,we proved the global asymptotical stable results of the disease-free equilibrium. The localasymptotical stable results of the epidemic equilibrium was proved by using the Hurwitzcriterion. Furthermore, we proved the global stability of the unique endemic equilibriumwhen α1 = α2 = 0 and the disease persists at an endemic equilibrium state if it initiallyexists.