Qualitative Analyses And Numerical Simulation Of Epidemic Dynamic Models By Pulse Effects

In this paper, we investigate some epidemical models with pulse effects. We establish existence and stabilities of periodic solutions to epidemic dynamic models with pulse vaccination. We also obtain some sufficient conditions for stabilities of periodic solutions to epidemic models with pulse removal. Numerical simulations confirm our theoretical results. The article encompassing six chapters is divided into two main parts. The second, the third and the forth chapters constitute partâ… , which deal with epidemic models with pulse vaccination. The partâ…¡consists of the fifth chapter; it contains the epidemic models with pulse removal.Firstly, we consider SIQR epidemical models with continuous and pulse vaccinations; the reproduction numbers have been obtained for those models; by using Dulac function, we prove the global stabilities of equilibrium of SIQR model with continuous vaccination. In the SIQR epidemical models with pulse vaccinations, we have also discussed the existence of the infection-free periodic solution, the global stabilities of the infection-free periodic solutions, and the effectiveness of pulse vaccination and continuous vaccination policies has been compared for the two models. Author also discussed pulse vaccination in the SIR epidemic model with vertical transmission. We obtain basic reproductive number and some sufficient conditions for the global stability of an infection-free periodic solution. Our theoretical results are confirmed by numerical simulations. Moreover, pulse vaccination in the DS-I-R epidemic model with differential susceptibility is studied. The existence of infection-free periodic solution is proved. The basic reproductive number of this model is defined and used to determine the threshold of the disease extinction. We prove the global stability of an infection-free periodic solution. At last, we consider pulse removal in the SIS epidemical models with vertical transmission. The reproduction numbers have been obtained for the model. We analyses the asymptotic behavior of the total number of infected individuals and the total population in our model.