Pulse, Stage Structure And Prey Infected Infectious Disease Model

Recent years, with highly developed economy, medicine with the kinds increasing being used,convenient transportation and frequent economical intercourse, the social development is promoted and the human's survival quality is improved. At the same time, they also provide the extremely convenient conditions to the variation of infectious pathogen and the dissemination and spread of the infections. When the infection models are constructed, we often consider some factors, such as the dissemination of the disease between multi-populations, population's staged structure, the diffusion of diseases between the patches, some strategy to control the infectious diseases and so on. Aiming to these factors mentioned above, some infections disease models are developed in this article. The primary coverage is as follows.In chapter 2, a prey-predator model with the prey infected and the nonlinear incidence rateλS^qI^P is firstly studied. In this part,the boundary equilibrium point and positive equilibrium point are got,and the stability of this system is discussed. In order to control some infections, the infected population are sometimes killed at the stationary time to reduce the density of population. Consequently, a prey-predator model with impulsive effect and the prey infected is established. In this model, the disease is controlled by the impulsive culling to the prey. By using impulsive differential inequality,the boundedness of the system is proved. The existence of the positive periodic solution of the system is proved by use of the coincidence degree theorem.In chapter 3, This paper established a infectious disease mathematical model with two age stage structure and the lifelong immunity.Next it carry on the qualitative analysis on the model,analyzed the model of the balance points approach stability through using comparison theorem, linearization and structured suitable Lyapunov function. At the same time, it obtains the conclusion of the model's approach nature and their balance points' partial approach stable under the suitable condition. Meantime, it obtains the condition when the disease finally eliminates. In chapter 4, an SIR epidemic model with vertical transmission and impulse constant vaccination is considered. The threshold R₀ is obtained,and prove the local and global asymptotic stability of periodic infection-free solution if R₀ < 1. Then considering each member of population diffuses between the two patches under the periodically impulsive effect, a SI infection model with impulsive diffusion between two patches is constructed. And the existence and local stability of the infection-free periodic solution are proved.