Study On The Dynamics Of An Epidemic Model And Eco-epidemic Models With Time Delay And Impulsive Effect

Infective diseases dynamics is a very important branch of biomathematics. With the development of study, ordinary differential equation systems have been unable to" meet research needs. In this thesis more complex systems with time delay and impulse are considered in order to reflect the actual situation better. It is of much importance in theory and practice to study these models. The main results are summarized as follows:In the first chapter, the development of infective diseases dynamics and population dynamics is given. The major work in this paper is also introduced.In the second chapter, a SIR epidemic model with stage structure is studied. It is assumed that only the mature individuals can be infected. The boundness of solutions and the existence of equilibriums are obtained. The conditions under which equilibriums are stable are discussed. And the numerical simulation is given.In the third chapter, a prey-predator eco-epidemiological system with stage structure is discussed. The model with both time delay and impulsive effect contains a special functional response and a saturated incidence of infection. By the theory of delay equations and impulsive comparison theorem, the sufficient conditions of global attractivity of prey- eradication periodic solution and permanence of the system are obtained. And the numerical simulation is used to indicate the results.In the last chapter, an eco-epidemiological model with impulsive control strategy is studied. We consider a special functional response and assumed that the periods of releasing natural enemies and spraying pesticide are different. And the infected predator can't to prey. The conditions of locally asymptotic stability of pest-eradication periodic solution are obtained by Floquet theorem and comparison theorem of impulsive differential equation. Furthermore, the conditions under which the system is permanent are discussed. And the numerical simulation is given.