The Study On The Dynamical Behaviors Of Epidemic Models With State Dependent Impulse Control

In recent years, population dynamics model and microbial cultivation model have been attracted widespread concern of domestic and international scholars owing to its efficiency and economy with state dependent impulsive control strategies. This disserta-tion has carried out a detailed research on SIVS epidemic model, West Nile Virus model and the model of releasing sterile mosquitoes with state dependent impulse control, the effects on disease of elimination and popularity with state dependent impulsive control are investigated. The main contents can be summarized as follows:1. In the first part (corresponding to the section 2), we mainly discuss dynamical behaviors of a kind of SIVS epidemic model with state dependent impulsive effects. Firstly, regarding the density of infected individuals as monitoring threshold value, we obtained some sufficient conditions of the existence and orbitally asymptotical stability of two order-k(k=1,2) periodic solutions by qualitative analysis method, direct analysis method, comparison principle and so on. Secondly, thinking of susceptible population as monitoring threshold value, we obtained some sufficient conditions of the existence and orbitally asymptotical stability of the two semi-trivial periodic solutions and two order-I periodic solutions. Thirdly, numerical simulations illustrate the validity of the theoretical results and the feasibility of the state dependent pulse control strategies.2. In the second part (corresponding to the section 3), a West Nile Virus model with state dependent impulsive curing infected birds and culling mosquitoes has been mainly proposed, we obtained some sufficient conditions of the existence and orbitally asymp-totical stability of two order-k(k= 1,2) periodic solutions by constructing Poincare map, using qualitative analysis method, analogue of Poincare criterion, comparison principle and so on. Our results show that the control measure is effective and feasible by means of numerical simulations.3. In the third part (corresponding to the section 4), Based on control mechanism of vector infectious diseases, we formulate an ODE model for the interactions between wild and sterile mosquito population, which is subject to state-dependent impulsive releasing sterile mosquitoes and culling mosquitpes. We obtain sufficient conditions of the global asymptotical stability of the model without impulsive state feedback control via comprehensively qualitative analysis, using LaSalle invariance principle. By constructing Poincare map, using analogue of Poincare criterion, theory of differential inequalities, differential equation geometry and so on, we obtain that the model with impulsive state feedback control has a positive periodic solution of order-1 which is asymptotical stability. Our results show that the control measure is effective and feasible by means of numerical simulations. Therefore, this strategy can curb the spread of vector infectious disease.