The Study On Species And Epidemic Dynamic Models With Impulsive Effects

The impulsive differential equations have obtained much attention from many authors, and deeply during the past a few years. It is widely applied in various domains such as biological technology, medicine dynamics, physics, economy, popu-lation dynamics and epidemiology. It is well-known that many natural phenomena and human activities do exhibit impulsive effects in the fields of population dynam-ics and epidemiology. We consider the nonautonomous species models and epidemic models with impulsive effects. Obtained sufficient conditions of permanence and extinction of competition and predator-prey models; and sufficient conditions of the permanence and extinction of the disease are given.In the second part, we discuss the nonautonomous species models with impul-sive effects. Firstly, we studied the nonautonomous N-species Lotka-Valterra com-petitive system with impulses, some criteria on the permanence, global attractivity, extinction of partial species are established by used the methods of inequalities estimate and Liapunov functions. Secondly, we investigated the nonautonomous predator-prey system with infinite delays and impulse, the sufficient and necessary conditions of integrable form on the permanence of the species and two species are established by using the comparison theorem of impulsive differential equation.In the last part, we studied the epidemic models with impulsive effects. Firstly, two delayed SEIR epidemic models with continuous and impulsive vaccination and saturating incidence are investigated. The dynamical behaviors of the disease are analyzed, we establish the sufficient conditions of the extinction and the permanence of the disease by using the comparison theorem of impulsive differential equations and nonlinear analysis method. Secondly, three different vaccination and treatment strategies in the SIR epidemic models with saturated infectious force and verti-cal transmission are analyzed. The dynamics of the epidemic model is globally investigated. For every treatment and vaccination strategy, the disease-free peri-odic solution of the impulsive system has been obtained and is found to be globally asymptotically stable when the basic reproduction number is less than one, equiva-lently the cure rate is larger than the threshold value, whereas the disease is persist when the basic reproduction number is larger than one.