Analysis Of Three Kinds Of Epidemic Models With Time-delay

The occurrence of infectious disease,a very common phenomenon,is bringing the huge harm.The infectious disease dynamics is a method to discuss the spreading laws of infectious disease of population qualitatively and quantitively.By analyzing the dynamic behaviors of the system of infectious diseases can understand and predict the develop-ment trend of the population of the epidemic disease,also further explore the strategies for preventing and controlling the disease.While the time-delay also makes a big d-ifference in studying the system of infectious disease and should be one of the factors taken into account.At the same time,the species can't be existed isolated.In nature,there is interaction between two species or even among a variety of species all the time.Therefore,to consider the relationship of the infectious disease dynamics and population dynamics is much more practical.While in the study of group interaction,most of the researchers take the growing process of the population as a whole,which is obviously unreasonable.On the one hand,there is obvious differences that species have different physiology in different life stages,on the other hand,the interaction are different in dif-ferent life stages,thus considering the growing and developing stages seems to be more meaningful.In addition,the pulse effect,existing in ecology system generally,describes the rapid changes and jumping in the fixed and unfixed moments,which is the more true reflections of nature's developing process.So,after uniting these factors above totally,this paper is diveded into several aspects below:The first chapter:Introduction.(including the research background and significance,and problems researched in this paper).The second chapter:An SEIR epidemic model of single species with double delays and continuous vaccination is established,in which the incubation period?2 of the dis-ease and vaccination failure period?1 are both considered.The existences of disease-free equilibrium and the epidemic equilibrium and the Hopf branch of the endemic equilib-rium are discussed by applying the qualitative and stability theory method of time-delay differential equation.The third chapter:An ecological infectious diseases model with time-delay and the disease spreading in predator of two species is established and the conditions when every equilibrium exists are analyzed.Then the local asymptotic stabilities of equilibriums and the Hopf's existences of one of the boundary equilibriums and the positive equilib-rium are analyzed by using the time-delay differential equation's stability theory and the characteristic root method,and some corresponding conditions are obtained respectively.The forth chapter:A delayed ecological epidemic model with stage structure in prey and disease in predator is investigated(the predator only prey the adult prey),in which impulsive harvesting and impulsive input for the younger prey are brought in,also impul-sive harvesting and impulsive birth for the healthy predator are both considered.Then the existence of the disease-free periodic solution of the system is analyzed by applying the relevant theories of impulsive differential equations with time-delay,the global stability of the infection-free periodic solution and the sufficient conditions of persistence of the system are obtained.