The Study On The Epidemic Model With Vaccination And Nonlinear Infectious Rate

According to the statistical data of the Health Ministry,in recent years,there has been more than 30 kinds new-style infectious diseases around the world,such as Ebola virus,West Nile virus,HIV Bird flu,SARS and so on,and there are nearly 20 million people dying of different infectious diseases each year,so does a new kind of infectious virus emerge.So,preventing and controlling the infectious diseases is still a problem for people to deal with.At present,the researches which set up the related mathematical model by using dy-namic method,study these models from the aspects of dynamic behaviors and numerical simulation analysis,and reveal the spreading laws of diseases(making a good theoretical basis for the previous prevention of the sudden or unknown infectious diseases),have got a lot of achievements.In this paper,a epidemic model with nolinear rate of infection,impulse vaccination and isolation is studied by analyzing its dynamic behaviors,making a further supplement for the infectious,the work is divided into several parts below.Firstly,a kind of SEIR epidemic model with continuous vaccination and nonlin-ear incidence rate of infection,also the incubation period,infection period and recovery period are considered to be infectious was established.Then the model is analyzed qual-itatively and the corresponding conditions of the equilibriums's asymptotic stability are proved by using the theory of differential equation,constructing V function and Jacobian matrix.At the same time,the model's persistence is obtained according to the theory of semi-dynamic system and uniform persistence theory.Secondly,a kind of SEIR epidemic model with pulse vaccination and nonlinear infection rate is considered,then the existence of periodic solutions of disease-free and the conditions of global asymptotic stability are given by using the Floquet multiplier theory and comparison theory of impulsive differential equation,and the persistence of the model is proved.Finally,using the basic reproductive number to compare vaccination with impulsive vaccination.Finally,the isolation term is brought in on the base of the model that the SEIR epi-demic model with impulse vaccination and nonlinear infection,and a SEIQR epidemic model with pulse vaccination,nonlinear incidence rate and isolation is established,which focuses on the existence of periodic solutions of disease-free,global asymptotic stability and the system's persistence,while analysis the isolation rate and impulse vaccination rate with the basic reproductive number.