Stability Analysis Of Infectious Disease Model With Stage Structure

For a long time,the spread of infectious diseases has been the focus of attention of all sectors of society.The development of modern medical science has been abled to ef-fectively prevent and control many infectious diseases,but there are still some outbreaks and epidemics of infectious diseases,such as avian influenza,mutating every year.Social,economic,cultural,customs and habits all affect the spread of infectious diseases.The most direct factor is the number of infectious persons,their distribution in the popula-tion and the number of infected persons.Different types of infectious diseases have their own characteristics in their transmission process.And different populations have differ-ent transmission abilities at different age stages,and some infectious diseases only spread at different growth stages.In this paper,we mainly study infections disease model with stage-structured.We divide the population into adults and juveniles,and assume that only adult individuals can be infected.Establishing mathematical models to study the dynam-ics of three different epidemic models quantitative analysis was carried out to reflect the changing law and epidemic trend of infectious diseases,and the asymptotic stability of the system at disease-free equilibrium and endemic equilibrium was obtained.The correctness of some conclusions is verified by numerical simulation.Chapter one,this paper mainly introduces the research status and development trends of epidemic models with stage structure at home and abroad,and the necessary preparatory knowledge in this paper.The second chapter,the stability of a SIR epidemic model with stage structure and Logistic input is studied.The population is divided into adults and young adults,and only adult individuals are assumed to be infected.The local asymptotic stability and global asymptotic stability of disease-free equilibrium and endemic equilibrium are obtained by using the Hurwitz criterion,LaSalle invariant set principle and appropriate Lyapunov function.The third chapter,on the basis of chapter two,the latent person is added to the infectious warehouse,and the time lag factor is added to the process of transformation from infancy to adulthood.A SEIR epidemic model with stage structure and time delay is studied.The population is divided into adults and juveniles,assuming that diseases only spread among adults.The boundedness of solutions is proved by the qualitative and stability theory of differential equations,and the thresholds for disease elimination and endemic disease formation are obtained.The dynamic behavior of the model is obtained.The fourth chapter,on the basis of chapter three,the isolation warehouse is added to optimize the model.Since both latent and infected persons have infectious capacity,we assume that latent and infected persons have different infectious capacity.A stage structure SEIQR epidemic model with latent term and isolation term is studied.The local asymptotic stability and global asymptotic stability of the equilibrium point are judged by the Hurwitz criterion,LaSalle invariant set principle and its appropriately constructed Lyapu,nov function.The accuracy of the model is verified by numerical simulation with matlab.Chapter five summarizes the contents of the whole paper and puts forward the short-comings and future research directions.