Analysis Of A Class Of Epidemic Model With Age Structure

In recent years,epidemiology has been an important branch of ecology.The development of population dynamics is very rapid,and many mathematical models are used to analyze various infectious diseases.With the in-depth understanding of the epidemic model,we found that some infectious diseases only spread in children,while some infectious diseases only spread in adults.And some virus carriers of infectious diseases have a higher risk of infection in the early incubation period.Therefore,studying the age structure of people makes the epidemic model more realistic.For age-structured epidemic models,two cases are discussed in this paper: one is the susceptible-exposed-infectiverecovered-susceptible(SEIRS)epidemic model with vertical transmission and time delay,the other is susceptible-infective-quarantined-recovered(SIQR)epidemic model with pulse vaccination.The main work is described as follows:1.It is studied that an age-structured SEIRS epidemic model with time delay and vertical transmission.Firstly,the epidemic model is established and described,then the traveling wave solution of system can be obtained by using the method of characteristic.And the existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses.Moreover,the age-structured SEIRS system is reduced to ordinary differential equations with time delay by using some insignificant simplifications.It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the epidemic model.Furthermore,the local stability for the disease-free equilibrium point and the endemic equilibrium point with time delay τ = 0 and τ > 0 are established.Finally,some numerical simulations are carried out to illustrate theoretical results.2.It is studied that an age-structured SIQR epidemic model with pulse vaccination.First of all,the epidemic model is established and described.For a special form of disease spread function,the model is simplified by using a reduction method,and then sixdimensional impulsive ordinary differential equations are obtained.Finally,by using the method of comparison theorem in impulse differential comparison system,sufficient condition for the global attractiveness of the disease-free periodic solution and the consistent persistence of diseases.