The Analysis On Identifiablity And Stability Of SIR Epidemic Models

This paper studies the identification problem on the epidemic model of SIR with drug treatment, and the stability of the SIR epidemic model with impulsive vaccination and the age structure.First we discuss an identification analysis to the epidemic model of SIR with drug treatment. Through the identification analysis, we show that there are infinite-dimensional of different parameter vectors which can give rise to the same output data, that is to say, the model is unidentifiable. In addition, if all parameters arc unknown, it is inappropriate to estimate the transmission proportion between the susceptible and the infective class, but the model can still identify the basic reproduction number R0.Second we discuss the impulse vaccination strategy that can prevent and control some infectious diseases, since some diseases transmission depend on chronological and infection age of individual, we established the age-structured SIR model. The results show that there exists a globally stable infection-free situation if the impulsive period T and the proportion p satisfy R0(p,T)< 1. Finally, we discuss the problem of optimal vaccination strategy.