Chaos control for a class of SIR epidemic model with seasonal fluctuation

Abstract

In this paper, the problems of chaos control for a class of susceptible-infected-removed (SIR) epidemic model with seasonal fluctuation are investigated. The seasonality in outbreak is natural among infectious diseases, such as the common influenza, the type H1N1 influenza and so on. It is known that there exist chaotic phenomena in the epidemic model. Furthermore, the tracking control method is used to regulate chaotic motions in the epidemic model. A feedback control input is designed to achieve tracking of an ideal output. Thus, the density of infected individuals can converge to zero, in other words, the disease can be eliminated. Finally, numerical simulations are given to illustrate that the feedback control input is effective.