Chaos Analysis and Control for a Class of SIR Epidemic Model with Seasonal Fluctuation

Authors

Yi Zhang, Northeastern University; Shenyang University of Technology
Qingling L. Zhang, Northeastern University
Fuzhen Zhang, Nova Southeastern UniversityFollow
Fenglan Bai, Dalian Jiaotong University

Document Type

Article

Publication Date

1-1-2013

Publication Title

International Journal of Biomathematics

Keywords

Epidemic model, Differential-algebraic system, Seasonal fluctuation, Chaos, Tracking control

ISSN

1793-5245

Volume

6

Issue/No.

1

First Page

11pp

Abstract

In this paper, the problems of chaos and 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, as the common influenza, A type H1N1 influenza and so on. It is shown that there exist chaotic phenomena in the epidemic model. Furthermore, the tracking control method is used to control chaotic motions in the epidemic model. A feedback controller 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 disappeared. Finally, numerical simulations illustrate that the controller is effective

Comments

AMSC: 37G10

NSUWorks Citation

Zhang, Yi; Zhang, Qingling L.; Zhang, Fuzhen; and Bai, Fenglan, "Chaos Analysis and Control for a Class of SIR Epidemic Model with Seasonal Fluctuation" (2013). Mathematics Faculty Articles. 37.
https://nsuworks.nova.edu/math_facarticles/37

DOI

10.1142/S1793524512500635