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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 979217, 17 pages
Research Article

Stability Analysis of a Delayed SIR Epidemic Model with Stage Structure and Nonlinear Incidence

Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 28 April 2009; Accepted 21 August 2009

Academic Editor: Antonia Vecchio

Copyright © 2009 Xiaohong Tian and Rui Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the stability of an SIR epidemic model with stage structure and time delay. By analyzing the eigenvalues of the corresponding characteristic equation, the local stability of each feasible equilibrium of the model is established. By using comparison arguments, it is proved when the basic reproduction number is less than unity, the disease free equilibrium is globally asymptotically stable. When the basic reproduction number is greater than unity, sufficient conditions are derived for the global stability of an endemic equilibrium of the model. Numerical simulations are carried out to illustrate the theoretical results.