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International Journal of Engineering Mathematics
Volume 2014 (2014), Article ID 487589, 6 pages
Research Article

Global Stability of a Delayed SIRI Epidemic Model with Nonlinear Incidence

1Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, Campus Universitaire, BP 133, 14000 Kénitra, Morocco
2Département d’Economie et de Gestion, Faculté des Sciences Juridiques, Economiques et Sociales, Université Mohammed V-Souissi, Route Outa Hsaine, BP 5295, 11100 Sala Al Jadida, Morocco

Received 25 July 2014; Accepted 14 November 2014; Published 7 December 2014

Academic Editor: Shouming Zhong

Copyright © 2014 Amine Bernoussi et al. 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.


In this paper we propose the global dynamics of an SIRI epidemic model with latency and a general nonlinear incidence function. The model is based on the susceptible-infective-recovered (SIR) compartmental structure with relapse (SIRI). Sufficient conditions for the global stability of equilibria (the disease-free equilibrium and the endemic equilibrium) are obtained by means of Lyapunov-LaSalle theorem. Also some numerical simulations are given to illustrate this result.