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Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 826052, 8 pages
http://dx.doi.org/10.1155/2012/826052
Research Article

Global Stability Analysis of SEIR Model with Holling Type II Incidence Function

1Department of Mathematics, The Hashemite University, Zarqa 13115, Jordan
2Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

Received 27 June 2012; Revised 9 August 2012; Accepted 12 September 2012

Academic Editor: Jacek Waniewski

Copyright © 2012 Mohammad A. Safi and Salisu M. Garba. 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.

Abstract

A deterministic model for the transmission dynamics of a communicable disease is developed and rigorously analysed. The model, consisting of five mutually exclusive compartments representing the human dynamics, has a globally asymptotically stable disease-free equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number (), is less than unity; in such a case the endemic equilibrium does not exist. On the other hand, when the reproduction number is greater than unity, it is shown, using nonlinear Lyapunov function of Goh-Volterra type, in conjunction with the LaSalle's invariance principle, that the unique endemic equilibrium of the model is globally asymptotically stable under certain conditions. Furthermore, the disease is shown to be uniformly persistent whenever .