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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 56, Pages 2971-2987
http://dx.doi.org/10.1155/S0161171204310380

On stability and bifurcation of solutions of an SEIR epidemic model with vertical transmission

Department of Mathematics, Faculty of Science, Minoufiya University, Shebin El-Koom 230511, Egypt

Received 31 October 2003

Copyright © 2004 Hindawi Publishing Corporation. 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 four-dimensional SEIR epidemic model is considered. The stability of the equilibria is established. Hopf bifurcation and center manifold theories are applied for a reduced three-dimensional epidemic model. The boundedness, dissipativity, persistence, global stability, and Hopf-Andronov-Poincaré bifurcation for the four-dimensional epidemic model are studied.