International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 56, Pages 2971-2987
doi: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 M. M. A. El-Sheikh and S. A. A. El-Marouf. 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.