International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 56, Pages 2971-2987

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

M. M. A. El-Sheikh and S. A. A. El-Marouf

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.


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.