International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 53-56, Pages 2971-2987
doi:10.1155/S0161171204310380
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
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.