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

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.