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

摘要

A four-dimensional SEIR epidemic model is considered. The stabilityof the equilibria is established. Hopf bifurcation and centermanifold theories are applied for a reduced three-dimensional epidemicmodel. The boundedness, dissipativity, persistence, globalstability, and Hopf-Andronov-Poincaré bifurcation for thefour-dimensional epidemic model are studied.