×

On stability and bifurcation of solutions of an SEIR epidemic model with vertical transmission. (English) Zbl 1077.34044

The authors consider a four-dimensional SEIR epidemic model. 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.

MSC:

34C23 Bifurcation theory for ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D23 Global stability of solutions to ordinary differential equations
92D30 Epidemiology
PDF BibTeX XML Cite
Full Text: DOI EuDML