El-Sheikh, M. M. A.; El-Marouf, S. A. A. On stability and bifurcation of solutions of an SEIR epidemic model with vertical transmission. (English) Zbl 1077.34044 Int. J. Math. Math. Sci. 2004, No. 53-56, 2971-2987 (2004). 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. Reviewer: Chen Lan Sun (Beijing) Cited in 2 Documents 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 Keywords:stability; bifurcation of solution; SEIR epidemic model PDF BibTeX XML Cite \textit{M. M. A. El-Sheikh} and \textit{S. A. A. El-Marouf}, Int. J. Math. Math. Sci. 2004, No. 53--56, 2971--2987 (2004; Zbl 1077.34044) Full Text: DOI EuDML OpenURL