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Bifurcation analysis of an SIS epidemic model with nonlinear birth rate. (English) Zbl 1197.37117

Summary: This paper deals with an SIS epidemic model with delay. By regarding p as the bifurcation parameter and analyzing the characteristic equation of the linearized system of the original system at the positive equilibrium, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. The explicit formulae determining the direction of the bifurcations, the stability and other properties of the bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. Some numerical simulations are also included.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
37N25Dynamical systems in biology
92D30Epidemiology
34K18Bifurcation theory of functional differential equations