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Zbl 1131.92055
Jiang, Zhichao; Wei, Junjie
Stability and bifurcation analysis in a delayed SIR model. (English)
[J] Chaos Solitons Fractals 35, No. 3, 609-619 (2008). ISSN 0960-0779

Summary: A time-delayed SIR model with a nonlinear incidence rate is considered. The existence of Hopf bifurcations at the endemic equilibrium is established by analyzing the distribution of the characteristic values. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out.

MSC 2000:: *92D30 Epidemiology
34K18 Bifurcation theory of functional differential equations
34K20 Stability theory of functional-differential equations
37N25 Dynamical systems in biology
34K13 Periodic solutions of functional differential equations
34K60 Applications of functional-differential equations

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Zentralblatt MATH Berlin [Germany]