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Stability and bifurcation analysis in a delayed SIR model. (English) Zbl 1131.92055
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:
92D30Epidemiology
34K18Bifurcation theory of functional differential equations
34K20Stability theory of functional-differential equations
37N25Dynamical systems in biology
34K13Periodic solutions of functional differential equations
34K60Qualitative investigation and simulation of models