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Bifurcation analysis of a delayed epidemic model. (English) Zbl 1186.92042

Summary: Hopf bifurcation for a delayed SIS epidemic model with stage structure and nonlinear incidence rate is investigated. Through theoretical analysis, we show the positive equilibrium stability and the conditions that Hopf bifurcations occur. Applying the normal form theory and a center manifold argument, we derive explicit formulas determining the properties of the bifurcating periodic solutions. In addition, we also study the inhibition effect on the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.

MSC:

92D30 Epidemiology
34K18 Bifurcation theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
65C60 Computational problems in statistics (MSC2010)
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