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Bifurcation analysis of an epidemic model with nonlinear incidence. (English) Zbl 1168.92323
Summary: We consider an epidemic model with the nonlinear incidence of a sigmoidal function. By mathematical analysis, it is shown that the model exhibits bistability and undergoes Hopf bifurcations and Bogdanov-Takens bifurcations. By numerical simulations, it is found that the incidence rate can induce multiple limit cycles, and a little change of the parameter could lead to quite different bifurcation structures.

MSC:
92D30Epidemiology
34C05Location of integral curves, singular points, limit cycles (ODE)
34D05Asymptotic stability of ODE
65C20Models (numerical methods)
34C60Qualitative investigation and simulation of models (ODE)
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References:
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