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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.

34C05Location of integral curves, singular points, limit cycles (ODE)
34D05Asymptotic stability of ODE
65C20Models (numerical methods)
34C60Qualitative investigation and simulation of models (ODE)
Full Text: DOI
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