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Complex dynamics of a simple epidemic model with a nonlinear incidence

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  • A simple epidemic model with a nonlinear incidence rate and two compartments is studied. The backward bifurcation is described and the corresponding threshold is calculated. The Hopf bifurcation and Bogdanov-Takens bifurcation are analyzed and numerical evidences for the stable or unstable limit cycle are provided.
    Mathematics Subject Classification: Primary: 92D30, 34K20; Secondary: 34K25.

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