Subharmonic bifurcation in an S-I-R epidemic model

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Abstract
An S → I → R epidemic model with annual oscillation in the contact rate is analyzed for the existence of subharmonic solutions of period two years. We prove that a stable period two solution bifurcates from a period one solution as the amplitude of oscillation in the contact rate exceeds a threshold value. This makes rigorous earlier formal arguments of Z. Grossman, I. Gumowski, and K. Dietz [4].

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