Subharmonic bifurcation in an S-I-R epidemic model.

An S leads to I leads to 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].