BIFURCATION-ANALYSIS OF PERIODIC SEIR AND SIR EPIDEMIC MODELS

The bifurcations of the periodic solutions of SEIR and SIR epidemic mo dels with sinusoidally varying contact rate are investigated. The anal ysis is carried out with respect to two parameters: the mean value and the degree of seasonality of the contact rate. The corresponding port raits in the two-parameter space are obtained by means of a numerical continuation method. Codimension two bifurcations (degenerate flips an d cusps) are detected, and multiple stable modes of behavior are ident ified in various regions of the parameter space. Finally, it is shown how the parametric portrait of the SEIR model tends to that of the SIR model when the latent period tends to zero.