## Bifurcation analysis of periodic SEIR and SIR epidemic models.(English)Zbl 0786.92022

Summary: The bifurcations of the periodic solutions of $$SEIR$$ and $$SIR$$ epidemic models with sinusoidally varying contact rate are investigated. The analysis is carried out with respect to two parameters: the mean value and the degree of seasonality of the contact rate. The corresponding portraits in the two-parameter space are obtained by means of a numerical continuation method. Codimension two bifurcations (degenerate flips and cusps) are detected, and multiple stable modes of behavior are identified 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.

### MSC:

 92D30 Epidemiology 34C23 Bifurcation theory for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations

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### References:

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