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Bifurcation analysis of periodicSEIRandSIRepidemic models

✍ Scribed by Yu. A. Kuznetsov; C. Piccardi

Publisher
Springer
Year
1994
Tongue
English
Weight
763 KB
Volume
32
Category
Article
ISSN
0303-6812

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✦ Synopsis

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.

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