Bifurcation analysis of periodic SEIR and SIR epidemic models
Copyright policy )Bifurcation analysis of periodic SEIR and SIR epidemic models
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.
- Russian Academy of Sciences Russian Federation
- Polytechnic University of Milan Italy
- National Research Council Italy
- Institute of Mathematical Problems of Biology Russian Federation
subharmonic solutions, Bifurcation theory for ordinary differential equations, flips, cusps, Epidemiology, latent period, \(SIR\) epidemic models, SEIR model, Models, Biological, numerical continuation method, Disease Outbreaks, degree of seasonality, Data Interpretation, Statistical, mean value, Humans, Periodic solutions to ordinary differential equations, Mathematics, Software, sinusoidally varying contact rate
subharmonic solutions, Bifurcation theory for ordinary differential equations, flips, cusps, Epidemiology, latent period, \(SIR\) epidemic models, SEIR model, Models, Biological, numerical continuation method, Disease Outbreaks, degree of seasonality, Data Interpretation, Statistical, mean value, Humans, Periodic solutions to ordinary differential equations, Mathematics, Software, sinusoidally varying contact rate
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