NDLI: Seasonal dynamics in an SIR epidemic system

Content Provider	Springer Nature Link
Author	Augeraud Véron, E. Sari, N.
Copyright Year	2013
Abstract	We consider a seasonally forced SIR epidemic model where periodicity occurs in the contact rate. This periodical forcing represents successions of school terms and holidays. The epidemic dynamics are described by a switched system. Numerical studies in such a model have shown the existence of periodic solutions. First, we analytically prove the existence of an invariant domain $$D$$ containing all periodic (harmonic and subharmonic) orbits. Then, using different scales in time and variables, we rewrite the SIR model as a slow-fast dynamical system and we establish the existence of a macroscopic attractor domain $$K$$ , included in $$D$$ , for the switched dynamics. The existence of a unique harmonic solution is also proved for any value of the magnitude of the seasonal forcing term which can be interpreted as an annual infection. Subharmonic solutions can be seen as epidemic outbreaks. Our theoretical results allow us to exhibit quantitative characteristics about epidemics, such as the maximal period between major outbreaks and maximal prevalence.
Ending Page	725
Page Count	25
Starting Page	701
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	3
Volume Number	68
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-02-13
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Slow-fast system Canard solution Canard solutions Periodic SIR epidemic model Periodic solutions Mathematical and Computational Biology Nonlinear oscillations, coupled oscillators Averaging Periodic motion Applications of Mathematics Singular perturbations, general theory Epidemiology
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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