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Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator
J. Kopfová, P. Nábělková, D. Rachinskii, SC. Rouf
Language English Country Germany
Document type Journal Article, Research Support, Non-U.S. Gov't
NLK
ProQuest Central
from 1997-11-01 to 1 year ago
Medline Complete (EBSCOhost)
from 2005-01-01 to 1 year ago
Health & Medicine (ProQuest)
from 1997-11-01 to 1 year ago
- MeSH
- Models, Biological MeSH
- Epidemics * MeSH
- Communicable Diseases * epidemiology MeSH
- Humans MeSH
- Vaccination MeSH
- Check Tag
- Humans MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition for the global stability of the infection-free equilibrium state. If this condition does not hold true, the model has a connected set of endemic equilibrium states characterized by different proportion of infected and immune individuals. In this case, we show that every trajectory converges either to an endemic equilibrium or to a periodic orbit. Under additional natural assumptions, the periodic attractor is excluded, and we guarantee the convergence of each trajectory to an endemic equilibrium state. The global stability analysis uses a family of Lyapunov functions corresponding to the family of branches of the hysteresis operator.
Mathematical Institute of the Silesian University Na Rybníčku 1 746 01 Opava Czech Republic
University of Texas at Dallas 800 W Campbell Richardson TX 75080 United States
References provided by Crossref.org
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- $a We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition for the global stability of the infection-free equilibrium state. If this condition does not hold true, the model has a connected set of endemic equilibrium states characterized by different proportion of infected and immune individuals. In this case, we show that every trajectory converges either to an endemic equilibrium or to a periodic orbit. Under additional natural assumptions, the periodic attractor is excluded, and we guarantee the convergence of each trajectory to an endemic equilibrium state. The global stability analysis uses a family of Lyapunov functions corresponding to the family of branches of the hysteresis operator.
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