Resistance mechanisms matter in SIR models

Timothy C. Reluga; Jan Medlock

doi:10.3934/mbe.2007.4.553

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2007, Volume 4, Issue 3: 553-563. Doi: 10.3934/mbe.2007.4.553

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Resistance mechanisms matter in SIR models

Timothy C. Reluga^1, and
Jan Medlock^2,

1.
Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545
2.
Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT 06520

Received: December 31, 2006

Revised: March 31, 2007

Published: April 2007

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Abstract

We compare four SIR-style models describing behavioral or immunological disease resistance that may be both partial and temporary in parameter regions feasible for interpandemic influenza. For the models studied, backward bifurcations and bistability may occur in contexts where resistance is due to behavior change, but they do not occur when resistance originates from an immune response. Care must be exercised to ensure that modeling assumptions about resistance are consistent with the biological mechanisms under study.

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Mathematics Subject Classification: 92D25.

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