Resistance mechanisms matter in SIR models

Timothy C. Reluga; Jan Medlock; Timothy C. Reluga; Jan Medlock

doi:10.3934/mbe.2007.4.553

Mathematical Biosciences and Engineering

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

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Resistance mechanisms matter in SIR models

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: 01 January 2007 Accepted: 29 June 2018 Published: 01 May 2007
MSC : 92D25.

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.
- immunological resistance,
- immunity,
- resistance bookkeeping.,
- behavioral resistance
Citation: Timothy C. Reluga, Jan Medlock. Resistance mechanisms matter in SIR models[J]. Mathematical Biosciences and Engineering, 2007, 4(3): 553-563. doi: 10.3934/mbe.2007.4.553

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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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