Mathematical Biosciences and Engineering (MBE)

Resistance mechanisms matter in SIR models

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

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Timothy C. Reluga - Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, United States (email)
Jan Medlock - Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT 06520, United States (email)

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.

Keywords:  behavioral resistance, immunological resistance, immunity, resistance bookkeeping.
Mathematics Subject Classification:  92D25.

Received: January 2007;      Accepted: April 2007;      Published: May 2007.