Backward bifurcation in epidemic control

For a class of epidemiological SIRS models that include public health policies, the stability at the uninfected state and the prevalence at the infected state are investigated. Backward bifurcation from the uninfected state and hysteresis effects are shown to occur for some range of parameters. In s...

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Bibliographic Details
Published in:Mathematical biosciences 1997-11, Vol.146 (1), p.15-35
Main Authors: Hadeler, K.P., Van den Driessche, P.
Format: Article
Language:English
Subjects:
Biological and medical sciences
Disease Outbreaks - prevention & control
Disease Outbreaks - statistics & numerical data
General aspects
Humans
Mathematics
Medical sciences
Models, Biological
Parasitic Diseases - epidemiology
Parasitic Diseases - prevention & control
Planification. Prevention (methods). Intervention. Evaluation
Public Health
Public health. Hygiene
Public health. Hygiene-occupational medicine
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Summary:For a class of epidemiological SIRS models that include public health policies, the stability at the uninfected state and the prevalence at the infected state are investigated. Backward bifurcation from the uninfected state and hysteresis effects are shown to occur for some range of parameters. In such cases, the reproduction number does not describe the necessary elimination effort; rather the effort is described by the value of the critical parameter at the turning point. An explicit expression is given for this quantity. The phenomenon of subcritical bifurcation in epidemic modeling is also discussed in terms of group models, pair formation, and macroparasite infection.
ISSN:0025-5564
1879-3134
DOI:10.1016/S0025-5564(97)00027-8