Backward bifurcation in epidemic models: Problems arising with aggregated bifurcation parameters

Wangari, I, Davis, S and Stone, L 2016, 'Backward bifurcation in epidemic models: Problems arising with aggregated bifurcation parameters', Applied Mathematical Modelling, vol. 40, no. 2, pp. 1669-1675.


Document type: Journal Article
Collection: Journal Articles

Title Backward bifurcation in epidemic models: Problems arising with aggregated bifurcation parameters
Author(s) Wangari, I
Davis, S
Stone, L
Year 2016
Journal name Applied Mathematical Modelling
Volume number 40
Issue number 2
Start page 1669
End page 1675
Total pages 7
Publisher Elsevier Inc.
Abstract This study addresses problems that have arisen in the literature when calculating backward bifurcations, especially in the context of epidemic modeling. Backward bifurcations are generally studied by varying a bifurcation parameter which in epidemiological models is usually the so-called basic reproduction number R-0. However, it is often overlooked that R-0 is an aggregate of parameters in the model. One cannot simply vary the aggregate R-0 while leaving all model parameters constant as has happened many times in the literature. We investigate two scenarios. For the incorrect approach we fix all parameters in the aggregate R-0 to constant values, but R-0 is nevertheless varied as a bifurcation parameter. In the correct approach, a key parameter in R-0 is allowed to vary, and hence R-0 itself varies and acts as a natural bifurcation parameter. We explore how the outcomes of these two approaches are substantially different.
Subject Applied Mathematics not elsewhere classified
Keyword(s) Backward bifurcation
Backward bifurcation threshold Rc
Basic reproduction number
Epidemic models
DOI - identifier 10.1016/j.apm.2015.07.022
Copyright notice © 2015 Elsevier Inc
ISSN 0307-904X
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