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Bifurcation Thresholds in an SIR Model withInformation-Dependent Vaccination

Published online by Cambridge University Press:  15 June 2008

A. d'Onofrio ,
P. Manfredi  and
P. Manfredi
A. d'Onofrio
Affiliation:
Division of Epidemiology and Biostatistics, European Institute of Oncology Via Ripamonti 435, 20141 Milano, Italy
P. Manfredi
Affiliation:
Dipartimento di Statistica e Matematica Applicata all' Economia, Università di Pisa Via Ridolfi 10, 5612 Pisa, Italy
P. Manfredi*
Affiliation:
Dipartimento di Scienze Economiche e Metodi Quantitativi, Università del Piemonte Orientale “A. Avogadro”, Via Perrone 18, 28100 Novara, Italy
*
[email protected]
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Abstract

Simple epidemiological models with information dependent vaccination functions cangenerate sustained oscillations via Hopf bifurcation of the endemic state. The onset of these oscillations depend on the shape of the vaccination function. A “global” approach is used to characterize the instability condition and identify classes of functions that always lead to stability/instability. The analysis allows the identification of an analytically determined “threshold vaccination function” having a simple interpretation: coverage functions lying always above the threshold always lead to oscillations, whereas coverage functions always below never lead to instability.

Keywords

SIR epidemiological modelsinformation-dependent vaccinationstabilityHopf bifurcations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 2 , Issue 1: Epidemiology , 2007 , pp. 26 - 43
Copyright
© EDP Sciences, 2007

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