| Issue |
Math. Model. Nat. Phenom.
Volume 2, Number 1, 2007
Epidemiology
|
|
|---|---|---|
| Page(s) | 26 - 43 | |
| DOI | https://doi.org/10.1051/mmnp:2008009 | |
| Published online | 15 June 2008 | |
Bifurcation Thresholds in an SIR Model with Information-Dependent Vaccination
1
Division of Epidemiology and Biostatistics, European Institute of Oncology
Via Ripamonti 435, 20141 Milano, Italy
2
Dipartimento di Statistica e Matematica Applicata all' Economia,
Università di Pisa Via Ridolfi 10, 5612 Pisa, Italy
3
Dipartimento di Scienze Economiche e Metodi Quantitativi, Università
del Piemonte Orientale “A. Avogadro”, Via Perrone 18, 28100 Novara, Italy
Corresponding author: alberto.donofrio@ieo.it
Simple epidemiological models with information dependent vaccination functions can generate 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.
Mathematics Subject Classification: 92D30
Key words: SIR epidemiological models / information-dependent vaccination / stability / Hopf bifurcations
© EDP Sciences, 2007
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