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 characterise 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.

Bifurcation thresholds in an SIR model with information-dependent vaccination

MANFREDI, PIETRO ANGELO MANFREDO FRANCESCO;
2007

Abstract

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 characterise 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.
Donofrio, A; Manfredi, PIETRO ANGELO MANFREDO FRANCESCO; Salinelli, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/110152
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