Bifurcation Thresholds in an SIR Model with Information-Dependent Vaccination

Simple epidemiological models with information dependent vaccination functions can generate sustained oscillations via Hopf bifurcation of the endemic state. The onset of these oscil- lations 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 func- tion" having a simple interpretation: coverage functions lying always above the threshold always lead to oscillations, whereas coverage functions always below never lead to instability.

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