Bifurcation Thresholds in an SIR Model with Information-Dependent Vaccination

d'Onofrio, A., Manfredi, P., and Manfredi, P.. "Bifurcation Thresholds in an SIR Model with Information-Dependent Vaccination." Mathematical Modelling of Natural Phenomena 2.1 (2010): 26-43. <http://eudml.org/doc/222369>.

@article{dOnofrio2010,
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 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. },
author = {d'Onofrio, A., Manfredi, P., Manfredi, P.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {SIR epidemiological models; information-dependent vaccination; stability; Hopf bifurcations},
language = {eng},
month = {3},
number = {1},
pages = {26-43},
publisher = {EDP Sciences},
title = {Bifurcation Thresholds in an SIR Model with Information-Dependent Vaccination},
url = {http://eudml.org/doc/222369},
volume = {2},
year = {2010},
}

TY - JOUR
AU - d'Onofrio, A.
AU - Manfredi, P.
AU - Manfredi, P.
TI - Bifurcation Thresholds in an SIR Model with Information-Dependent Vaccination
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 2
IS - 1
SP - 26
EP - 43
AB - 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.
LA - eng
KW - SIR epidemiological models; information-dependent vaccination; stability; Hopf bifurcations
UR - http://eudml.org/doc/222369
ER -