Open AccessRational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicity
Author(s) -
Bruno Buonomo,
Alberto d’Onofrio,
Deborah Lacitignola
Publication year - 2010
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2010.7.561
Subject(s) - vaccination , meaning (existential) , mathematical economics , set (abstract data type) , hopf bifurcation , interpretation (philosophy) , mathematics , epidemic model , rational expectations , rational agent , econometrics , economics , medicine , bifurcation , computer science , environmental health , psychology , immunology , population , artificial intelligence , physics , nonlinear system , quantum mechanics , psychotherapist , programming language
'Rational' exemption to vaccination is due to a pseudo-rational comparison between the low risk of infection, and the perceived risk of side effects from the vaccine. Here we consider rational exemption in an SI model with information dependent vaccination where individuals use information on the disease's spread as their information set. Using suitable assumptions, we show the dynamic implications of the interaction between rational exemption, current and delayed information. In particular, if vaccination decisions are based on delayed informations, we illustrate both global attractivity to an endemic state, and the onset, through Hopf bifurcations, of general Yakubovich oscillations. Moreover, in some relevant cases, we plot the Hopf bifurcation curves and we give a behavioural interpretation of their meaning.