# American Institute of Mathematical Sciences

2010, 7(3): 561-578. doi: 10.3934/mbe.2010.7.561

## Rational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicity

 1 Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples 2 Department of Experimental Oncology, European Institute of Oncology, Via Ripamonti 435, I-20141 Milan, Italy 3 Department of Mathematics, University of Salento, via Provinciale Lecce-Arnesano, I-73100 Lecce, Italy

Received  August 2009 Revised  September 2009 Published  June 2010

'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.
Citation: Bruno Buonomo, Alberto d’Onofrio, Deborah Lacitignola. Rational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicity. Mathematical Biosciences & Engineering, 2010, 7 (3) : 561-578. doi: 10.3934/mbe.2010.7.561
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