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

  • Received: 01 August 2009 Accepted: 29 June 2018 Published: 01 June 2010
  • MSC : Primary: 92D30; Secondary: 34D23, 34C15.

  • '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[J]. Mathematical Biosciences and Engineering, 2010, 7(3): 561-578. doi: 10.3934/mbe.2010.7.561

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  • '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.


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