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

Primary: 92D30; Secondary: 34D23, 34C15.

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

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
3. Department of Mathematics, University of Salento, via Provinciale Lecce-Arnesano, I-73100 Lecce

'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.
  Article Metrics

Keywords Information; global stability.; vaccination; SIS epidemic model; rational exemption

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


This article has been cited by

  • 1. Zhenguo Bai, Global dynamics of a SEIR model with information dependent vaccination and periodically varying transmission rate, Mathematical Methods in the Applied Sciences, 2015, 38, 11, 2403, 10.1002/mma.3231
  • 2. Alberto D'Onofrio, Cruz Vargas-De-León, Global stability of infectious disease models with contact rate as a function of prevalence index, Mathematical Biosciences and Engineering, 2017, 14, 4, 1019, 10.3934/mbe.2017053
  • 3. B. Buonomo, A. d’Onofrio, D. Lacitignola, Modeling of pseudo-rational exemption to vaccination for SEIR diseases, Journal of Mathematical Analysis and Applications, 2013, 404, 2, 385, 10.1016/j.jmaa.2013.02.063
  • 4. Frederik Verelst, Lander Willem, Philippe Beutels, Behavioural change models for infectious disease transmission: a systematic review (2010–2015), Journal of The Royal Society Interface, 2016, 13, 125, 20160820, 10.1098/rsif.2016.0820
  • 5. Bruno Buonomo, Alberto d’Onofrio, Modeling the Influence of Public’s Memory on the Corruption–Popularity Dilemma in Politics, Journal of Optimization Theory and Applications, 2013, 158, 2, 554, 10.1007/s10957-012-0218-z
  • 6. B. Buonomo, A. d’Onofrio, D. Lacitignola, Globally stable endemicity for infectious diseases with information-related changes in contact patterns, Applied Mathematics Letters, 2012, 25, 7, 1056, 10.1016/j.aml.2012.03.016
  • 7. Anuj Kumar, Prashant K. Srivastava, Yasuhiro Takeuchi, Modeling the role of information and limited optimal treatment on disease prevalence, Journal of Theoretical Biology, 2017, 414, 103, 10.1016/j.jtbi.2016.11.016
  • 8. Bruno Buonomo, Alberto d’Onofrio, Deborah Lacitignola, , Modeling the Interplay Between Human Behavior and the Spread of Infectious Diseases, 2013, Chapter 18, 289, 10.1007/978-1-4614-5474-8_18
  • 9. Anuj Kumar, Prashant K. Srivastava, RP Gupta, Nonlinear dynamics of infectious diseases via information-induced vaccination and saturated treatment, Mathematics and Computers in Simulation, 2018, 10.1016/j.matcom.2018.09.024

Reader Comments

your name: *   your email: *  

Copyright Info: 2010, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved