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Mathematical Biosciences and Engineering

2010, Volume 7, Issue 3: 561-578. doi: 10.3934/mbe.2010.7.561
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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
  • 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.


  • This article has been cited by:

    1. Zhenguo Bai, Global dynamics of a SEIR model with information dependent vaccination and periodically varying transmission rate, 2015, 38, 01704214, 2403, 10.1002/mma.3231
    2. Cruz Vargas-De-León, Alberto d'Onofrio, Global stability of infectious disease models with contact rate as a function of prevalence index, 2017, 14, 1551-0018, 1019, 10.3934/mbe.2017053
    3. Bruno Buonomo, Alberto d’Onofrio, Deborah Lacitignola, 2013, Chapter 18, 978-1-4614-5473-1, 289, 10.1007/978-1-4614-5474-8_18
    4. B. Buonomo, A. d’Onofrio, D. Lacitignola, Modeling of pseudo-rational exemption to vaccination for SEIR diseases, 2013, 404, 0022247X, 385, 10.1016/j.jmaa.2013.02.063
    5. Frederik Verelst, Lander Willem, Philippe Beutels, Behavioural change models for infectious disease transmission: a systematic review (2010–2015), 2016, 13, 1742-5689, 20160820, 10.1098/rsif.2016.0820
    6. Bruno Buonomo, Alberto d’Onofrio, Modeling the Influence of Public’s Memory on the Corruption–Popularity Dilemma in Politics, 2013, 158, 0022-3239, 554, 10.1007/s10957-012-0218-z
    7. B. Buonomo, A. d’Onofrio, D. Lacitignola, Globally stable endemicity for infectious diseases with information-related changes in contact patterns, 2012, 25, 08939659, 1056, 10.1016/j.aml.2012.03.016
    8. Anuj Kumar, Prashant K. Srivastava, Yasuhiro Takeuchi, Modeling the role of information and limited optimal treatment on disease prevalence, 2017, 414, 00225193, 103, 10.1016/j.jtbi.2016.11.016
    9. Anuj Kumar, Prashant K. Srivastava, R.P. Gupta, Nonlinear dynamics of infectious diseases via information-induced vaccination and saturated treatment, 2019, 157, 03784754, 77, 10.1016/j.matcom.2018.09.024
    10. Lili Liu, Jian Zhang, Yazhi Li, Xinzhi Ren, An age-structured tuberculosis model with information and immigration: Stability and simulation study, 2023, 16, 1793-5245, 10.1142/S1793524522500760
    11. Shaday Guerrero‐Flores, Osvaldo Osuna, Cruz Vargas‐De‐León, Periodic solutions of seasonal epidemiological models with information‐dependent vaccination, 2023, 0170-4214, 10.1002/mma.9728
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  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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