Rational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicity
'Rational' exemption to vaccination is due to a pseudo-rational comparison betweenthe low risk of infection, and the perceived risk of side effects fromthe vaccine. Here we consider rational exemption in an SI model withinformation dependent vaccination where individuals use information o...
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AIMS Press
2010-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.561 |
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| author | Bruno Buonomo Alberto d’Onofrio Deborah Lacitignola |
| author_facet | Bruno Buonomo Alberto d’Onofrio Deborah Lacitignola |
| author_sort | Bruno Buonomo |
| collection | DOAJ |
| description | 'Rational' exemption to vaccination is due to a pseudo-rational comparison betweenthe low risk of infection, and the perceived risk of side effects fromthe vaccine. Here we consider rational exemption in an SI model withinformation dependent vaccination where individuals use information on thedisease's spread as their information set. Using suitable assumptions, we show the dynamic implications of theinteraction between rational exemption, current and delayed information. In particular, if vaccination decisions are basedon 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. |
| format | Article |
| id | doaj-art-e8c7878553834c4d80a03f7f97cff45b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e8c7878553834c4d80a03f7f97cff45b2025-01-24T02:00:43ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-05-017356157810.3934/mbe.2010.7.561Rational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicityBruno Buonomo0Alberto d’Onofrio1Deborah Lacitignola2Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 NaplesDepartment of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 NaplesDepartment of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples'Rational' exemption to vaccination is due to a pseudo-rational comparison betweenthe low risk of infection, and the perceived risk of side effects fromthe vaccine. Here we consider rational exemption in an SI model withinformation dependent vaccination where individuals use information on thedisease's spread as their information set. Using suitable assumptions, we show the dynamic implications of theinteraction between rational exemption, current and delayed information. In particular, if vaccination decisions are basedon 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.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.561informationglobal stability.vaccinationsis epidemic modelrational exemption |
| spellingShingle | 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 information global stability. vaccination sis epidemic model rational exemption |
| title | Rational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicity |
| title_full | Rational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicity |
| title_fullStr | Rational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicity |
| title_full_unstemmed | Rational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicity |
| title_short | Rational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicity |
| title_sort | rational exemption to vaccination for non fatal sis diseases globally stable and oscillatory endemicity |
| topic | information global stability. vaccination sis epidemic model rational exemption |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.561 |
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