Dynamic behaviour of a discrete-time SIR model with information dependent vaccine uptake

Alberto d’Onofrio, Piero Manfredi, Ernesto Salinelli

Research output: Contribution to journalArticlepeer-review


This paper proposes and analyzes a discrete-time deterministic SIR model with information dependent immunization behaviour, where vaccination coverage at birth during any period of time is a general phenomenological function of the risk of infection that is perceived at the beginning of the period. Results on existence of equilibria, their local stability, and system persistence are proved. Then, by considering the noteworthy subcase of a piecewise linear ‘prevalence-dependent’ coverage function, the local stability of the endemic state is proved and conditions for its global asymptotic stability are given. Some insight on both Neimarck-Sacher and period-doubling bifurcations are provided. Overall we show that prevalence-dependent coverage is an essentially stabilising force. However period-doubling bifurcations are possible though under stressed parameter constellations.

Original languageEnglish
JournalJournal of Difference Equations and Applications
Publication statusAccepted/In press - Nov 15 2015


  • Discrete deterministic SIR models
  • global stability
  • oscillations
  • persistence
  • rational opposition to vaccination

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Analysis


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