Journal of Mathematical Biology

, Volume 75, Issue 6–7, pp 1655–1668 | Cite as

Chaotic dynamics in the seasonally forced SIR epidemic model

  • Pablo G. Barrientos
  • J. Ángel Rodríguez
  • Alfonso Ruiz-Herrera


We prove analytically the existence of chaotic dynamics in the forced SIR model. Although numerical experiments have already suggested that this model can exhibit chaotic dynamics, a rigorous proof (without computer-aided) was not given before. Under seasonality in the transmission rate, the coexistence of low birth and mortality rates with high recovery and transmission rates produces infinitely many periodic and aperiodic patterns together with sensitive dependence on the initial conditions.


Stretching along paths Seasonality SIR model Sensitive dependence on the initial conditions Chaos 

Mathematics Subject Classification

92B05 37F99 



The authors were supported by the grant MTM2014–56953-P.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Pablo G. Barrientos
    • 1
  • J. Ángel Rodríguez
    • 2
  • Alfonso Ruiz-Herrera
    • 2
  1. 1.Instituto de Matemática e EstatísticaUniversidade Federal FluminenseNiteróiBrazil
  2. 2.Departamento de MatemáticasUniversidad de OviedoOviedoSpain

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