Journal of Mathematical Biology

, Volume 67, Issue 2, pp 293–327

Chaos in a seasonally perturbed SIR model: avian influenza in a seabird colony as a paradigm

Authors

    • Department of Applied Mathematics, Western Gateway BuildingUniversity College Cork
    • Odum School of EcologyUniversity of Georgia
  • Thomas C. Kelly
    • Department of Zoology, Ecology and Plant Science, Distillery FieldsUniversity College Cork
  • Andrei Korobeinikov
    • MACSI, Department of Mathematics and StatisticsUniversity of Limerick
  • Michael J. A. O’Callaghan
    • Department of Applied Mathematics, Western Gateway BuildingUniversity College Cork
  • Alexei V. Pokrovskii
    • Department of Applied Mathematics, Western Gateway BuildingUniversity College Cork
  • Dmitrii Rachinskii
    • Department of Applied Mathematics, Western Gateway BuildingUniversity College Cork
Article

DOI: 10.1007/s00285-012-0550-9

Cite this article as:
O’Regan, S.M., Kelly, T.C., Korobeinikov, A. et al. J. Math. Biol. (2013) 67: 293. doi:10.1007/s00285-012-0550-9

Abstract

Seasonality is a complex force in nature that affects multiple processes in wild animal populations. In particular, seasonal variations in demographic processes may considerably affect the persistence of a pathogen in these populations. Furthermore, it has been long observed in computer simulations that under seasonal perturbations, a host–pathogen system can exhibit complex dynamics, including the transition to chaos, as the magnitude of the seasonal perturbation increases. In this paper, we develop a seasonally perturbed Susceptible-Infected-Recovered model of avian influenza in a seabird colony. Numerical simulations of the model give rise to chaotic recurrent epidemics for parameters that reflect the ecology of avian influenza in a seabird population, thereby providing a case study for chaos in a host– pathogen system. We give a computer-assisted exposition of the existence of chaos in the model using methods that are based on the concept of topological hyperbolicity. Our approach elucidates the geometry of the chaos in the phase space of the model, thereby offering a mechanism for the persistence of the infection. Finally, the methods described in this paper may be immediately extended to other infections and hosts, including humans.

Keywords

ChaosEpidemicsSIR modelSeabird colonySeasonalityAvian influenzaH5N1 virusHyperbolicity

Mathematics Subject Classification

37B5537D4592B0592D40

Copyright information

© Springer-Verlag 2012