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Bulletin of Mathematical Biology

, Volume 75, Issue 11, pp 2059–2078 | Cite as

Complex Dynamics in an Eco-epidemiological Model

  • Andrew M. BateEmail author
  • Frank M. Hilker
Original Article

Abstract

The presence of infectious diseases can dramatically change the dynamics of ecological systems. By studying an SI-type disease in the predator population of a Rosenzweig–MacArthur model, we find a wealth of complex dynamics that do not exist in the absence of the disease. Numerical solutions indicate the existence of saddle–node and subcritical Hopf bifurcations, turning points and branching in periodic solutions, and a period-doubling cascade into chaos. This means that there are regions of bistability, in which the disease can have both a stabilising and destabilising effect. We also find tristability, which involves an endemic torus (or limit cycle), an endemic equilibrium and a disease-free limit cycle. The endemic torus seems to disappear via a homoclinic orbit. Notably, some of these dynamics occur when the basic reproduction number is less than one, and endemic situations would not be expected at all. The multistable regimes render the eco-epidemic system very sensitive to perturbations and facilitate a number of regime shifts, some of which we find to be irreversible.

Keywords

Eco-epidemiology Period-doubling Chaos Bistability Tristability 

Notes

Acknowledgements

The authors would like to thank Faina Berezovsky and an anonymous reviewer for their constructive comments.

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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  1. 1.Centre for Mathematical Biology, Department of Mathematical SciencesUniversity of BathBathUK

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