Complex Dynamics in an Eco-epidemiological Model

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 indicat...

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Veröffentlicht in:Bulletin of mathematical biology 2013-11, Vol.75 (11), p.2059-2078
Hauptverfasser: Bate, Andrew M., Hilker, Frank M.
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description 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.
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subjects Animals
Cell Biology
Communicable Diseases - epidemiology
Communicable Diseases - transmission
Ecosystem
Epidemiologic Factors
Food Chain
Humans
Life Sciences
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Biological
Nonlinear Dynamics
Original Article
title Complex Dynamics in an Eco-epidemiological Model
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