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Predator-prey oscillations can shift when diseases become endemic.

Andrew M Bate1, Frank M Hilker

  • 1Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. A.M.Bate@bath.ac.uk

Journal of Theoretical Biology
|September 29, 2012
PubMed
Summary

Disease endemicity determination requires a time-averaged basic reproductive number (R(0)¯) in oscillating predator-prey systems, not equilibrium calculations. This impacts epidemiological modeling of density-dependent diseases.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Ecology

Background:

  • Determining disease endemicity is crucial in epidemiology.
  • Traditional methods rely on equilibrium-based calculations of the basic reproductive number, R(0).
  • Natural systems often exhibit oscillatory dynamics, such as predator-prey cycles.

Purpose of the Study:

  • To model disease transmission in an oscillating predator-prey system with density-dependent transmission.
  • To investigate the impact of oscillations on disease persistence and endemicity.
  • To identify the correct metric for determining endemicity in such dynamic systems.

Main Methods:

  • Development of a mathematical model for a density-dependent disease within an oscillating predator-prey framework.
  • Analysis of disease persistence conditions based on host population dynamics.
  • Comparison of time-averaged R(0) (R(0)¯) with equilibrium-based R(0).

Main Results:

  • Disease persistence in oscillating predator-prey systems depends on the time-average host density, not equilibrium density.
  • The time-averaged basic reproductive number, R(0)¯, dictates endemicity, not the equilibrium R(0).
  • Equilibrium-based R(0) analysis is insufficient for density-dependent diseases in oscillating systems.

Conclusions:

  • Standard epidemiological assessments using equilibrium R(0) are inadequate for diseases in oscillating predator-prey models.
  • Time-averaged R(0)¯ is the appropriate metric for endemicity in these dynamic ecological settings.
  • Findings necessitate a re-evaluation of R(0) analyses in epidemiological studies of density-dependent diseases within oscillating populations.