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Estimating the distance to an epidemic threshold.

Eamon B O'Dea1,2, Andrew W Park3,4, John M Drake2,3

  • 1Department of Ecology, College of Veterinary Medicine, University of Georgia, Athens, GA, USA ebodea@uga.edu.

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Estimating epidemic thresholds is challenging when host population dynamics are slow. This study reveals how slow dynamics hinder threshold distance estimation from susceptible population fluctuations, offering new insights for disease modeling.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Population Dynamics

Background:

  • The epidemic threshold in susceptible-infected-recovered (SIR) models separates parameters allowing epidemics from those that do not.
  • This threshold is linked to the instability of the system's equilibrium.
  • Estimating the distance to this threshold is crucial for understanding disease dynamics.

Purpose of the Study:

  • To analytically investigate how slow host population dynamics affect the estimation of the epidemic threshold distance.
  • To establish guidelines for accurate estimation of the threshold distance.
  • To develop a method for estimating the rate of approach to the epidemic threshold.

Main Methods:

  • Analytical derivation of how slow population dynamics impact threshold distance estimation.
  • Analysis of susceptible population fluctuations.
  • Simulations to assess the applicability of results across various system parameters (population size, noise, observation schemes).

Main Results:

  • Slow host population dynamics can prevent accurate estimation of the distance to the epidemic threshold from susceptible population fluctuations.
  • Guidelines were established for when threshold distance estimates are accurate.
  • A method using multiple distance estimates to determine the rate of approach to the threshold was illustrated.

Conclusions:

  • Slow vital dynamics pose a significant challenge for estimating epidemic threshold distances using fluctuations in susceptible populations.
  • The developed estimation approach is general and applicable to various infectious diseases, including zoonotic (e.g., MERS-CoV) and vaccine-preventable (e.g., measles) diseases.