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A sharp threshold for disease persistence in host metapopulations

Thanate Dhirasakdanon1, Horst R Thieme, P Van Den Driessche

  • 1Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, USA.

Journal of Biological Dynamics
|August 11, 2012
PubMed

Insights

A sharp threshold determines if small disease outbreaks persist or go extinct in metapopulation models. This threshold, based on the disease reproduction number, guides understanding of disease dynamics and control strategies.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Metapopulation models are crucial for understanding disease spread across connected populations.
  • Disease dynamics are influenced by factors like transmission rates, recovery, and spatial movement.
  • Previous models often require detailed knowledge of disease-free equilibria, limiting their applicability.

Purpose of the Study:

  • To establish a clear threshold distinguishing disease persistence from extinction in metapopulation models.
  • To analyze the impact of prevalence-dependent travel rates on disease dynamics.
  • To formulate the threshold using the basic replacement ratio and spectral bounds.

Main Methods:

  • Utilized an S→E→I→R→S metapopulation model.
  • Incorporated frequency-dependent (standard) incidence.
  • Defined a threshold based on the basic replacement ratio (R(0)) and the spectral bound of a transmission and travel matrix.

Main Results:

  • A sharp threshold was identified, separating disease persistence from extinction.
  • For R(0)>1, weak disease persistence was generally shown, with strong persistence proven for constant susceptible recruitment.
  • For R(0)<1, Lyapunov stability analysis confirmed small outbreaks die out.

Conclusions:

  • The established threshold provides a robust criterion for disease persistence or extinction in metapopulations.
  • Prevalence-dependent travel significantly influences disease dynamics.
  • The model offers insights into disease control without needing a disease-free equilibrium assumption.

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