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Immunometabolic Circuits in Infection for Advancing Host Directed Therapies
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Immunometabolic Circuits in Infection for Advancing Host Directed Therapies

Published on: September 13, 2024

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
Summary
This summary is machine-generated.

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.

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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.