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Backward bifurcation in epidemic control

K P Hadeler1, P van den Driessche

  • 1Universität Tübingen, Germany.

Mathematical Biosciences
|November 14, 1997
PubMed
Summary
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Public health policies in SIRS models can cause backward bifurcation and hysteresis, complicating disease elimination efforts. The critical parameter at the turning point, not just the reproduction number, determines necessary interventions.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health Policy

Background:

  • SIRS (Susceptible-Infected-Recovered-Susceptible) models are crucial for understanding infectious disease dynamics.
  • Public health interventions significantly influence disease transmission and prevalence.
  • The basic reproduction number (R0) is a key metric for disease control, but its limitations in complex scenarios require further investigation.

Purpose of the Study:

  • To investigate the stability of the uninfected state and disease prevalence in SIRS models incorporating public health policies.
  • To analyze the occurrence and implications of backward bifurcation and hysteresis effects.
  • To identify appropriate metrics for disease elimination efforts when standard metrics like R0 are insufficient.

Main Methods:

Related Experiment Videos

  • Analysis of a class of epidemiological SIRS models with public health policy parameters.
  • Mathematical investigation of model stability and bifurcation phenomena.
  • Derivation of an explicit expression for the critical parameter at the turning point.

Main Results:

  • Backward bifurcation from the uninfected state and hysteresis effects were observed for specific parameter ranges.
  • The reproduction number alone is insufficient to guide elimination efforts in these scenarios.
  • A critical parameter at the turning point provides a more accurate measure of the required elimination effort.

Conclusions:

  • Complex dynamics, including backward bifurcation and hysteresis, can arise in SIRS models with public health policies.
  • Disease elimination strategies must account for these phenomena, utilizing critical parameters beyond the basic reproduction number.
  • The findings offer insights into group models, pair formation, and macroparasite infection dynamics.