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Multiple attractors in the response to a vaccination program.

J L Aron1

  • 1Department of Population Dynamics, School of Hygiene.

Theoretical Population Biology
|August 1, 1990
PubMed
Summary

Multiple attractors in the SEIR model are crucial for understanding vaccination program impacts. The timing of vaccination introduction critically determines the epidemic

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Infectious Disease Dynamics

Background:

  • The Susceptible/Exposed/Infective/Recovered (SEIR) model with vital dynamics and seasonal forcing can exhibit multiple co-existing attractors.
  • The epidemiological significance of these multiple attractors has been debated in the context of disease dynamics.

Purpose of the Study:

  • To investigate the relevance of multiple attractors in the SEIR model when studying the introduction of vaccination programs.
  • To determine if the timing of vaccination introduction influences the resulting epidemic dynamics.

Main Methods:

  • Analysis of the SEIR epidemic model with vital dynamics and seasonal oscillations.
  • Simulation and examination of model responses to the introduction of a vaccination program at different phases of the epidemic cycle.

Main Results:

  • The co-existence of multiple attractors is epidemiologically significant when analyzing vaccination program introductions into a stable epidemic cycle.
  • The timing of vaccination program introduction relative to the existing epidemic cycle critically influences which attractor governs the post-vaccination dynamics.
  • The response to vaccination can manifest as more than one possible attractor state.

Conclusions:

  • Multiple attractors play a critical role in determining the outcome of vaccination programs within epidemic models.
  • Further investigation into the role of multiple attractors is warranted in more complex and realistic epidemiological models.
  • The timing of public health interventions, such as vaccination, is a key factor in achieving desired epidemiological outcomes.

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