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A threshold limit theorem for a multitype epidemic model

H Andersson1

  • 1Department of Mathematics, Stockholm University, Sweden.

Mathematical Biosciences
|September 1, 1993
PubMed
Summary
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This study analyzes infectious disease spread in large, closed populations using a multitype SIR model. We identified threshold behavior, enabling prediction of outbreak sizes in various subgroups.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Stochastic Processes

Background:

  • Understanding infectious disease dynamics in heterogeneous populations is crucial for public health.
  • Previous models often simplified population structures, limiting applicability to real-world scenarios.
  • The Martin-Löf process offers a framework for modeling discrete-time disease spread in multitype populations.

Purpose of the Study:

  • To derive the asymptotic final size distribution for a multitype Martin-Löf process.
  • To analyze the impact of population size and subgroup comparability on disease outbreak dynamics.
  • To identify threshold behaviors and characterize outbreak sizes in large, closed, multitype populations.

Main Methods:

  • Derivation of the final size distribution for a discrete-time SIR model with multiple population types.

Related Experiment Videos

  • Analysis under the condition of large total population size.
  • Investigation of scenarios with comparable subgroup sizes and irreducible infection patterns.

    • Main Results:

    • A clear threshold behavior in disease spread was identified for large populations with comparable subgroups.
    • Asymptotic distributions for both small and large outbreaks were determined.
    • A threshold limit theorem was established as a corollary for continuous-time SIR models with multiple types.

    Conclusions:

    • The multitype Martin-Löf process accurately predicts infectious disease spread and outbreak sizes in large, heterogeneous populations.
    • The identified threshold behavior is a key factor in understanding epidemic potential.
    • The findings provide a theoretical basis for developing targeted public health interventions in diverse populations.