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Contact tracing in stochastic and deterministic epidemic models.

J Müller1, M Kretzschmar, K Dietz

  • 1Biomathematik, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany. johannes.mueller@uni-tuebingen.de

Mathematical Biosciences
|March 8, 2000
PubMed
Summary

Contact tracing in stochastic epidemic models reveals interconnectedness among infected individuals. This analysis enables prediction of major outbreaks and disease dynamics using a deterministic approximation.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Stochastic Processes

Background:

  • Contact tracing is a key intervention in epidemic control.
  • Individual-based stochastic models offer detailed insights into disease spread.
  • Interactions between infected individuals are complex, especially with tracing.

Purpose of the Study:

  • To analyze a stochastic epidemic model incorporating contact tracing.
  • To derive threshold theorems and outbreak probabilities.
  • To develop an approximate deterministic model for epidemic dynamics.

Main Methods:

  • Analysis of an embedded non-stationary Galton-Watson process.
  • Derivation of threshold theorems and outbreak probabilities.
  • Development of a deterministic approximation for the stochastic model.

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Main Results:

  • Contact tracing creates dependencies between infected individuals.
  • Threshold theorems and major outbreak probabilities can be determined.
  • A deterministic model accurately approximates the stochastic process.

Conclusions:

  • The stochastic epidemic model with contact tracing is analytically tractable.
  • Contact tracing significantly influences epidemic dynamics and predictability.
  • The derived deterministic model allows for analysis of disease prevalence and epidemic dynamics in the quasi-stationary state.