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The correlation structure of epidemic models

P Donnelly1

  • 1School of Mathematical Sciences, Queen Mary and Westfield College, London, United Kingdom.

Mathematical Biosciences
|September 1, 1993
PubMed
Summary

Individuals

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Stochastic Processes

Background:

  • Understanding disease dynamics is crucial for public health interventions.
  • Correlations in disease spread can reveal underlying transmission mechanisms.

Purpose of the Study:

  • To investigate correlations in disease spread within epidemic models.
  • To analyze the impact of multiple diseases and different transmission assumptions on these correlations.

Main Methods:

  • Analysis of general Markov SIS (Susceptible-Infected-Susceptible) epidemic models.
  • Examination of general non-Markov SIR (Susceptible-Infected-Recovered) models.
  • Utilizing monotonicity properties and partial orders for SIS models.
  • Employing graphical constructions for SIR models.

Main Results:

  • Positive correlations observed in individual fates for general Markov SIS models.
  • Introduction of 'positive interference' (positive correlation within and between diseases) and 'competition' (negative correlation between diseases, positive within).
  • Generalization to two disease classes with interference and competition.
  • Positive correlation demonstrated in general non-Markov SIR models.

Conclusions:

  • Individual disease fates are positively correlated in general SIS and SIR epidemic models.
  • Interference and competition dynamics significantly shape correlations in multi-disease scenarios.
  • The study provides a theoretical framework for understanding complex disease interactions.

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