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Approximating steady state distributions for household structured epidemic models.

Alex Holmes1, Mike Tildesley2, Louise Dyson2

  • 1The Zeeman Institute for Systems Biology & Infectious Disease Epidemiology Research, School of Life Sciences and Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom; Mathematics for Real World Systems Centre for Doctoral Training, Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom.

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Summary
This summary is machine-generated.

Accurately calculating steady states in household infectious disease models is crucial for effective control strategies. This study compares approximations, finding accuracy varies with infection prevalence and household correlations.

Keywords:
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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Computational Science

Background:

  • Household-structured infectious disease models account for higher transmission within households.
  • Accurate steady-state calculations are vital for predicting disease dynamics and planning control measures.

Purpose of the Study:

  • To compare the accuracy and implementation ease of different methods for calculating steady states in household-structured infectious disease models.
  • To identify parameter space regions where specific approximation methods outperform others.

Main Methods:

  • Comparison of the full system steady-state calculation with two approximations: the single household master equation and the Fokker-Planck equation.
  • Analysis of accuracy and computational intensity for each method.

Main Results:

  • The single household master equation is easy to implement but can be inaccurate.
  • The Fokker-Planck equation offers an alternative approximation.
  • Accuracy of approximations depends on infection prevalence and correlation between household states.

Conclusions:

  • No single approximation method is universally superior for all parameter spaces.
  • Understanding parameter space characteristics is key to selecting the most appropriate method for steady-state calculations in household disease models.