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Inference in Gaussian state-space models with mixed effects for multiple epidemic dynamics.

Romain Narci1, Maud Delattre2, Catherine Larédo2

  • 1MaIAGE, INRAE, Université Paris-Saclay, 78350, Jouy-en-Josas, France. romain.narci@orange.fr.

Journal of Mathematical Biology
|September 26, 2022
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Summary
This summary is machine-generated.

This study introduces a novel statistical model to analyze multiple epidemics simultaneously, accounting for variability between outbreaks. The method accurately estimates epidemic parameters from incomplete data, outperforming separate analyses.

Keywords:
Kalman filterLatent variablesParametric inferenceRandom effectsSAEM algorithmStochastic compartmental models

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Area of Science:

  • Epidemiology
  • Statistical Modeling
  • Public Health

Background:

  • Estimating epidemic parameters is challenging due to incomplete and noisy data.
  • Inter-epidemic variability across different locations or time periods is often overlooked in analyses.

Purpose of the Study:

  • To develop a unified statistical model for analyzing multiple, simultaneous epidemics.
  • To explicitly account for and estimate inter-epidemic variability using a parsimonious model.

Main Methods:

  • Extended a Gaussian state-space model to incorporate mixed effects for multiple epidemics.
  • Developed a joint parameter estimation method using the Stochastic Approximation Expectation-Maximization (SAEM) algorithm coupled with Kalman-type filtering.
  • Created a new filtering algorithm version to handle incidence data.

Main Results:

  • The proposed method demonstrated superior performance compared to analyzing datasets separately.
  • Simulations on SIR (Susceptible-Infectious-Recovered) models showed effectiveness for both prevalence and incidence data.
  • Application to SEIR (Susceptible-Exposed-Infectious-Recovered) influenza outbreaks in France revealed significant variability between seasons.

Conclusions:

  • The developed model rigorously and explicitly addresses inter-epidemic variability in both modeling and inference.
  • The findings highlight the importance of considering season-to-season variations in transmission and reporting for influenza.
  • This approach offers a robust framework for analyzing complex epidemic scenarios.