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
Summary
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.
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.
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