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State-space modelling for infectious disease surveillance data: Dynamic regression and covariance analysis.

Infectious Disease Modelling·2025
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State-space modelling for infectious disease surveillance data: Stochastic simulation techniques and structural

Christopher D Prashad1

  • 1Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada.

Infectious Disease Modelling
|September 2, 2025
PubMed
Summary

Advanced stochastic simulation techniques, including Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC), effectively model infectious diseases. The horseshoe prior demonstrated superior performance in detecting changes and forecasting trends in COVID-19 data.

Keywords:
Infectious disease surveillance dataNonlinear dynamic regressionRao-blackwellized particle filterState-space modellingStochastic simulationStructural change detection

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Area of Science:

  • Computational statistics
  • Epidemiology
  • Mathematical modeling

Background:

  • Infectious disease modeling requires robust statistical techniques to capture dynamic transmission patterns.
  • State-space models offer a flexible framework for analyzing time-series data in public health.

Purpose of the Study:

  • To explore advanced stochastic simulation techniques for state-space models in infectious disease analysis.
  • To apply these methods to COVID-19 surveillance data for detecting structural changes and forecasting trends.
  • To evaluate the impact of different prior distributions on model performance.

Main Methods:

  • Utilized Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods.
  • Applied Kalman smoothing and Bayesian inference for non-linear dynamic regression models.
  • Assessed various priors (normal, Student's t, Laplace, horseshoe) with a Rao-Blackwellized particle filter.

Main Results:

  • The horseshoe prior exhibited superior performance in identifying change points and adapting to complex data structures.
  • Stochastic simulation techniques effectively detected structural changes in COVID-19 case counts.
  • Models provided insights for real-time monitoring and forecasting.

Conclusions:

  • State-space models, enhanced with sophisticated prior distributions like the horseshoe prior, offer a nuanced understanding of infectious disease transmission.
  • Advanced simulation techniques are crucial for accurate public health surveillance and prediction.
  • The findings support the use of these methods for real-time infectious disease management.