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Updated: Aug 12, 2026
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A Data-Driven Approach to Quantifying Immune States in Sepsis
Published on: February 7, 2025
Correcting Structural Bias in Dynamical Models of Infectious Disease Using a Bayesian State-Space Framework
Miracle Amadi1, José Carlos García-Merino2, Heikki Haario3
1LUT School of Engineering Sciences, Lappeenranta-Lahti University of Technology (LUT), Yliopistonkatu 34, Lappeenranta, Finland. miracle.amadi@lut.fi.
Bulletin of Mathematical Biology
|August 11, 2026
Summary
This study introduces a novel method to correct systematic biases in infectious disease models by adding a stochastic seasonal component. This approach improves accuracy and interpretability for epidemiological modeling.
Area of Science:
- Epidemiology
- Mathematical Biology
- Computational Statistics
Background:
- Deterministic dynamical models in infectious disease modeling often suffer from systematic bias due to simplified or omitted drivers like seasonality and environmental variation.
- Accurately capturing these unmodeled dynamics is crucial for reliable disease transmission predictions.
Purpose of the Study:
- To propose a practical framework for accounting for structural model discrepancy in mechanistic epidemiological models.
- To develop a method that preserves the interpretability of the underlying mechanistic model while correcting for bias.
Main Methods:
- An additive Bayesian state-space system combining a deterministic Ross malaria model with a latent seasonal component modeled as a periodically forced Ornstein-Uhlenbeck (OU) process.
- Utilized informative priors and non-centered parameterization for latent stochastic differential equation (SDE) states to address identifiability challenges.
- Employed Hamiltonian Monte Carlo (HMC) with the No-U-Turn Sampler (NUTS) in Stan for efficient joint inference.
Main Results:
- The proposed additive Ordinary Differential Equation-Stochastic Differential Equation (ODE-SDE) model demonstrated a close fit to observed malaria case data.
- Achieved coherent uncertainty quantification and flexible seasonal reconstruction, maintaining the interpretability of the mechanistic transmission model.
- Validation through OU examples and synthetic experiments confirmed the model's ability to handle complex dynamics and component interactions.
Conclusions:
- The developed framework offers a flexible and transferable method for correcting structural model discrepancy in dynamical systems.
- This approach enhances the reliability of infectious disease modeling by incorporating structured stochastic discrepancies.
- The method successfully integrates mechanistic understanding with data-driven seasonal dynamics for improved epidemiological insights.
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