Epidemiological Modeling of Seasonal Influenza Through Periodic Mean-Reverting Stochastic Processes
- 1Arizona State University
Abstract
Seasonal influenza follows annual cycles, but variation in epidemic magnitude and timing complicates preparedness. We applied periodic mean reverting stochastic differential equations (SDEs) to seven seasons of weekly Texas influenza surveillance data. Missing observations were imputed using MissForest and compared with four alternative methods. Stochastic variability was modeled using {sigma}X(t) dW(t), with p = 1/2,2/3,5/6, and 1, representing square root, intermediate sublinear, and multiplicative diffusion. Each specification was evaluated for direct influenza modeling and within a susceptible, exposed, infectious , and recovered model incorporating waning immunity, where the SDE governed transmission. Parameters were estimated using least squares and approximate maximum likelihood for direct models and sample-proportion weighted least squares for stochastic SEIR models. Model-based parametric bootstrap assessed direct-model parameter uncertainty. For direct modeling, p = 1/2 achieved the lowest RMSE (712.8) and AIC (5383.0), with similar AIC for p = 2/3 (5383.2). For stochastic SEIR modeling, p = 1 achieved the lowest RMSE (0.02926), compared with 0.03506 for p = 1/2. The deterministic SEIR model yielded R = 1.158. Transmission peaked approximately 10 weeks before infectious prevalence, while stochastic transmission generated variation in epidemic peak timing. Bootstrap analysis identified dependence between mean-reversion and diffusion parameters. Overall, the appropriate diffusion structure depended on the epidemiological quantity modeled, supporting flexible characterization of seasonal transmission variability while requiring prospective validation before operational forecasting.
Related
- H9N2 avian influenza virus in Muscovy ducks: a nationwide epidemiological survey and vaccine efficacy assessment
- Identifying the viral and epidemiological factors behind the apparent global extinction of influenza B/Yamagata
- Advancing influenza forecasting models by integrating key epidemiological features
- Ten-year epidemiological and clinical insights of pediatric influenza A and B hospitalizations: an observational study
- Visualizing Influenza A Virus Infection and Host Processes Using Fluorescence Microscopy.
BibTeX
@misc{mostafa2026epidemiological,
title = {{Epidemiological Modeling of Seasonal Influenza Through Periodic Mean-Reverting Stochastic Processes}},
author = {F. Mostafa and L. Allen},
howpublished = {medRxiv},
year = {2026},
month = nov,
doi = {10.64898/2026.11.05.26367374},
url = {https://www.medrxiv.org/content/10.64898/2026.11.05.26367374v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Epidemiological Modeling of Seasonal Influenza Through Periodic Mean-Reverting Stochastic Processes
AU - F. Mostafa
AU - L. Allen
PY - 2026
DA - 2026/11/05
PB - medRxiv
DO - 10.64898/2026.11.05.26367374
UR - https://www.medrxiv.org/content/10.64898/2026.11.05.26367374v1
AB - Seasonal influenza follows annual cycles, but variation in epidemic magnitude and timing complicates preparedness. We applied periodic mean reverting stochastic differential equations (SDEs) to seven seasons of weekly Texas influenza surveillance data. Missing observations were imputed using MissForest and compared with four alternative methods. Stochastic variability was modeled using {sigma}X(t) dW(t), with p = 1/2,2/3,5/6, and 1, representing square root, intermediate sublinear, and multiplicative diffusion. Each specification was evaluated for direct influenza modeling and within a susceptible, exposed, infectious , and recovered model incorporating waning immunity, where the SDE governed transmission. Parameters were estimated using least squares and approximate maximum likelihood for direct models and sample-proportion weighted least squares for stochastic SEIR models. Model-based parametric bootstrap assessed direct-model parameter uncertainty. For direct modeling, p = 1/2 achieved the lowest RMSE (712.8) and AIC (5383.0), with similar AIC for p = 2/3 (5383.2). For stochastic SEIR modeling, p = 1 achieved the lowest RMSE (0.02926), compared with 0.03506 for p = 1/2. The deterministic SEIR model yielded R = 1.158. Transmission peaked approximately 10 weeks before infectious prevalence, while stochastic transmission generated variation in epidemic peak timing. Bootstrap analysis identified dependence between mean-reversion and diffusion parameters. Overall, the appropriate diffusion structure depended on the epidemiological quantity modeled, supporting flexible characterization of seasonal transmission variability while requiring prospective validation before operational forecasting.
ER -