June 2022 Inference for stochastic kinetic models from multiple data sources for joint estimation of infection dynamics from aggregate reports and virological data
Oksana A. Chkrebtii, Yury E. García, Marcos A. Capistrán, Daniel E. Noyola
Author Affiliations +
Ann. Appl. Stat. 16(2): 959-981 (June 2022). DOI: 10.1214/21-AOAS1527


Before the current pandemic, influenza and respiratory syncytial virus (RSV) were the leading etiological agents of seasonal acute respiratory infections (ARI) around the world. In this setting, medical doctors typically based the diagnosis of ARI on patients’ symptoms alone and did not routinely conduct virological tests necessary to identify individual viruses, limiting the ability to study the interaction between multiple pathogens and to make public health recommendations. We consider a stochastic kinetic model (SKM) for two interacting ARI pathogens circulating in a large population and an empirically-motivated background process for infections with other pathogens causing similar symptoms. An extended marginal sampling approach, based on the linear noise approximation to the SKM, integrates multiple data sources and additional model components. We infer the parameters defining the pathogens’ dynamics and interaction within a Bayesian model and explore the posterior trajectories of infections for each illness based on aggregate infection reports from six epidemic seasons collected by the state health department and a subset of virological tests from a sentinel program at a general hospital in San Luis Potosí, México. We interpret the results and make recommendations for future data collection strategies.

Funding Statement

This research was supported in part by the Mathematical Biosciences Institute (MBI) and the National Science Foundation under grant DMS-1440386.


The authors thank the following people for helpful comments and suggestions: Grzegorz A. Rempala (Mathematical Biosciences Institute, The Ohio State University) and Leticia Ramirez (Centro de Investigación en Matemáticas). The authors also wish to thank The Ohio State University and Centro de Investigación en Matemáticas for making this collaboration possible. Finally, we thank the anonymous reviewers and Associate Editor for invaluable comments and suggestions.

The first two authors are equal contributors.


Download Citation

Oksana A. Chkrebtii. Yury E. García. Marcos A. Capistrán. Daniel E. Noyola. "Inference for stochastic kinetic models from multiple data sources for joint estimation of infection dynamics from aggregate reports and virological data." Ann. Appl. Stat. 16 (2) 959 - 981, June 2022. https://doi.org/10.1214/21-AOAS1527


Received: 1 August 2019; Revised: 1 August 2021; Published: June 2022
First available in Project Euclid: 13 June 2022

MathSciNet: MR4438819
zbMATH: 1498.62201
Digital Object Identifier: 10.1214/21-AOAS1527

Keywords: acute respiratory disease , Bayesian modeling , influenza , linear noise approximation , RSV , Stochastic kinetic models

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 2 • June 2022
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