Bayesian workflow for time-varying transmission in stratified compartmental infectious disease transmission models
Authors: Bouman Judith A. , Hauser Anthony , Grimm Simon L. , Wohlfender Martin , Bhatt Samir , Semenova Elizaveta , Gelman Andrew , Althaus Christian L. , Riou Julien 
Published: October 2023

Compartmental models that describe infectious disease transmission across subpopulations are central for assessing the impact of non-pharmaceutical interventions, behavioral changes and seasonal effects on the spread of respiratory infections. We present a Bayesian workflow for such models, including four features: (1) an adjustment for incomplete case ascertainment, (2) an adequate sampling distribution of laboratory-confirmed cases, (3) a flexible, time-varying transmission rate, and (4) a stratification by age group. We benchmarked the performance of various implementations of two of these features (2 and 3). For the second feature, we used SARS-CoV-2 data from the canton of Geneva (Switzerland) and found that a quasi-Poisson distribution is the most suitable sampling distribution for describing the overdispersion in the observed laboratory-confirmed cases. For the third feature, we implemented three methods: Brownian motion, B-splines, and approximate Gaussian processes (aGP). We compared their performance in terms of the number of effective samples per second, and the error and sharpness in estimating the time-varying transmission rate over a selection of ordinary differential equation solvers and tuning parameters, using simulated seroprevalence and laboratory-confirmed case data. Even though all methods could recover the time-varying dynamics in the transmission rate accurately, we found that B-splines perform up to four and ten times faster than Brownian motion and aGPs, respectively. We validated the B-spline model with simulated age-stratified data. We applied this model to 2020 laboratory-confirmed SARS-CoV-2 cases and two seroprevalence studies from the canton of Geneva. This resulted in detailed estimates of the transmission rate over time and the case ascertainment. Our results illustrate the potential of the presented workflow including stratified transmission to estimate age-specific epidemiological parameters. The workflow is freely available in the R package HETTMO, and can be easily adapted and applied to other surveillance data.

Author summary

Mathematical models are a central tool for understanding the spread of infectious diseases. These models can be fitted to surveillance data such as the number of laboratory-confirmed cases and seroprevalence over time. To provide insightful information for managing an epidemic, the models require several crucial features. In our study, we compare the performance of several implementations of two such features. First, we find that a quasi-Poisson distribution describes best how the number of laboratory-confirmed cases of SARS-CoV-2 from the canton of Geneva (Switzerland) are sampled from the total incidence of the infection. Second, we conclude that a B-spline based implementation of time-variation in the transmission rate performs better than a Brownian motion or approximate Gaussian processes based model. Moreover, we confirm that the B-spline based model can recover time-varying transmission also in an age-stratified population. This structural comparison of methods results in a Bayesian workflow. Such a comprehensive workflow is crucial to move the field of mathematical modeling for infectious disease dynamics forward and make methods widely applicable.