Modelled SARS-CoV-2 epidemic in Vaud, Switzerland.

(A) Posterior predictive plot for laboratory-confirmed cases (left y-axis, orange ribbon) and cumulative incidence (right y-axis, gray ribbon). Green circles are weekly counts of laboratory-confirmed cases and red triangles show monthly seroprevalence estimates from data. (B) Estimates of the time-varying change in transmission rate using B-splines. (C) Estimated ascertainment rates for first and second wave. (TIF)</p

A description of the age-stratified version of the SEIR transmission model and a definition of the priors used within the Bayesian analysis.

A description of the age-stratified version of the SEIR transmission model and a definition of the priors used within the Bayesian analysis.</p

Benchmark for hyper-parameters approximate Gaussian processes model.

Analysis of the optimal number of basis functions and boundary factor for the approximate Gaussian Processes based time-varying transmission model of SARS-CoV-2 using simulated data. The number of warm-up and sampling iterations are both fixed to 300 and the trapezoidal solver is used. (TIF)</p

Knot sequences.

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. Within the workflow, 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 infectious diseases.</div

Parameters adapted from the unstratified model for simulating stratified data using the B-splines.

Parameters adapted from the unstratified model for simulating stratified data using the B-splines.</p

Modelled SARS-CoV-2 epidemic in Geneva, Switzerland, in 2020.

(A) Posterior predictive plot for laboratory-confirmed cases (left y-axis, colored ribbon) and cumulative incidence (right y-axis, gray ribbon) per age group. Circles are weekly counts of laboratory-confirmed cases and pluses are estimates of seroprevalence at two time points. (B) Estimates of the time-varying change in transmission rate per age group using B-splines. (C) Estimates of the ascertainment rate per age group and time period.</p

Benchmark for approximate Gaussian processes model.

Comparison of computational performance for the approximate Gaussian processes model of the time-varying transmission rate of SARS-CoV-2 for simulated, non-stratified data for various tuning parameters: tolerance, ODE solver and number of warm-up iterations. (A) The root mean squared error (RMSE) in estimating the time-variation in the transmission. (B) The sharpness (size of the 90% confidence interval) of the time-variation in the transmission. (TIF)</p

Schematic overview of the SEIR transmission model for SARS-CoV-2 and the steps to generate the number of laboratory-confirmed cases and the observed seroprevalence.

Schematic overview of the SEIR transmission model for SARS-CoV-2 and the steps to generate the number of laboratory-confirmed cases and the observed seroprevalence.</p

Parameters for simulating unstratified data using the B-splines model.

Parameters for simulating unstratified data using the B-splines model.</p

Seroprevalence data from the canton of Geneva, obtained from Stringhini et al (2020) and Stringhini et al (2021) [13, 49].

Seroprevalence data from the canton of Geneva, obtained from Stringhini et al (2020) and Stringhini et al (2021) [13, 49].</p