Bayesian workflow for time-varying transmission in stratified compartmental infectious disease transmission models.

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

Genotype-specific risk factors for Staphylococcus aureus in Swiss dairy herds with an elevated yield-corrected herd somatic cell count

Bovine mastitis is a frequent problem in Swiss dairy herds. One of the main pathogens causing significant economic loss is Staphylococcus aureus. Various Staph. aureus genotypes with different biological properties have been described. Genotype B (GTB) of Staph. aureus was identified as the most contagious and one of the most prevalent strains in Switzerland. The aim of this study was to identify risk factors associated with the herd-level presence of Staph. aureus GTB and Staph. aureus non-GTB in Swiss dairy herds with an elevated yield-corrected herd somatic cell count (YCHSCC). One hundred dairy herds with a mean YCHSCC between 200,000 and 300,000cells/mL in 2010 were recruited and each farm was visited once during milking. A standardized protocol investigating demography, mastitis management, cow husbandry, milking system, and milking routine was completed during the visit. A bulk tank milk (BTM) sample was analyzed by real-time PCR for the presence of Staph. aureus GTB to classify the herds into 2 groups: Staph. aureus GTB-positive and Staph. aureus GTB-negative. Moreover, quarter milk samples were aseptically collected for bacteriological culture from cows with a somatic cell count ≥150,000cells/mL on the last test-day before the visit. The culture results allowed us to allocate the Staph. aureus GTB-negative farms to Staph. aureus non-GTB and Staph. aureus-free groups. Multivariable multinomial logistic regression models were built to identify risk factors associated with the herd-level presence of Staph. aureus GTB and Staph. aureus non-GTB. The prevalence of Staph. aureus GTB herds was 16% (n=16), whereas that of Staph. aureus non-GTB herds was 38% (n=38). Herds that sent lactating cows to seasonal communal pastures had significantly higher odds of being infected with Staph. aureus GTB (odds ratio: 10.2, 95% CI: 1.9-56.6), compared with herds without communal pasturing. Herds that purchased heifers had significantly higher odds of being infected with Staph. aureus GTB (rather than Staph. aureus non-GTB) compared with herds without purchase of heifers. Furthermore, herds that did not use udder ointment as supportive therapy for acute mastitis had significantly higher odds of being infected with Staph. aureus GTB (odds ratio: 8.5, 95% CI: 1.6-58.4) or Staph. aureus non-GTB (odds ratio: 6.1, 95% CI: 1.3-27.8) than herds that used udder ointment occasionally or regularly. Herds in which the milker performed unrelated activities during milking had significantly higher odds of being infected with Staph. aureus GTB (rather than Staph. aureus non-GTB) compared with herds in which the milker did not perform unrelated activities at milking. Awareness of 4 potential risk factors identified in this study guides implementation of intervention strategies to improve udder health in both Staph. aureus GTB and Staph. aureus non-GTB herds

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

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

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

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

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

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