The consistent modelling methodology for secondary settling tanks (SSTs) leads to a partial differential equation (PDE) of nonlinear convection-diffusion type as a one-dimensional model for the solids concentration as a function of depth and time. This PDE includes a flux that depends discontinuously on spatial position modelling hindered settling and bulk flows, a singular source term describing the feed mechanism, a degenerating term accounting for sediment compressibility, and a dispersion term for turbulence. In addition, the solution itself is discontinuous. A consistent, reliable and robust numerical method that properly handles these difficulties is presented. Many constitutive relations for hindered settling, compression and dispersion can be used within the model, allowing the user to switch on and off effects of interest depending on the modelling goal as well as investigate the suitability of certain constitutive expressions. Simulations show the effect of the dispersion term on effluent suspended solids and total sludge mass in the SST. The focus is on correct implementation whereas calibration and validation are not pursued.

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We present a compartmental extended SEIQRD metapopulation model for SARS-CoV-2 spread in Belgium. We demonstrate the robustness of the calibration procedure by calibrating the model using incrementally larger datasets and dissect the model results by computing the effective reproduction number at home, in workplaces, in schools, and during leisure activities. We find that schools are an important transmission pathway for SARS-CoV-2, with the potential to increase the effective reproduction number from (95 % CI) to (95 % CI) under lockdown measures. The model accounts for the main characteristics of SARS-CoV-2 transmission and COVID-19 disease and features a detailed representation of hospitals with parameters derived from a dataset consisting of 22 136 hospitalized patients. Social contact during the pandemic is modeled by scaling pre-pandemic contact matrices with Google Community Mobility data and with effectivity-of-contact parameters inferred from hospitalization data. The calibrated social contact model with its publically available mobility data, although coarse-grained, is a readily available alternative to social-epidemiological contact studies under lockdown measures, which were not available at the start of the pandemic.

An improved one-dimensional (1-D) model for the secondary clarifier, i.e. the Bürger-Diehl model, was recently presented. The decisive difference to traditional layer models is that every detail of the implementation is in accordance with the theory of partial differential equations. The Bürger-Diehl model allows accounting for hindered and compressive settling as well as inlet dispersion. In this contribution, the impact of specific features of the Bürger-Diehl model on settler underflow concentration predictions, plant sludge inventory and mixed liquor suspended solids based control actions are investigated by using the benchmark simulation model no. 1. The numerical results show that the Bürger-Diehl model allows for more realistic predictions of the underflow sludge concentration, which is essential for more accurate wet weather modelling and sludge waste predictions. The choice of secondary settler model clearly has a profound impact on the operation and control of the entire treatment plant and it is recommended to use the Bürger-Diehl model as of now in any wastewater treatment plant modelling effort.

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