SARS-CoV-2 adsorption on suspended solids along a sewerage network: mathematical model formulation, sensitivity analysis, and parametric study

Margaritis Kostoglou,Maria Petala,Anna Papa,Nikolaos Papaioannou,Efstratios Stylianidis,Chrysostomos Dovas,Emmanuel Roilides,Thodoris Karapantsios,Agis Papadopoulos,Simeon Metallidis

doi:10.1007/s11356-021-16528-0

Abstract

Accounting for SARS-CoV-2 adsorption on solids suspended in wastewater is a necessary step towards the reliable estimation of virus shedding rate in a sewerage system, based on measurements performed at a terminal collection station, i.e., at the entrance of a wastewater treatment plant. This concept is extended herein to include several measurement stations across a city to enable the estimation of spatial distribution of virus shedding rate. This study presents a pioneer general model describing the most relevant physicochemical phenomena with a special effort to reduce the complicated algebra. This is performed both in the topology regime, introducing a discrete-continuous approach, and in the domain of independent variables, introducing a monodisperse moment method to reduce the dimensionality of the resulting population balance equations. The resulting simplified model consists of a large system of ordinary differential equations. A sensitivity analysis is performed with respect to some key parameters for a single pipe topology. Specific numerical techniques are employed for the integration of the model. Finally, a parametric case study for an indicative—yet realistic—sewerage piping system is performed to show how the model is applied to SARS-CoV-2 adsorption on wastewater solids in the presence of other competing species. This is the first model of this kind appearing in scientific literature and a first step towards setting up an inverse problem to assess the spatial distribution of virus shedding rate based on its concentration in wastewater.

Highlights

The majority of wastewater-based epidemiology (WBE) studies aiming at population-wide surveillance for SARS-CoV-2 focuses on the detection of viral genetic remnants in the sewage entering a wastewater treatment plant
The idea originally advanced in (Petala et al 2021) of setting up an inverse problem based on the relation between the shedding rate of SARS-CoV-2 to a sewerage system and the measured concentration of virus at different locations along the pipe network is further developed in the present work
This work presents the mathematical formulation for the development of a general model based on the adsorption dynamics of virus parts on solid particles suspended in wastewater, for an arbitrary topology of a sewage system

Summary

Introduction

The majority of wastewater-based epidemiology (WBE) studies aiming at population-wide surveillance for SARS-CoV-2 focuses on the detection of viral genetic remnants in the sewage entering a wastewater treatment plant (la Rosa et al 2020; Orive et al 2020; Medema et al 2020; Ahmed et al 2020; Nemudryi et al 2020; Rimoldi et al 2020; Corpuz et al 2020; D’Aoust et al 2021; Saguti et al 2021). Due to their small size and internal porous network suspended solid particles have a much larger surface area than the biofilms In this respect, at this stage of model development, virus part adsorption by biofilms is considered negligible. As of April 2020, our interdisciplinary team in the Aristotle University of Thessaloniki (Greece) in cooperation with Thessaloniki’s Water Supply and Sewerage company quantifies SARS-CoV-2 in sewage right before they enter the main wastewater treatment plant of the city On this account, a comprehensive mathematical model was developed for the adsorption of virus parts onto porous solids suspended in wastewater along a city sewerage network (Petala et al 2021). To the best of our knowledge, this is the first time that WBE is addressed through a fine-grain resolution mathematical model with respect to discrete topological features within sewerage networks

Methods

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Findings

Conclusions