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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., (© 2021. The Author(s).)