The evident shedding of the SARS-CoV-2 RNA particles from infected individuals into the wastewater opened up a tantalizing array of possibilities for prediction of COVID-19 prevalence prior to symptomatic case identification through community testing. Many countries have therefore explored the use of wastewater metrics as a surveillance tool, replacing traditional direct measurement of prevalence with cost-effective approaches based on SARS-CoV-2 RNA concentrations in wastewater samples. Two important aspects in building prediction models are: time over which the prediction occurs and space for which the predicted case numbers is shown. In this review, our main focus was on finding mathematical models which take into the account both the time-varying and spatial nature of wastewater-based metrics into account. We used six main characteristics as our assessment criteria: i) modelling approach; ii) temporal coverage; iii) spatial coverage; iv) sample size; v) wastewater sampling method; and vi) covariates included in the modelling. The majority of studies in the early phases of the pandemic recognized the temporal association of SARS-CoV-2 RNA concentration level in wastewater with the number of COVID-19 cases, ignoring their spatial context. We examined 15 studies up to April 2023, focusing on models considering both temporal and spatial aspects of wastewater metrics. Most early studies correlated temporal SARS-CoV-2 RNA levels with COVID-19 cases but overlooked spatial factors. Linear regression and SEIR models were commonly used (n = 10, 66.6 % of studies), along with machine learning (n = 1, 6.6 %) and Bayesian approaches (n = 1, 6.6 %) in some cases. Three studies employed spatio-temporal modelling approach (n = 3, 20.0 %). We conclude that the development, validation and calibration of further spatio-temporally explicit models should be done in parallel with the advancement of wastewater metrics before the potential of wastewater as a surveillance tool can be fully realised.
