From time series to visibility algorithms: A novel approach to study the spread of SARS-CoV-2 in wastewater

The detection of SARS-CoV-2 in faeces encouraged various studies exploring wastewater as a disease surveillance tool from a wastewater-based epidemiology (WBE) perspective. Virus concentration data in wastewater are collected and arranged in time series and generally analysed by using statistical approaches. However, for studying complex and non-linear phenomena, this procedure may not be effective. In this regard, the present work introduces an alternative and innovative approach to analyse time series of SARS-CoV-2 concentration in wastewater based on visibility algorithms. The temporal evolution of the epidemic is transformed into a visibility graph that allows the study of time series from a nonlinear perspective. The connectivity structure of the visibility graph encapsulates significant information of the starting time series. By investigating the topological characteristics of the graph, it is possible to extract nontrivial evidence to give a physical interpretation of the phenomenon and to identify the factors that mainly influence the virus transmission. The proposed approach has been applied to the time series data collected at ten wastewater treatment plants to interpret the trend of the epidemic and attempt to forecast the phenomenon in the analysed basins. Overall, using visibility algorithms to study COVID-19 in sewage is a valuable tool for monitoring the community, with potential for predicting epidemics and community behaviours.