Relating SARS-CoV-2 shedding rate in wastewater to daily positive tests data: A consistent model based approach

Abstract

During the COVID-19 pandemic, wastewater-based epidemiology (WBE) has been engaged to complement medical surveillance and in some cases to also act as an early diagnosis indicator of viral spreading in the community. Most efforts worldwide by the scientific community and commercial companies focus on the formulation of protocols for SARS-CoV-2 analysis in wastewater and approaches addressing the quantitative relationship between WBE and medical surveillance are lacking. In the present study, a mathematical model is developed which uses as input the number of daily positive medical tests together with the highly non-linear shedding rate curve of individuals to estimate the evolution of global virus shedding rate in wastewater along calendar days. A comprehensive parametric study by the model using as input actual medical surveillance and WBE data for the city of Thessaloniki (~700,000 inhabitants, North Greece) during the outbreak of November 2020 reveals the conditions under which WBE can be used as an early warning tool for predicting pandemic outbreaks. It is shown that early warning capacity is different along the days of an outbreak and depends strongly on the number of days apart between the day of maximum shedding rate of infected individuals in their disease cycle and the day of their medical testing. The present data indicate for Thessaloniki an average early warning capacity of around 2 days. Moreover, the data imply that there exists a proportion between unreported cases (asymptomatic persons with mild symptoms that do not seek medical advice) and reported cases. The proportion increases with the number of reported cases. The early detection capacity of WBE improves substantially in the presence of an increasing number of unreported cases. For Thessaloniki at the peak of the pandemic in mid-November 2020, the number of unreported cases reached a maximum around 4 times the number of reported cases.

Graphical abstract

Fig. 1

Time distribution of normalized individual's shedding rate per person in stool at different shedding durations and shedding peak days.

Fig. 2

Medical surveillance data reported for the city of Thessaloniki from September 1st, 2020 to January 6th, 2021 and corresponding fit curve.

Fig. 3

Experimental relative global shedding rate in sewage expressed as the ratio of the measured daily shedding rate (R_exp) over the reference shedding rate (R_expo) from October 5th, 2020 to January 6th, 2021. Error bars correspond to standard deviation of relative global shedding rate values.

Fig. 4

The probability density distribution of the number of infected people with respect to the days of the disease.

Fig. 5

Comparison of the relative global viral shedding rate in sewage with the number of the daily and total reported infected people per surveillance day. In all cases individual's shedding duration in stool is set as 32 days, laboratory test is assumed at DAY 8, whereas the day of individual's shedding peak in stool is at: DAY 6 (a), DAY 2 (b) and DAY 12 (c).

Fig. 6

Comparison of the theoretical relative global shedding rate in sewage with the relative medical surveillance data of the smoothed daily reported cases for different scenarios of unreported daily cases. Unreported daily cases vary proportionally with the number of reported daily cases starting from 0 and reaching a maximum value of 0, 50, 200, 400% of reported cases at the date of maximum global shedding rate.

Fig. 7

Experimental relative global shedding rate in sewage, R_exp(t)/R_expo, versus the estimated total number of infected people (reported and unreported), F. The latter is estimated assuming that, on the average, the shedding duration in stool is 32 days and medical tests are taken at DAY 8 during the disease. Red circles denote increasing global shedding rates whereas green squares denote decreasing global shedding rates. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 8

Evolution of the ratio of the total number of infected people (reported + unreported) over the number of reported infected people. The ratio is calculated from unsmoothed raw data in Fig. 2, Fig. 3. Red circles denote increasing global shedding rates whereas green squares denote decreasing global shedding rates. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 9

Variation of the ratio of the total number of infected people (reported + unreported) over the number of reported infected people with regards to (a) the total number of reported infected people and (b) the daily number of infected people. The ratio is calculated from unsmoothed raw data in Fig. 2, Fig. 3. Red circles denote increasing global shedding rates whereas green squares denote decreasing global shedding rates. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)