Data suggest COVID-19 affected numbers greatly exceeded detected numbers, in four European countries, as per a delayed SEIQR model

Abstract

People in many countries are now infected with COVID-19. By now, it is clear that the number of people infected is much more than the number of reported cases. To estimate the infected but undetected/unreported cases using a mathematical model, we can use a parameter called the probability of quarantining an infected individual. This parameter exists in the time-delayed SEIQR model (Scientific Reports, article number: 3505). Two limiting cases of a network of such models are used to estimate the undetected population. The first limit corresponds to the network collapsing onto a single node and is referred to as the mean-$\beta$ model. In the second case, the number of nodes in the network is infinite and results in a continuum model, treating the infectivity as statistically distributed. We use a shifted Pareto distribution to model the infectivity. This distribution has a long tail and incorporates the presence of super-spreaders that contribute to the disease progression. While both the models capture the {\em detected} numbers equally well, the predictions of {\em affected} numbers from the continuum model are more realistic. Results suggest that affected people outnumber detected people by one to two orders of magnitude in Spain, UK, Italy, and Germany.

Calculating the number of undetected active SARS-CoV-2 infections from results of population-wide antigen tests

“…So far, it was expected that a high number of SARS-CoV-2 infections were undetected. Previous European studies based their results on statistical modeling [ 5 , 7 – 9 , 11 ], serological testing in study participants [ 3 , 6 , 10 ], and the application of study results from a third country to their own [ 4 ]. The authors report two to 130 undetected cases per detected case for Austria, Germany, Italy, Spain, and the United Kingdom [ 3 , 4 , 6 – 11 ], estimates we cannot confirm.…”

“…Previous European studies based their results on statistical modeling [ 5 , 7 – 9 , 11 ], serological testing in study participants [ 3 , 6 , 10 ], and the application of study results from a third country to their own [ 4 ]. The authors report two to 130 undetected cases per detected case for Austria, Germany, Italy, Spain, and the United Kingdom [ 3 , 4 , 6 – 11 ], estimates we cannot confirm. According to our calculations, 0.01 to 1.25 cases (Slovakia) and 0.15 to 0.71 (South Tyrol) cases per one positive PCR result must be added – the latter is in line with the retrospective analysis of the COVID-19 pandemic in Italy by Fochesato and colleagues [ 5 ].…”

“…The objective of this work was to calculate the number of undetected active cases, commonly known as “dark figure”, from the results of the population-wide antigen tests. In contrast to previous European studies [ 3 – 11 ], our calculations are based on the diagnostic criteria of the antigen tests and therefore take false-positive and false-negative results into account. This leads to a more precise calculation of the dark figure.…”

Accurately Estimating Total COVID-19 Infections using Information Theory

“…However, it has been estimated that there were already more than 28000 total infections in those cities by then [5]. Similar trends were observed in Italy, Germany, and the UK [58], and this continues to be a challenge even today [8,30].…”

Complex Temporal behavior Modeling for Pandemic Spread: Not a Simple Delayed Response!

“…The delays pertaining to mitigation strategies are another important dynamic that directly impacts the behavior of the system at endemic state. There has been limited work to incorporate the delays corresponding to the implementation of mitigation strategies, as part of the state-space infectious disease modeling, e.g., (28) (29) (10) (45) (46). However, the proposed models oversimplify the probabilistic nature of transition and the temporal inter-dependency between p, ω, S , and I when an exposed individual incubates the virus for σ unit-time.…”