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

Sankalp Tiwari, C. P. Vyasarayani, Anindya Chatterjee

Received date: 7th October 2020

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.

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This is an abstract of a preprint hosted on a preprint server, which is currently undergoing peer review at Scientific Reports. The findings have yet to be thoroughly evaluated, nor has a decision on ultimate publication been made. Therefore, the results reported should not be considered conclusive, and these findings should not be used to inform clinical practice, or public health policy, or be promoted as verified information.

### Scientific Reports

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