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

People in many countries are now infected with COVID-19. By now, it is clear that the number of people infected is much greater 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). Here, 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-$$\beta$$ β model. In the second case, the number of nodes in the network is infinite and results in a continuum model wherein the infectivity is statistically distributed. We use a generalized Pareto distribution to model the infectivity. This distribution has a fat tail and models the presence of super-spreaders that contribute to the disease progression. While both models capture the detected numbers well, the predictions of affected numbers from the continuum model are more realistic. Our results suggest that affected people outnumber detected people by one to two orders of magnitude in Spain, the UK, Italy, and Germany. Our results are consistent with corresponding trends obtained from published serological studies in Spain, the UK and Italy. The match with limited studies in Germany is poor, possibly because Germany’s partial lockdown approach requires different modeling.