Modeling the COVID-19 outbreaks and the effectiveness of the containment measures adopted across countries

Edward De Brouwer; Daniele Raimondi; Yves Moreau

Data biases and heterogeneity in the testing strategies limit the ability to draw clear conclusions. The models fits presented in the Results section are based on the officially available COVID-19 cases counts from China, Italy, Belgium, and Spain. Even from a superficial analysis of this data, several biases that hinder the modeling of these outbreaks become clear. First, the number of tests that can be run each day is finite, because of the limited availability of supplies and personnel, making blanket testing currently impossible to perform in many countries. This results in a large number of unreported cases with respect to the available data. Second, if tests are performed mainly on symptomatic patients for diagnostic purposes, because of the generally higher age of the hospitalized cases, the resulting official COVID-19 cases data will show a striking proportion of patients over 60 years old, regardless of the actual demographic structure of the population (see Suppl. Fig. 9 ). Another reason why the sheer number of tests performed is not a clear indication of the level of bias present in the data is that the number of test performed is just an upper bound for the actual number of individuals screened, because for example medical personnel with high risk of exposure may undergo periodic tests. Moreover, the directives of the Italian Ministry of Health indicates that a COVID-19 patient must be negative to two consecutive tests performed with a 24h delay (19) to be considered as having recovered from the disease. The cumulative number of cases we used to fit the SEIR model is therefore most probably both severely underestimated and skewed towards older age groups in the population. Both in Belgium and in Italy, for instance, patients who are diagnosed as suspect COVID-19 case over the phone by their GP, but who present no immediate risk of complication, are nor tested, nor reported as new cases. As the epidemic progresses and healthcare resources become mobilized, testing capacity increases and we observe a growing number of newly tested individuals. Yet a key assumption of our model is that new infections are caused by contamination from currently reported infectious individuals, because our modeling is based on the observed cases, for which official data exists. However, in practice, many of the newly diagnosed patients have been infected by the majority of unreported infectious people. Our model will thus infer an higher R 0 to compensate for the underestimated pool of infectious patients. This might explain the seemingly high values of R 0 estimates in the inter-lockdowns period in Belgium for instance. Interestingly, the estimation of the actual (vs. reported) number of cases on March 12, 2020 in Italy suggests that, although heavily under-represented in the official data because of testing bias, the 20-29 age group is the most affected by COVID-19. Given that age group is particularly socially active, one might speculate that infections via this age group may have played a key role in the spread of COVID-19 across Italy, even though these cases ended up almost completely unreported. There are however some limitations to this analysis. While South Korea's testing strategy has clearly been comprehensive, it is not clear that it has been completely unbiased. In particular, the low number of cases in the 10-19 years bin compared to the 20-29 years bin might be explained by a radical difference in the true proportion of cases betwe