Covid-19 testing strategies and lockdowns: the European closed curves, analysed by “skew-normal” distributions, the forecasts for the UK, Sweden, and the USA, and the ongoing outbreak in Brazil
Authors: Leo Stefano De 
Published: June 2020

AbstractAs the number of Covid-19 infections worldwide overtakes 6 millions of Total Confirmed Cases (TCC), the data reveal almost closed outbreaks in many European countries. Using the European data as a basis for our analysis, we study the spreading rate of Covid-19 and model the Daily Confirmed Cases and Deaths per Million (DCCpM and DDpM) curves by using “skew-normal” probability density functions. The use of these asymmetrical distributions allows to get a more realistic prediction of the end of the disease in each country and to evaluate the effectiveness of the local authorities strategies in facing the European outbreak. The initial stage of the Brazilian disease is compared with the early phase of the European one. This is done by using the weekly spreading rate of Covid-19. For Sweden, UK, and USA, we shall give a forecast for the end of pandemic and for Brazil the prediction of the peak of DDpM. We also discuss additional factors that could play an important role in the fight against Covid-19, such as the fast response of the local authorities, the testing strategies, the number of beds in the intensive care units, and, last but not least, the measures of isolation adopted. The Brazilian mitigation measures can be placed between the strict lockdown of many European countries and the Swedish approach, but clearly much comparable to the European ones (in particular to the Netherlands).MethodsFor Brazil, the weekly spreading rates of Covid-19, as more people are getting infected, was used to compare the outbreak in these countries with the ones of the European countries when they were at the same stage of infection. In the early stage of the disease, normal distributions have been used to obtain what we call a dynamic prediction of the peaks. After reaching the peak of daily infections and/or deaths, skew-normal distributions are required to correctly fit the asymmetrical DCCpM and DDpM curves and get a realistic forecast of the pandemic end.FindingsThe European data analysis shows that the spreading rate of Covid-19 increased similarly for all countries in its initial stage, but it changed as the number of TCCpM in each country grew. This was caused by the different timely action of the authorities in adopting isolation measures and/or massive testing strategies. The early stage of the outbreak in the USA and Brazil shows for theirαfactor (DCCpM) a behaviour similar to Italy and Sweden, respectively. For theβfactor (DDpM), the American spreading is similar to the one of Switzerland, whereas the Brazilian factor is greater than the ones of Portugal, Germany, and Austria (which showed, in terms of TDpM, the best results in Europe) but, at the moment, it is lower than the other European countries.InterpretationThe fitting skew parameters used to model the DCCpM and DDpM curves allow a more realistic prediction of the end of the pandemic and give us the possibility to compare the mitigation measures adopted by the local authorities by analysing their respective skew normal parameters (mean, mode, standard deviation, and skewness). In Europe, Sweden and the UK show the greatest asymmetries, a kind of marathon instead of the sprint of other European countries (as observed by Swedish authorities). This also happens for the USA. The Brazilian weekly spreading rate for deaths is lower than most of the European countries at the same stage of the outbreak.FundingIndividual grants by CNPq (2018/303911) and Fapesp (2019/06382–9).