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

Edward De Brouwer; Daniele Raimondi; Yves Moreau

More than 100 countries (1) in the world are currently affected by the coronavirus disease (COVID- 19) pandemic (2) . COVID-19 is a respiratory infectious disease caused by the SARS-CoV-2 virus (previously known as 2019-nCOV), and it originated in December 2019 in Wuhan (China), most probably following a zoonotic event (3, 4) . COVID-19 epidemics are now affecting many European countries, which are at different stages of contagion and containment measures (4) . The virus can be found in the respiratory tract of patients 1-2 days before the onset of symptoms, where it shows active replication (5), persisting 7-15 days (4) . Italy was the first to be seriously affected (6) , with Spain, France, Belgium, and other countries being 7-14 days behind. Although definitive data on the COVID-19 Case Fatality Rate (CFR) are still missing and the current ones are biased by the testing policies and the demographic structure of the population, the observed CFR may be as high as of 10.0% in Italy, 4.0% in China, 6.0% in Spain, and 4.3% worldwide. In Italy, it has been observed that 7-11% of the cases present Acute Respiratory Distress syndrome (ARDS) caused by SARS-CoV-2 pneumonia, and thus require respiratory support in Intensive Care Units (ICUs) (6, 7) . European Countries tend to have between 4.2 (Portugal) and 29.2 (Germany) ICU beds per 100,000 inhabitants (8) (EU average is 11.5). This indicates that an exponential-like growth of the COVID-19 cases can rapidly reach oversaturation of the available ICU beds, thereby decreasing the quality of the medical treatments provided to patients and worsening the case fatality rate (6, 9) . To avoid this scenario, almost every country affected by the COVID-19 pandemic has put in place measures to contain the epidemic, limiting travels and minimizing physical social interactions, in an attempt to relieve the strain on the healthcare system, in particular ICU units. When it comes to epidemic modeling, these measures affect the basic reproduction ratio R 0 , which is typically interpreted as the expected number of cases directly generated by an infected individual in a population susceptible to infection (10) . Current estimates of this value range from 2 and 6.5 in China (11) (12) (13) (14) and 3.1 in the first phase of the outbreak in Italy (15) . In SEIR (Susceptible, Exposed, Infected, Removed) (16) modeling of epidemics, R 0 = β/γ, with β representing the number of contacts from an infected individual per unit of time and γ −1 the period in which a patient is infectious. When R 0 > 1, the number of cases is growing, else, the epidemic is receding. Countries affected by COVID-19 epidemics deployed containment measures that acted on these two parameters. China, for example acted on R 0 by quarantining or hospitalizing cases as soon as they were becoming symptomatic, with an average time elapsed between symptoms and hospitalization of 2.3 (12, 13) or 2.9 days (14) . At the same time, China instituted incremental forms of quarantine in Wuhan and the Hubei province, reducing the average number of physical social contacts between residents of the most affected zones, and introduced the use of selfprophylaxis praxis to further reduce the risk of infection, thus effectively reducing β. Similar measures have been adopted by the European countries in which COVID-19 started spreading (4) . Italy was the first country affected in Europe, and the first COVID-19 cluster prompted the lockdown of the town of Codogno and