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

Edward De Brouwer; Daniele Raimondi; Yves Moreau

About "flattening the curve". Despite their limitations, our models show that the idea of "flattening the curve" (i.e., reducing the R 0 of the epidemic to a level that would allow the gradual build up of natural immunity in the population) is likely to be unfeasible. Any significant reduction of R 0 that would not bring it extremely close to 1 would overwhelm the healthcare system because the ICU capacity and the height of the epidemic peak in a immunologically naïve population are simply on different scales (in the SIR, the proportion of the population infectious at the epidemic peak is given by 1 − 1/R 0 − ln(R 0 )/R 0 . For example, 30% of the population is infectious at the epidemic peak for R 0 = 3, while the ICU capacity in for example Belgium is 15.9 beds per 100,000 inhabitants (8)). Even if the epidemic could be controlled at a fixed level corresponding to a heavy but non-overloading load of the ICU capacity, the time needed to build herd immunity would be measured in years. As an example, a back-of-theenvelope calculation for Belgium based on a permanent ICU capacity of 1,000 beds for coronavirus patients (compared to the pre-existing capacity of 1,750 (8) beds, which would mean a major continuing strain on the hospital system and thus the need to maintain supplementary capacity for several years), assuming an average ICU stay of 10 days (6, 20) , and assuming that 2% of patients affected in the general population would eventually require ICU care, would mean that 100 patients would be admitted at ICU care per day and that 5,000 individuals in the general population would be infected by the disease each day. Reaching a level where 50% of the population (of about 11 million people) has achieved natural immunity would require 1,100 days or 3 years. Given that the immunity to the disease might be relatively short-lived (around 2 years for SARS (21) ), it might simply be next to impossible to achieve herd immunity without overwhelming the healthcare system. Moreover, such a strategy would require maintaining the number of cases in the population at a tightly controlled level with R 0 being maintained on average at 1. Whenever R 0 would be above 1, the disease would flare up, which would quickly overload a healthcare system maintained at saturation. When R 0 would be below 1, the disease would start vanishing, which would extend the time needed to build herd immunity. Given that it is completely unclear what the precise impact of any containment measure is on R 0 , a strategy based on lifting and reimposing measures to switch between R 0 slightly below 1 and R 0 slightly above 1 does not appear realistic.