This article, published in the prestigious journal Nature, shows that in France, many COVID-19 patients have not consulted or alerted public health to their condition, leading to problematic under-detection of cases. This study is based on a mathematical model, the parameters of which were optimized using the NOMAD software developed at GERAD by the team of professors Charles Audet and Sébastien Le Digabel and the research associates Viviane Rochon Montplaisir and Christophe Tribes. This blackbox optimization software has been in continuous development for over twenty years and represents the state of the art in derivative-free optimization.