Derivation of the effective reproduction number R for COVID-19 in relation to mobility restrictions and confinement

Alex Arenas; Wesley Cota; Jesus Gomez-Gardenes; Sergio Gomez; Clara Granell; Joan T. Matamalas; David Soriano-Panos; Benjamin Steinegger

This example illustrates the difficult task of making accurate early evaluations of containment measures. It is observed that the reduction of mobility due to the confinement of the population has a highly nonlinear effect on the reduction of the epidemic. This makes the task of policy makers notoriously difficult, as they need to design realistic, implementable, confinement measures that reduce the impact of the epidemic sufficiently within the shortest time frame possible. If the interventions planned are too weak, the epidemic will not cease and the surge capacity of healthcare systems will be surpassed, leaving many individuals requiring hospitalization out of the attention they need. Furthermore, once policy makers realize the insufficiency of the interventions put in place, the epidemic may have spread up to a point such that only the most severe interventions will be of real use. On the other side, implementing very strict confinement measures from an early stage would give governments a much needed time to prepare against the attack of the disease, but would most likely take a huge toll in the economy, and consequently, in the population.