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

We first show that our model is able to capture the effects of implementing confinement measures by using demographic and mobility data for Spain (see Methods section). Once initialized the equations with the initial infectious seeds with the first reported cases up to March 3, we let the model evolve in the free-mobility regime until March 14, when the first mobility restrictions enter into play in Spain and, consequently, confinement is imposed in the model. Once validated the model, we study how enforcing mobility restriction and social distancing can drastically change the course of the epidemics. In the left panel of Figure 2 , we show the number of new cases per day for different levels of confinement, κ 0 . The real value of κ 0 has been assessed from official data on the use of public transportation, cars entrance and exits in cities, and pedestrians flows tracked through cellphones. The confinement is applied at time t c corresponding to March 14. It is observed that, as confinement is applied to a small fraction of the population (κ 0 > 0), the curve for the number of new cases per day starts to broaden and the maximum shifts forward in time. Such a mitigation strategy is known as -flattening the curve-, in which containment delays and lowers the incidence peak. The consequence of the flattening scenario is that the impact over health systems is ameliorated at the expense of a larger epidemic period. However, as confinement is increased (higher κ 0 ), there is a dramatic 8 . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.