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

Dependence on time of the effective reproduction number In Eq. (2), we assume that the fraction of susceptible individuals as well as the average number of contacts is constant during the infectious period. However, the fraction of susceptible individuals obviously changes during that time. More importantly, as containment measures are put in place, the number of contacts varies as well. To account for the temporal variability of these quantities, we calculate the contributions to R g i (t) of the infections produced since the individual became asymptomatically infected at time t. Since the infectious period is divided in two phases, one asymptomatic with infectious rate α g , and another symptomatic with infectious rate µ g , what we have is a coupled 17 . 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.