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

In this subsection, we detail our parameters choice to study the current epidemic outbreak in Spain. Regarding epidemiological parameters, the incubation period has been reported to be η −1 + α −1 = 5.2 days [12] in average which, in our formalism, must be distributed into the exposed and asymptomatic compartments. In principle, if one does not expect asymptomatic transmissions, most of this time should be spent inside the exposed compartment, thus being the asymptomatic infectious compartment totally irrelevant for disease spreading. However, along the line of several recent works [13, 15, 5] we have found that the unfolding of COVID-19 cannot be explained without accounting for infections from individuals not developing any symptoms previously. In particular, our best fit to reproduce the evolution of the real cases reported so far in Spain yields α −1 = 2.86 days as asymptomatic infectious period. In turn, the infectious period while being symptomatic is established as µ −1 = 7 days [1, 20] , except for the young strata, for which we have reduced it to 1 day, assigning the remaining 6 days as asymptomatic; this is due to the reported mild symptoms in young individuals, which may become inadvertent [2] . Furthermore, we have included an isolation factor ν = 0.6 which reduces the infectiousness of symptomatic agents as a result of their self-isolation. We fix the fatality rate ω = 42% of ICU patients by studying historical records of dead individuals as a function of those requiring intensive care. In turn, we estimate the period from ICU admission to death as ψ −1 = 7 days [19] and the stay in ICU for those overcoming the disease as χ −1 = 20 days [1] .