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 order to explicitly relate the reduction of mobility and confinement measures with the reproductive ratio R of the epidemics, we first develop a mathematical model, in the line of previous approaches [5] [6] [7] [8] [9] [10] [11] , to predict the epidemic prevalence of COVID-19 throughout a territory. We develop an age-stratified metapopulation compartmental model that encapsulates the particularities of the spreading of COVID-19 regarding (i) its transmission among individuals, (ii) the specificities of certain demographic groups with respect to the impact of COVID- 19, and (iii) the human mobility patterns inside and among regions. The full dynamics of the epidemics is formalized in terms of a Microscopic Markov Chain Approach (MMCA) [12] [13] [14] . We refer the reader to the Methods section for a full description of the model and to the Supplementary Note 1 for the complete analysis of the Markovian equations. This model has been used to assess the necessity for total lockdown in Spain, finally enforced on March 30th 15 , for it allows a direct assessment of mobility restrictions and confinement policies.