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

where p g denotes the degree of mobility of individuals within age group g, R g ij is the mobility matrix (fraction of individuals of group age g that choose destination j while living in region i), and P g i (t) denotes the probability that those agents get infected by the pathogen inside patch i. This way, the first term in the r.h.s. of Eq. (S9) denotes the probability of contracting the disease inside the residence patch, whereas the second term contains those contagions taking place in any of the neighboring areas. Furthermore, we assume that the number of contacts increases with the density of each area according to a monotonously increasing function f . Finally, we introduce an age-specific contact matrix, C, whose elements C gh define the fraction of contacts that individuals of age group g perform with individuals belonging to age group h. With the above definitions, P g i reads