Before revision: One of the biggest challenges raised by the Covid-19 outbreaks involves school openings and in-class vs. remote learning, affecting more than one billion students worldwide. One of the main issues herein concerns the potential effect of in person school activities on the spread of the epidemic: many studies have been conducted, often reaching divergent conclusions. In this paper, we first identify one apparently unobserved feature of the interrelation between virus transmissions in two subpopulations : as the contact rate of one subpopulation is varied, there is a phase transition between almost irrelevance to heavy influence of the transmission rate in the subpopulation on the overall outbreak; such transition is seen to occur during outbreaks or new strains upsurge, lockdowns, and vaccination campaigns , albeit at different transition points.
After revision: One of the biggest challenges raised by the Covid-19 pandemic. The mathematical analysis of compartmental models with subpopulations shows that the in-school contact rates affects the overall course of the pandemic only above a certain threshold that separates an influence phase from a non-influence one. The threshold, that we calculate via linear approximation in several cases, seems to appear in all contexts, including outbreaks or new strains upsurge, lockdowns, and vaccination campaigns , albeit at different transition points.