  The diffusion of COVID19 is calling governments and public health authorities
to interventions that limit new infections and contain the expected number of
critical cases and deaths. Most of these measures rely on the compliance of
people, who are asked to reduce their social contacts to a minimum. In this
note we argue that individuals' adherence to prescriptions and reduction of
social activity may not be efficacious if not implemented robustly on all
social groups, especially on those characterized by intense mixing patterns.
Actually, it is possible that, if those who have many contacts reduce them
proportionally less than those who have few, then the effect of a policy could
backfire: the disease would take more time to die out, up to the point that it
could become endemic. In a nutshell, unless one gets everyone to act, and
specifically those who have more contacts, a policy may even be
counterproductive.
