  It is recognized that social heterogeneities in terms of the contact
distribution have a strong influence on the spread of infectious diseases.
Nevertheless, few data are available on the group composition of social
contacts, and their statistical description does not possess universal patterns
and may vary spatially and temporally. It is therefore essential to design
robust control strategies, mimicking the effects of non-pharmaceutical
interventions, to limit efficiently the number of infected cases. In this work,
starting from a recently introduced kinetic model for epidemiological dynamics
that takes into account the impact of social contacts of individuals, we
consider an uncertain contact formation dynamics leading to slim-tailed as well
as fat-tailed distributions of contacts. Hence, we analyse the effects of an
optimally robust control strategy of the system of agents. Thanks to classical
methods of kinetic theory, we couple uncertainty quantification methods with
the introduced mathematical model to assess the effects of social limitations.
Finally, using the proposed modelling approach and starting from available
data, we show the effectiveness of the proposed selective measures to dampen
uncertainties together with the epidemic trends.
