**J. Franceschi, A. Medaglia, M. Zanella. **

Preprint arXiv, 2022.

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 and their statistical description does not possess universal patterns and may vary spatially and temporally. It is therefore essential to design optimal 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 optimal 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.