  In this paper, we propose a Boltzmann-type kinetic model of the spreading of
an infectious disease on a network. The latter describes the connections among
countries, cities or districts depending on the spatial scale of interest. The
disease transmission is represented in terms of the viral load of the
individuals and is mediated by social contacts among them, taking into account
their displacements across the nodes of the network. We formally derive the
hydrodynamic equations for the density and the mean viral load of the
individuals on the network and we analyse the large-time trends of these
quantities with special emphasis on the cases of blow-up or eradication of the
infection. By means of numerical tests, we also investigate the impact of
confinement measures, such as quarantine or localised lockdown, on the
diffusion of the disease on the network.
