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In this paper, we propose a Boltzmann-type kinetic model of the spreading ofan infectious disease on a network. The latter describes the connections amongcountries, cities or districts depending on the spatial scale of interest. Thedisease transmission is represented in terms of the viral load of theindividuals and is mediated by social contacts among them, taking into accounttheir displacements across the nodes of the network. We formally derive thehydrodynamic equations for the density and the mean viral load of theindividuals on the network and we analyse the large-time trends of thesequantities with special emphasis on the cases of blow-up or eradication of theinfection. By means of numerical tests, we also investigate the impact ofconfinement measures, such as quarantine or localised lockdown, on thediffusion of the disease on the network.

A viral load-based model for epidemic spread on spatial networks