Non-conservative Boltzmann-type kinetic equations for multi-agent systems with label switching

Nadia Loy, Andrea Tosin

Published 2020-06-28Version 1

In this paper, we propose a Boltzmann-type kinetic description of mass-varying interacting multi-agent systems. Our agents are characterised by a microscopic state, which changes due to their mutual interactions, and by a label, which identifies a group to which they belong. Besides interacting within and across the groups, the agents may change label according to a state-dependent Markov-type jump process. Hence the mass of each group is not conserved. We derive general kinetic equations for the joint interaction/label switching processes in each group. Moreover, for prototypical birth/death dynamics we characterise the transient and equilibrium kinetic distributions of the groups via a Fokker-Planck asymptotic analysis. Finally, we introduce and discuss, both analytically and numerically, a new model for the contagion of infectious diseases with quarantine based on this non-conservative kinetic framework.