Boltzmann-type equations for multi-agent systems with label switching

TL;DR

This paper develops a Boltzmann-type kinetic framework for multi-agent systems with changing labels, incorporating interactions and label switches, and applies it to disease contagion and quarantine modeling.

Contribution

It introduces a novel kinetic model combining interaction dynamics with label switching, including Markov processes, and analyzes disease contagion with quarantine measures.

Findings

Derived general kinetic equations for multi-agent label switching.

Characterized transient and equilibrium distributions via Fokker-Planck analysis.

Modeled contagion dynamics incorporating quarantine strategies.

Abstract

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. We derive general kinetic equations for the joint interaction/label switch processes in each group. For prototypical birth/death dynamics, we characterise the transient and equilibrium kinetic distributions of the groups via a Fokker-Planck asymptotic analysis. Then we introduce and analyse a simple model for the contagion of infectious diseases, which takes advantage of the joint interaction/label switch processes to describe quarantine measures.