---
abstract: 'The mean-field analysis of a multi-population agent-based model is performed. The model couples a particle dynamics driven by a nonlocal velocity with a Markow-type jump process on the probability that each agent has of belonging to a given population. A general functional analytic framework for the well-posedness of the problem is established, and some concrete applications are presented, both in the case of discrete and continuous set of labels. In the particular case of a leader-follower dynamics, the existence and approximation results recently obtained in [@ABRS2018] are recovered and generalized as a byproduct of the abstract approach proposed.'
address:
- 
- 'Dipartimento di Scienze Matematiche “G. L. Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy'
- 'Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy'
author:
- Marco Morandotti
- Francesco Solombrino
title: |
    Mean-field analysis of multi-population dynamics\
    with label switching
---

**Keywords**: kinetic equations, mean-field limits, continuity equations, jump processes, superposition principle.

Introduction {#sec:intro}
============

The concept of mean-field interaction, originally used in statistical physics with Kac [@Kac] and then McKean [@mckean1967propagation] to describe the collisions between particles in 