Vol. 8, No. 3, 2020
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A kinetic model for epidemic spread

Mario Pulvirenti and Sergio Simonella

Vol. 8 (2020), No. 3, 249–260
DOI: 10.2140/memocs.2020.8.249
Abstract

We present a Boltzmann equation for mixtures of three species of particles reducing to the Kermack–McKendrick (SIR) equations for the time evolution of the density of infected agents in an isolated population. The kinetic model is potentially more detailed and might provide information on space mixing of the agents.

Keywords
Boltzmann equation, SIR model, low-density limit, stochastic particle system, forward cluster
Mathematical Subject Classification
Primary: 00A71
Milestones
Received: 16 May 2020
Accepted: 26 June 2020
Published: 2 September 2020

Communicated by Raffaele Esposito
Authors
Mario Pulvirenti
Dipartimento di Matematica
Università di Roma La Sapienza
Rome
Italy
Sergio Simonella
Unité de Mathématiques Pures et Appliquées
CNRS UMR 5669
École Normale Supérieure de Lyon
Lyon
France