A kinetic model for epidemic spread

TL;DR

This paper introduces a kinetic Boltzmann model for epidemic spread that generalizes the classic SIR equations, offering potential insights into spatial mixing of infected agents.

Contribution

It develops a kinetic framework for epidemics that extends traditional models by incorporating spatial and particle interactions.

Findings

Derives a Boltzmann equation for epidemic modeling

Reduces to classical SIR equations in specific limits

Suggests potential for detailed spatial analysis

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.