Per i Seminari di Fisica Matematica Federico II, martedì 3 febbraio 2026 dalle ore 15:30, nella Sala Riunioni 2L, il dottor Giorgio Martalò dell’Università di Pavia terrà il seminario:

A kinetic framework for SIR-type epidemic models: mean-field limit and asymptotic analysis

Abstract: The goal of the talk is to provide a multi-scale perspective bridging kinetic theory with classical epidemic models. To this aim, we propose a kinetic framework to describe the time evolution of the statistical distributions of susceptible, infectious and recovered populations, under epidemic transmission driven by susceptible-infectious interactions. The resulting formulation consists of a system of Boltzmann-like equations modelling the binary interactions between susceptible and infectious individuals, supplemented by linear redistribution operators accounting for recovery and reinfection dynamics.

At the macroscopic scale, the first order moments of the kinetic system are governed by an SIR-type model with reinfection, whose parameters are rigorously derived from the underlying microscopic interaction rules. Moreover, in the grazing collision regime, the Boltzmann system is properly approximated by a system of Fokker–Planck equations, yielding a more tractable and detailed analysis of the long-time behaviour of the population distributions. Within this setting, we can rigorously prove convergence to equilibrium of the mean-field system through the energy distance method. The analysis also highlights the dissipative nature of the dynamics and clarifies the role of interaction terms in driving the system toward a stable equilibrium.