Formulation a new SIR model with non-local mobility

TL;DR

This paper introduces a novel nonlocal mobility-based SIR model that incorporates spatial motion of particles to better understand pandemic dynamics, analyzing long-term behavior and comparing new and classical reproduction numbers.

Contribution

It develops a new SIR model with nonlocal spatial mobility, bridging epidemiological modeling with real-world movement patterns, and introduces a new reproduction number $R_0^m$.

Findings

Analysis of long-term behavior and moments of the system

Introduction of a new reproduction number $R_0^m$

Examination of intermittency phenomena

Abstract

In this manuscript, we develop a mobility-based Susceptible-Infectious-Recovered (SIR) model to elucidate the dynamics of pandemic propagation. While traditional SIR models within the field of epidemiology aptly characterize transitions among susceptible, infected, and recovered states, they typically neglect the inherent spatial mobility of particles. To address this limitation, we introduce a novel dynamical SIR model that incorporates nonlocal spatial motion for three distinct particle types, thereby bridging the gap between epidemiological theory and real-world mobility patterns. This paper primarily focuses on analyzing the long-term behavior of this dynamic system, with specific emphasis on the computation of first and second moments. We propose a new reproduction number $R_0^m$ and compare it with the classical reproduction number $R_0$ in the traditional SIR model. Furthermore, we rigorously examine the phenomenon of intermittency within the context of this enhanced SIR model. The results contribute to a more comprehensive understanding of pandemic spread dynamics, considering both the interplay between disease transmission and population mobility and the impact of spatial motion on the system's behavior over time.