Hyperbolic compartmental models for epidemic spread on networks with uncertain data: application to the emergence of Covid-19 in Italy

TL;DR

This paper introduces a hyperbolic compartmental model on networks that accounts for spatial movement, population heterogeneity, and data uncertainty to better understand epidemic spread, demonstrated through COVID-19 in Italy.

Contribution

It develops a multiscale hyperbolic model incorporating uncertainty and mobility patterns, advancing epidemic modeling on complex networks.

Findings

Model accurately captures spatial heterogeneity of COVID-19 in Italy.

The approach effectively handles data uncertainty in epidemic modeling.

Numerical simulations align with observed outbreak patterns.

Abstract

The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the values reported by official sources, such as the amount of infectious individuals. In this paper we address the above aspects through a hyperbolic compartmental model on networks, in which nodes identify locations of interest, such as cities or regions, and arcs represent the ensemble of main mobility paths. The model describes the spatial movement and interactions of a population partitioned, from an epidemiological point of view, on the basis of an extended compartmental structure and divided into commuters, moving on a suburban scale, and non-commuters, acting on an urban scale. Through a diffusive rescaling, the model allows us to recover classical diffusion equations related to commuting dynamics. The numerical solution of the resulting multiscale hyperbolic system with uncertainty is then tackled using a stochastic collocation approach in combination with a finite-volume IMEX method. The ability of the model to correctly describe the spatial heterogeneity underlying the spread of an epidemic in a realistic city network is confirmed with a study of the outbreak of COVID-19 in Italy and its spread in the Lombardy Region.