A viral load-based model for epidemic spread on spatial networks

TL;DR

This paper introduces a kinetic model based on viral load to simulate infectious disease spread on spatial networks, analyzing long-term trends and effects of confinement measures.

Contribution

It develops a novel Boltzmann-type kinetic model incorporating viral load and social contacts, deriving hydrodynamic equations for epidemic dynamics on networks.

Findings

Hydrodynamic equations describe disease spread and viral load evolution.

Large-time behavior analysis reveals conditions for infection blow-up or eradication.

Numerical tests show confinement measures impact disease diffusion on networks.

Abstract

In this paper, we propose a Boltzmann-type kinetic model of the spreading of an infectious disease on a network. The latter describes the connections among countries, cities or districts depending on the spatial scale of interest. The disease transmission is represented in terms of the viral load of the individuals and is mediated by social contacts among them, taking into account their displacements across the nodes of the network. We formally derive the hydrodynamic equations for the density and the mean viral load of the individuals on the network and we analyse the large-time trends of these quantities with special emphasis on the cases of blow-up or eradication of the infection. By means of numerical tests, we also investigate the impact of confinement measures, such as quarantine or localised lockdown, on the diffusion of the disease on the network.