Global and Distributed Reproduction Numbers of a Multilayer SIR Model with an Infrastructure Network

TL;DR

This paper introduces a multilayer SIR model with infrastructure networks, defining local and global reproduction numbers to analyze and predict pathogen spread more accurately.

Contribution

It develops a novel framework of distributed reproduction numbers for multilayer networks, enhancing the understanding of local and global epidemic dynamics.

Findings

DRNs provide more precise analysis than global R in network spread.

Threshold conditions relate infection peaks to effective reproduction numbers.

Simulation results validate the analytical predictions.

Abstract

In this paper, we propose an SIR spread model in a population network coupled with an infrastructure network that has a pathogen spreading in it. We develop a threshold condition to characterize the monotonicity and peak time of a weighted average of the infection states in terms of the global (network-wide) effective reproduction number. We further define the distributed reproduction numbers (DRNs) of each node in the multilayer network which are used to provide local threshold conditions for the dynamical behavior of each entity. Furthermore, we leverage the DRNs to predict the global behavior based on the node-level assumptions. We use both analytical and simulation results to illustrate that the DRNs allow a more accurate analysis of the networked spreading process than the global effective reproduction number.