Distributed Reproduction Numbers of Networked Epidemics

TL;DR

This paper introduces distributed reproduction numbers for networked epidemic models, enabling detailed analysis of individual communities' spreading behaviors and providing new outbreak conditions and stability criteria.

Contribution

It proposes a novel concept of distributed reproduction numbers for networked SIS and SIR models, allowing finer-grained epidemic analysis and new outbreak prediction conditions.

Findings

Distributed reproduction numbers can be computed from network parameters.

New outbreak conditions based on distributed reproduction numbers.

Simulations show improved analysis of epidemic spread.

Abstract

Reproduction numbers are widely used for the estimation and prediction of epidemic spreading processes over networks. However, reproduction numbers do not enable estimation and prediction in individual communities within networks, and they can be difficult to compute due to the aggregation of infection data that is required to do so. Therefore, in this work we propose a novel concept of distributed reproduction numbers to capture the spreading behaviors of each entity in the network, and we show how to compute them using certain parameters in networked SIS and SIR epidemic models. We use distributed reproduction numbers to derive new conditions under which an outbreak can occur. These conditions are then used to derive new conditions for the existence, uniqueness, and stability of equilibrium states. Finally, in simulation we use synthetic infection data to illustrate how distributed reproduction numbers provide more fine-grained analyses of networked spreading processes than ordinary reproduction numbers.