Simulating SIR processes on networks using weighted shortest paths

TL;DR

This paper introduces a novel framework for simulating SIR epidemic processes on networks by mapping dynamics to weighted shortest paths, enabling efficient analysis of propagation times and intervention strategies.

Contribution

The paper presents a new method that models SIR processes using weighted shortest paths, applicable to both Markovian and non-Markovian dynamics, with improved computational efficiency.

Findings

Efficient simulation of SIR dynamics on empirical networks.

Enhanced source detection and vaccination strategies.

Analysis of propagation times between nodes.

Abstract

We present a framework to simulate SIR processes on networks using weighted shortest paths. Our framework maps the SIR dynamics to weights assigned to the edges of the network, which can be done for Markovian and non-Markovian processes alike. The weights represent the propagation time between the adjacent nodes for a particular realization. We simulate the dynamics by constructing an ensemble of such realizations, which can be done by using a Markov Chain Monte Carlo method or by direct sampling. The former provides a runtime advantage when realizations from all possible sources are computed as the weighted shortest paths can be re-calculated more efficiently. We apply our framework to three empirical networks and analyze the expected propagation time between all pairs of nodes. Furthermore, we have employed our framework to perform efficient source detection and to improve strategies for time-critical vaccination.