On the use of Markov chains for epidemic modeling on networks

TL;DR

This paper examines the application of Markov chains in epidemic modeling on networks, highlighting their limitations and proposing methods for more accurate predictions of virus spread and infection times.

Contribution

It introduces an improved algorithm for estimating infection times and a new indicator based on these times, enhancing epidemic modeling accuracy.

Findings

Markov chains tend to overestimate infection times in epidemic models.

The proposed sampling algorithm efficiently estimates infection times.

The new indicator shows promising node ranking properties compared to existing measures.

Abstract

We discuss various models for epidemics on networks that rely on Markov chains. Random walks on graphs are often used to predict epidemic spread and to investigate possible control actions to mitigate them. In this study, we demonstrate that they do not fully reflect the dynamics of epidemics, as they overestimate infection times. Accordingly, we explain how Markov chains may still be used to accurately model the virus spread, and to correctly predict infection times. We also provide an algorithm that efficiently estimates infection times via a sampling strategy. Finally, we present a novel indicator based on infection times, and we compare its node ranking properties with other centrality measures based on random walks.