Disease spread over randomly switched large-scale networks

TL;DR

This paper analyzes disease spread over large-scale networks with randomly switching edges, providing scalable conditions for infection die-out based on spectral properties of associated matrices.

Contribution

It introduces scalable sufficient conditions for disease extinction in large networks, leveraging spectral theory of random matrices, improving over existing eigenvalue-based criteria.

Findings

Conditions for disease extinction are derived for large networks.

Spectral properties of random matrices are used for scalable analysis.

The proposed criteria are computationally feasible for large-scale networks.

Abstract

In this paper we study disease spread over a randomly switched network, which is modeled by a stochastic switched differential equation based on the so called $N$-intertwined model for disease spread over static networks. Assuming that all the edges of the network are independently switched, we present sufficient conditions for the convergence of infection probability to zero. Though the stability theory for switched linear systems can naively derive a necessary and sufficient condition for the convergence, the condition cannot be used for large-scale networks because, for a network with $n$ agents, it requires computing the maximum real eigenvalue of a matrix of size exponential in $n$. On the other hand, our conditions that are based also on the spectral theory of random matrices can be checked by computing the maximum real eigenvalue of a matrix of size exactly $n$.