Estimating the covariance structure of heterogeneous SIS epidemics on networks

TL;DR

This paper develops a method to estimate the covariance structure of heterogeneous SIS epidemic processes on networks, improving accuracy over mean-field models by using matrix factorization and stochastic differential equations.

Contribution

It introduces a novel approach combining non-negative matrix factorization and SDEs to analyze metastable states and covariance in heterogeneous SIS epidemics.

Findings

Accurate identification of metastable states using matrix factorization.

Covariance estimates enable significant accuracy improvements over NIMFA.

Modeling epidemic behavior with high-dimensional SDEs enhances prediction precision.

Abstract

Heterogeneous Markovian Susceptible-Infected-Susceptible (SIS) epidemics with a general infection rate matrix $\widetilde{A}$ are considered. Using a non-negative matrix factorization to approximate $\widetilde{A}$, we are able to identify when a metastable state can be expected, and that the metastable distribution, under certain conditions, will feature a normal distribution with known expectation and covariance. Furthermore, we model a heterogeneous Markovian SIS epidemic, that starts with a fraction of initially infected nodes different from that in the metastable state, by approximating its behaviour by a standard linear stochastic differential equation (SDE) in sufficiently high dimensions. By exploiting the knowledge of the covariance matrix from the SDE, we demonstrate significant accuracy improvements over the first-order mean-field approximation NIMFA.