Estimating the covariance structure of heterogeneous SIS epidemics on networks

2016/09/24 by E. Cator, Cator, E., H. Don +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1609.07636

20 pages and 5 figures

arxiv created 2017/07/25 · arxiv updated 2017/07/27

Abstract

Heterogeneous Markovian Susceptible-Infected-Susceptible (SIS) epidemics with a general infection rate matrix \widetildeA are considered. Using a non-negative matrix factorization to approximate \widetildeA, 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.

Related

• Variance of the SIS Epidemic on Networks: A Diffusion Approximation
• The Accuracy of Mean-Field Approximation for Susceptible-Infected-Susceptible Epidemic Spreading
• Analysis of Exact and Approximated Epidemic Models over Complex Networks
• Heterogeneous network epidemics: real-time growth, variance and extinction of infection
• SIS Epidemic Spreading with Heterogeneous Infection Rates