Burst of virus infection and a possibly largest epidemic threshold of non-Markovian susceptible-infected-susceptible processes on networks

Qiang Liu, Piet Van Mieghem

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian susceptible-infected-susceptible (SIS) process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infection rate exceeds 1/ln(λ1+1), where λ1 is the largest eigenvalue of the network's adjacency matrix, then the infection will persist on the network under the mean-field approximation. Thus, 1/ln(λ1+1) is possibly the largest epidemic threshold for a general non-Markovian SIS process with a Poisson curing process under the mean-field approximation. Furthermore, non-Markovian SIS processes may result in a multimodal prevalence. As a byproduct, we show that a limiting Weibullian SIS process has the potential to model bursts of a synchronized infection.

Original languageEnglish
Article number022309
Pages (from-to)1-6
Number of pages6
JournalPhysical Review E
Volume97
Issue number2
DOIs
Publication statusPublished - 2018

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  • Spreading on Networks

    Liu, Q., 2019, Delft. 142 p.

    Research output: ThesisDissertation (TU Delft)

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