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Qiang Liu, Piet Van Mieghem
Research output: Contribution to journal › Article › Scientific › peer-review
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 language | English |
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Article number | 022309 |
Pages (from-to) | 1-6 |
Number of pages | 6 |
Journal | Physical Review E |
Volume | 97 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2018 |