Susceptible-infected-susceptible epidemics on networks with general infection and cure times

被引:43
作者
Cator, E. [1 ]
van de Bovenkamp, R. [2 ]
Van Mieghem, P. [2 ]
机构
[1] Radboud Univ Nijmegen, Fac Sci, NL-6500 GL Nijmegen, Netherlands
[2] Delft Univ Technol, Fac Elect Engn Math & Comp Sci, NL-2628 CD Delft, Netherlands
来源
PHYSICAL REVIEW E | 2013年 / 87卷 / 06期
关键词
D O I
10.1103/PhysRevE.87.062816
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.
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