Print Email Facebook Twitter Survival time of the susceptible-infected-susceptible infection process on a graph Title Survival time of the susceptible-infected-susceptible infection process on a graph Author Van de Bovenkamp, R. Van Mieghem, P. Faculty Electrical Engineering, Mathematics and Computer Science Department Intelligent Systems Date 2015-08-15 Abstract The survival time T is the longest time that a virus, a meme, or a failure can propagate in a network. Using the hitting time of the absorbing state in an uniformized embedded Markov chain of the continuous-time susceptible-infected-susceptible (SIS) Markov process, we derive an exact expression for the average survival time E[T ] of a virus in the complete graph KN and the star graph K1,N?1. By using the survival time, instead of the average fraction of infected nodes, we propose a new method to approximate the SIS epidemic threshold ?c that, at least for KN and K1,N?1, correctly scales with the number of nodes N and that is superior to the epidemic threshold ? (1) c = 1 ?1 of the N-intertwined mean-field approximation, where ?1 is the spectral radius of the adjacency matrix of the graph G. Although this new approximation of the epidemic threshold offers a more intuitive understanding of the SIS process, it remains difficult to compare outbreaks in different graph types. For example, the survival in an arbitrary graph seems upper bounded by the complete graph and lower bounded by the star graph as a function of the normalized effective infection rate ? ? (1) c . However, when the average fraction of infected nodes is used as a basis for comparison, the virus will survive in the star graph longer than in any other graph, making the star graph the worst-case graph instead of the complete graph. Finally, in non-Markovian SIS, the distribution of the spreading attempts over the infectious period of a node influences the survival time, even if the expected number of spreading attempts during an infectious period (the non-Markovian equivalent of the effective infection rate) is kept constant. Both early and late infection attempts lead to shorter survival times. Interestingly, just as in Markovian SIS, the survival times appear to be exponentially distributed, regardless of the infection and curing time distributions. To reference this document use: http://resolver.tudelft.nl/uuid:73f582f9-bd66-41b7-bad9-e1fa250b2860 DOI https://doi.org/10.1103/PhysRevE.92.032806 Publisher American Physical Society ISSN 1539-3755 Source Physical Review E, 92 (3), 2015 Part of collection Institutional Repository Document type journal article Rights © 2015 American Physical Society Files PDF PhysRevE.92.032806.pdf 1.24 MB Close viewer /islandora/object/uuid:73f582f9-bd66-41b7-bad9-e1fa250b2860/datastream/OBJ/view