Print Email Facebook Twitter Epidemics in networks with nodal self-infection and the epidemic threshold Title Epidemics in networks with nodal self-infection and the epidemic threshold Author Van Mieghem, P.F.A. Cator, E. Faculty Electrical Engineering, Mathematics and Computer Science Department Telecommunications Date 2012-07-30 Abstract Since the Susceptible-Infected-Susceptible (SIS) epidemic threshold is not precisely defined in spite of its practical importance, the classical SIS epidemic process has been generalized to the ??SIS model, where a node possesses a self-infection rate ?, in addition to a link infection rate ? and a curing rate ?. The exact Markov equations are derived, from which the steady state can be computed. The major advantage of the ??SIS model is that its steady state is different from the absorbing (or overall-healthy state) and approximates, for a certain range of small ?>0, the in reality observed phase transition, also called the “metastable” state, that is characterized by the epidemic threshold. The exact steady-state analysis for the complete graph illustrates the effect of small ? and the quality of the first-order mean-field approximation, the N-intertwined model, proposed earlier. Apart from duality principles, often used in the mathematical literature, we present an exact recursion relation for the Markov infinitesimal generator. To reference this document use: http://resolver.tudelft.nl/uuid:30f373cf-9c66-49ac-9d1e-d69fac80d153 DOI https://doi.org/10.1103/PhysRevE.86.016116 Publisher American Physical Society ISSN 1539-3755 Source http://link.aps.org/doi/10.1103/PhysRevE.86.016116 Source Physical Review E, 86 (1), 2012 Part of collection Institutional Repository Document type journal article Rights © 2012 American Physical Society Files PDF VanMieghem_2012.pdf 703.12 KB Close viewer /islandora/object/uuid:30f373cf-9c66-49ac-9d1e-d69fac80d153/datastream/OBJ/view