title: Solvable non-Markovian dynamic network.
abstract: Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law interevent times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times. We further discuss possible generalizations of our result.
authors.affiliation: School of Mathematics and Physical Sciences, University of Sussex, Brighton BN1 9QH, United Kingdom.
authors.forename: Nicos
authors.initials: N
authors.lastname: Georgiou
authors.affiliation: School of Mathematics and Physical Sciences, University of Sussex, Brighton BN1 9QH, United Kingdom.
authors.forename: Istvan Z
authors.initials: IZ
authors.lastname: Kiss
authors.affiliation: School of Mathematics and Physical Sciences, University of Sussex, Brighton BN1 9QH, United Kingdom.
authors.forename: Enrico
authors.initials: E
authors.lastname: Scalas
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical