Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories are shown to result from seeking approximate solutions of the master equations. Applications to the calculation of SIS epidemic thresholds and critical points of nonequilibrium spin models are also demonstrated.
Hurd, Thomas R; Gleeson, James P.; Melnik, Sergey(Public Library of Science, 2017)
We introduce a probabilistic framework that represents stylized banking networks with the aim of predicting the size of contagion events. Most previous work on random financial networks assumes independent connections ...
Gleeson, James P.; Melnik, Sergey(American Physical Society, 2009)
An analytical approach to calculating bond percolation thresholds, sizes of k-cores, and sizes of giant connected components on structured random networks with nonzero clustering is presented. The networks are generated ...
Fennell, Peter G.; Melnik, Sergey; Gleeson, James P.(American Physical Society, 2016)
Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, ...
Fennell, Peter G.; Gleeson, James P.; Cellai, Davide(American Physical Society, 2014)
Facilitated spin models were introduced some decades ago to mimic systems characterized by a glass transition. Recent developments have shown that a class of facilitated spin models is also able to reproduce characteristic ...
Onaga, Tomokatsu; Gleeson, James P.; Masuda, Naoki(American Physical Society, 2017)
Social contact networks underlying epidemic processes in humans and animals are highly dynamic. The spreading of infections on such temporal networks can differ dramatically from spreading on static networks. We theoretically ...
