Epidemic threshold determined by the first moments of network with alternating degree distributions

© 2014, Elsevier B.V. All rights reserved. During the alternating day-night cycle, people have differing behavior and hence different connection patterns - such as going to work or home, shopping and so on. Hence, the true topological structure of human contact networks are not only time-varying but also exhibit certain distribution regularity. In this paper, we will investigate epidemic spreading on time-varying human contact networks, which follow one degree distribution during daytime, but another at night. Based on SIS (susceptible/infected/susceptible) propagation mechanism, we study the epidemic threshold of this network with alternating distributions. A surprising result is that for the discrete-time case the epidemic threshold is determined only by the first moments of the two alternating degree distributions, if the degree of each node is constant for all nights. A similar result is valid for the continuous-time case if the duration is sufficiently small. This work shows that the spreading dynamics of time-varying networks with alternating distributions is completely different from the widely studied case of static spreading networks.