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

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.