title: Contagion processes on the static and activity-driven coupling networks.
abstract: The evolution of network structure and the spreading of epidemic are common coexistent dynamical processes. In most cases, network structure is treated as either static or time-varying, supposing the whole network is observed in the same time window. In this paper, we consider the epidemics spreading on a network which has both static and time-varying structures. Meanwhile, the time-varying part and the epidemic spreading are supposed to be of the same time scale. We introduce a static and activity-driven coupling (SADC) network model to characterize the coupling between the static ("strong") structure and the dynamic ("weak") structure. Epidemic thresholds of the SIS and SIR models are studied using the SADC model both analytically and numerically under various coupling strategies, where the strong structure is of homogeneous or heterogeneous degree distribution. Theoretical thresholds obtained from the SADC model can both recover and generalize the classical results in static and time-varying networks. It is demonstrated that a weak structure might make the epidemic threshold low in homogeneous networks but high in heterogeneous cases. Furthermore, we show that the weak structure has a substantive effect on the outbreak of the epidemics. This result might be useful in designing some efficient control strategies for epidemics spreading in networks.
authors.affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, China.|LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China.
authors.forename: Yanjun
authors.initials: Y
authors.lastname: Lei
authors.affiliation: LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China.|Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Ilinois 60208, USA.
authors.forename: Xin
authors.initials: X
authors.lastname: Jiang
authors.affiliation: LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China.
authors.forename: Quantong
authors.initials: Q
authors.lastname: Guo
authors.affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, China.|Center for Complex Network Research, Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA.
authors.forename: Yifang
authors.initials: Y
authors.lastname: Ma
authors.affiliation: LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China.
authors.forename: Meng
authors.initials: M
authors.lastname: Li
authors.affiliation: LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China.
authors.forename: Zhiming
authors.initials: Z
authors.lastname: Zheng