Contagion processes on the static and activity driven coupling networks

TL;DR

This paper introduces a coupled network model combining static and dynamic structures to analyze epidemic spreading, revealing how different coupling strategies influence outbreak thresholds and dynamics.

Contribution

The study develops the SADC model to unify static and time-varying networks, providing analytical thresholds that generalize classical epidemic models.

Findings

Weak structures lower epidemic thresholds in homogeneous coupling.

Heterogeneous coupling makes epidemics harder to spread via weak structures.

A threshold ratio of weak to strong structure significantly impacts epidemic outbreaks.

Abstract

The evolution of network structure and the spreading of epidemic are common coexistent dynamical processes. In most cases, network structure is treated either static or time-varying, supposing the whole network is observed in a same time window. In this paper, we consider the epidemic spreading on a network consisting of both static and time-varying structures. At 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 static (strong) structure and dynamic (weak) structure. Epidemic thresholds of SIS and SIR model are studied on SADC both analytically and numerically with various coupling strategies, where the strong structure is of homogeneous or heterogeneous degree distribution. Theoretical thresholds obtained from SADC model can both recover and generalize the classical results in static and time-varying networks. It is demonstrated that weak structures can make the epidemics break out much more easily in homogeneous coupling but harder in heterogeneous coupling when keeping same average degree in SADC networks. Furthermore, we show there exists a threshold ratio of the weak structure to have substantive effects on the breakout of the epidemics. This promotes our understanding of why epidemics can still break out in some social networks even we restrict the flow of the population.