Contagion processes on the static and activity driven coupling networks

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

Modeling memory effects in activity-driven networks

Activity-driven networks (ADNs) have recently emerged as a powerful paradigm to study the temporal evolution of stochastic networked systems. All the information on the time-varying nature of the system is encapsulated into a constant activity parameter, which represents the propensity to generate connections. This formulation has enabled the scientific community to perform effective analytical studies on temporal networks. However, the hypothesis that the whole dynamics of the system is summarized by constant parameters might be excessively restrictive. Empirical studies suggest that activity evolves in time, intertwined with the system evolution, causing burstiness and clustering phenomena. In this paper, we propose a novel model for temporal networks, in which a self-excitement mechanism governs the temporal evolution of the activity, linking it to the evolution of the networked system. We investigate the effect of self-excitement on the epidemic inception by comparing the epidemic threshold of a Susceptible-Infected-Susceptible model in the presence and in the absence of the self-excitement mechanism. Our results suggest that the temporal nature of the activity favors the epidemic inception. Hence, neglecting self-excitement mechanisms might lead to harmful underestimation of the risk of an epidemic outbreak. Extensive numerical simulations are presented to support and extend our analysis, exploring parameter heterogeneities and noise, transient dynamics, and immunization processes. Our results constitute a first, necessary step toward a theory of ADNs that accounts for memory effects in the network evolution

Activity‑driven network modeling and control of the spread of two concurrent epidemic strains

The emergency generated by the current COVID-19 pandemic has claimed millions of lives worldwide. There have been multiple waves across the globe that emerged as a result of new variants, due to arising from unavoidable mutations. The existing network toolbox to study epidemic spreading cannot be readily adapted to the study of multiple, coexisting strains. In this context, particularly lacking are models that could elucidate re-infection with the same strain or a different strain—phenomena that we are seeing experiencing more and more with COVID-19. Here, we establish a novel mathematical model to study the simultaneous spreading of two strains over a class of temporal networks. We build on the classical susceptible–exposed–infectious–removed model, by incorporating additional states that account for infections and re-infections with multiple strains. The temporal network is based on the activity-driven network paradigm, which has emerged as a model of choice to study dynamic processes that unfold at a time scale comparable to the network evolution. We draw analytical insight from the dynamics of the stochastic network systems through a mean-field approach, which allows for characterizing the onset of different behavioral phenotypes (non-epidemic, epidemic, and endemic). To demonstrate the practical use of the model, we examine an intermittent stay-at-home containment strategy, in which a fraction of the population is randomly required to isolate for a fixed period of time