Rumour Spreading



Most of real-world temporal networks are generated by non-Markovian processes, i.e. by processes that include memory effects. We analyzed a real world dataset of mobile phone calls and provided a simple empirical characterization of the effects of memory in its microscopic dynamical evolution. Considering the empirical evidences, we defined a novel generative model for time-varying networks with memory. The model mirrors many of the structural properties observed in the real network, like degree and weight heterogeneities, and shows the spontaneous emergence of non-trivial connectivity patterns characterized by strong and weak ties. We characterize the effects of non- Markovian and heterogeneous connectivity patterns on rumor spreading processes. Interestingly, we find that strong ties are responsible for constraining the rumor diffusion within localized groups of individuals. This evidence points out that strong ties may have an active role in weakening the spreading of information by constraining the dynamical process in clumps of strongly connected social groups.

The non-Markovian properties of real-world temporal networks have also been investigated. In particular, we have discussed which properties of a temporal network can lead to the slow-down or speed-up of propagation processes, and related these effects to the spectral properties of the network. We have indeed used a novel causality-preserving time-aggregated representation to analyze temporal networks from the perspective of spectral graph theory and provide one of the first analytical explanations for the frequently observed slow-down of information diffusion in empirical non-Markovian temporal networks. Using our approach we derived an analytical prediction for the magnitude of this slow-down and we validated our prediction against empirical data sets. Counter-intuitively, we further showed that non-Markovian properties could result in a speed-up of information diffusion that can be related to the spectral properties of the underlying temporal network.

Overall, the presented results underline the subtleties inherent to the analysis of dynamical processes in exogenous time-varying networks. No one-fits-all picture exists, and a classification of dynamical process behaviour calls for a thorough analysis of each particular processes and networks considered. 

Time Varying Networks and the weakness of strong ties

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

Competing Diseases

The competition between dynamical processes is an extremely relevant issue in the field of complex networks, in particular for the applications to epidemiology. Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place on a single level. In particular, interdependent contagion phenomena can be addressed only if we go beyond the scheme-one pathogen- one network. In [Sanz2014], we have proposed a framework that allows us to describe the spreading dynamics of two concurrent diseases. Specifically, we have characterized analytically the epidemic thresholds of the two diseases for different scenarios and compute the temporal evolution characterizing the unfolding dynamics. Results show that there are regions of the parameter space in which the onset of a disease’s outbreak is conditioned to the prevalence levels of the other disease. Moreover, we have shown, for the susceptible-infected-susceptible scheme, that under certain circumstances, finite and not vanishing epidemic thresholds are found even at the limit for scale-free networks. For the susceptible-infected-removed scenario, the phenomenology is richer and additional interdependencies show up. We have also found that the secondary thresholds for the susceptible-infected-susceptible and susceptible-infected-removed models are different, which results directly from the interaction between both diseases. Our modeling approach presents different advantages with respect to previous models, as it simultaneously allows analytical derivations of the epidemic thresholds and an approximate description of the temporal evolution of the system, in addition to providing a way to isolate the effects on spreading dynamics of each possible interaction mechanism, such as variations of infectivity, susceptibility, or infectious periods. In addition, it enables us to solve the two paradigmatic modeling scenarios (SIS and SIR), identifying relevant differences between the two cases that arise as a consequence of disease interactions. 

Dynamics of interacting diseases

How memory generates heterogeneous dynamics in temporal networks

Memory Effects for agents on Multilayer Networks  

We first proposed a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our construction uses random walks of variable length to produce time-extended structures with adjustable features. Our procedure enables one to obtain plausible and realistic instances of temporal networks when only the aggregated structure is known. Hence, it can be employed to compensate for the lack of time-resolved data or to provide alternative scenarios when access to empirical information is limited. Moreover, that the synthetic network has tunable properties is essential to assessing the influence of time- dependent features on the dynamical processes on networks, especially when only aggregated information is available. Finally, structural flexibility also makes it possible to test the relevance of various definitions of centrality measures for nodes and links in temporal networks.

We have defined a series of models of interacting agents, with tunable interaction rules. In particular, various interaction ingredients are based on memory effects empirically observed in human contact data, similar to rich-get-richer effects. While several memory effects are present at the same time in the data, the modeling framework allows us to analyze separately their individual roles in determining the complex phenomenology arising in the data, concerning in particular the heterogeneous distributions of contact durations and numbers and of inter-contact durations. We have hence disentangled the role of these mechanisms, shown which empirical characteristics emerge from each, and shown that the inclusion of all memory effects is necessary to recover an overall phenomenology fully resembling the one of the empirical data.

We have defined new network models to capture the non-Markovian nature of real-world datasets such as the interactions of mobile phone calls. In particular, in [Karsai2014] we have measured from a real-world dataset of mobile phone calls the activity of the agents that form the network and used such information to build a synthetic model that mimics the properties of real temporal networks. Such results provide a significant advance with respect to traditional modeling approaches, due to the inclusion of a number of realistic features in the modeling of temporal networks. 

Intervention Strategies


e considered the scenario of an epidemic in a school and tested the effect of different reactive interventions among the students. More specifically, we have simulated the dynamics of epidemic spread among school children by using an SEIR model on top of a high-resolution time-resolved contact network measured in a real primary school. The model included asymptomatic individuals and a generic risk of infection due to random contacts with the community when children are not at school. Using this model we have studied the targeted strategies for class and grade closure both in terms of their ability to mitigate the epidemic and in terms of their impact on the schooling system (and therefore indirectly on the whole community), measured by the number of cancelled days of class. Targeted strategies are implemented as reactive contact removals, i.e. the contact network of the students is modified according to certain rules that depend on the infectivity profile of each individual. We found that All targeted strategies lead to an important reduction in the probability of an outbreak reaching a large fraction of the school population. In the case of large outbreaks, targeted strategies significantly reduce the median number of individuals affected by the epidemic. The reduction is stronger if the strategies are triggered by a smaller number of symptomatic cases, and if longer closures durations are used. While the closure of one class yields a smaller mitigation effect than the closure of the whole school, the closure of the corresponding grade (two classes) leads to a reduction of large outbreak probability and a reduction of epidemic size that are similar to those obtained by closing the entire school. Remarkably, the reactive character of all strategies we studied, which are triggered by the detection of symptomatic individuals, limits the impact on the schooling system with respect to a closure of schools scheduled in a top-down fashion by public health authorities: the latter would be enforced even for schools that are free of infectious individuals. Second, targeted grade closure has in all cases a much lighter burden, in terms of lost class days, than whole-school closure. Given also its good performance in the mitigation of outbreaks, it thus represents an interesting alternative strategy to traditional approaches that are based on a simplified description of the epidemic process. 


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