Epidemic Spreading and Aging in Temporal Networks with Memory

Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this paper we analyze the combined effect of these two ingredients on epidemic dynamics on networks. We study the susceptible-infected-susceptible (SIS) and the susceptible-infected-removed (SIR) models on the recently introduced activity-driven networks with memory. By means of an activity-based mean-field approach we derive, in the long time limit, analytical predictions for the epidemic threshold as a function of the parameters describing the distribution of activities and the strength of the memory effects. Our results show that memory reduces the threshold, which is the same for SIS and SIR dynamics, therefore favouring epidemic spreading. The theoretical approach perfectly agrees with numerical simulations in the long time asymptotic regime. Strong aging effects are present in the preasymptotic regime and the epidemic threshold is deeply affected by the starting time of the epidemics. We discuss in detail the origin of the model-dependent preasymptotic corrections, whose understanding could potentially allow for epidemic control on correlated temporal networks.Comment: 10 pages, 8 fogure

Relevance of backtracking paths in recurrent-state epidemic spreading on networks

The understanding of epidemics on networks has greatly benefited from the recent application of message-passing approaches, which allow us to derive exact results for irreversible spreading (i.e., diseases with permanent acquired immunity) in locally treelike topologies. This success has suggested the application of the same approach to recurrent-state epidemics, for which an individual can contract the epidemic and recover repeatedly. The underlying assumption is that backtracking paths (i.e., an individual is reinfected by a neighbor he or she previously infected) do not play a relevant role. In this paper we show that this is not the case for recurrent-state epidemics since the neglect of backtracking paths leads to a formula for the epidemic threshold that is qualitatively incorrect in the large size limit. Moreover, we define a modified recurrent-state dynamics which explicitly forbids direct backtracking events and show that this modification completely upsets the phenomenology.Postprint (published version

Theories for influencer identification in complex networks

In social and biological systems, the structural heterogeneity of interaction networks gives rise to the emergence of a small set of influential nodes, or influencers, in a series of dynamical processes. Although much smaller than the entire network, these influencers were observed to be able to shape the collective dynamics of large populations in different contexts. As such, the successful identification of influencers should have profound implications in various real-world spreading dynamics such as viral marketing, epidemic outbreaks and cascading failure. In this chapter, we first summarize the centrality-based approach in finding single influencers in complex networks, and then discuss the more complicated problem of locating multiple influencers from a collective point of view. Progress rooted in collective influence theory, belief-propagation and computer science will be presented. Finally, we present some applications of influencer identification in diverse real-world systems, including online social platforms, scientific publication, brain networks and socioeconomic systems.Comment: 24 pages, 6 figure

Fundamentals of spreading processes in single and multilayer complex networks

Spreading processes have been largely studied in the literature, both analytically and by means of large-scale numerical simulations. These processes mainly include the propagation of diseases, rumors and information on top of a given population. In the last two decades, with the advent of modern network science, we have witnessed significant advances in this field of research. Here we review the main theoretical and numerical methods developed for the study of spreading processes on complex networked systems. Specifically, we formally define epidemic processes on single and multilayer networks and discuss in detail the main methods used to perform numerical simulations. Throughout the review, we classify spreading processes (disease and rumor models) into two classes according to the nature of time: (i) continuous-time and (ii) cellular automata approach, where the second one can be further divided into synchronous and asynchronous updating schemes. Our revision includes the heterogeneous mean-field, the quenched-mean field, and the pair quenched mean field approaches, as well as their respective simulation techniques, emphasizing similarities and differences among the different techniques. The content presented here offers a whole suite of methods to study epidemic-like processes in complex networks, both for researchers without previous experience in the subject and for experts.Comment: Review article. 73 pages, including 24 figure

Statistics of Epidemics in Networks by Passing Messages

Epidemic processes are common out-of-equilibrium phenomena of broad interdisciplinary interest. In this thesis, we show how message-passing approach can be a helpful tool for simulating epidemic models in disordered medium like networks, and in particular for estimating the probability that a given node will become infectious at a particular time. The sort of dynamics we consider are stochastic, where randomness can arise from the stochastic events or from the randomness of network structures. As in belief propagation, variables or messages in message-passing approach are defined on the directed edges of a network. However, unlike belief propagation, where the posterior distributions are updated according to Bayes\u27 rule, in message-passing approach we write differential equations for the messages over time. It takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source, and thus avoids echo chamber effects where a pair of adjacent nodes each amplify the probability that the other is infectious. In our first results, we develop a message-passing approach to threshold models of behavior popular in sociology. These are models, first proposed by Granovetter, where individuals have to hear about a trend or behavior from some number of neighbors before adopting it themselves. In thermodynamic limit of large random networks, we provide an exact analytic scheme while calculating the time dependence of the probabilities and thus learning about the whole dynamics of bootstrap percolation, which is a simple model known in statistical physics for exhibiting discontinuous phase transition. As an application, we apply a similar model to financial networks, studying when bankruptcies spread due to the sudden devaluation of shared assets in overlapping portfolios. We predict that although diversification may be good for individual institutions, it can create dangerous systemic effects, and as a result financial contagion gets worse with too much diversification. We also predict that financial system exhibits robust yet fragile behavior, with regions of the parameter space where contagion is rare but catastrophic whenever it occurs. In further results, we develop a message-passing approach to recurrent state epidemics like susceptible-infectious-susceptible and susceptible-infectious-recovered-susceptible where nodes can return to previously inhabited states and multiple waves of infection can pass through the population. Given that message-passing has been applied exclusively to models with one-way state changes like susceptible-infectious and susceptible-infectious-recovered, we develop message-passing for recurrent epidemics based on a new class of differential equations and demonstrate that our approach is simple and efficiently approximates results obtained from Monte Carlo simulation, and that the accuracy of message-passing is often superior to the pair approximation (which also takes second-order correlations into account)

Assessing node risk and vulnerability in epidemics on networks

Which nodes are most vulnerable to an epidemic spreading through a network, and which carry the highest risk of causing a major outbreak if they are the source of the infection? Here we show how these questions can be answered to good approximation using the cavity method. Several curious properties of node vulnerability and risk are explored: some nodes are more vulnerable than others to weaker infections, yet less vulnerable to stronger ones; a node is always more likely to be caught in an outbreak than it is to start one, except when the disease has a deterministic lifetime; the rank order of node risk depends on the details of the distribution of infectious periods.Comment: Note that Figure 2 does not appear in the final published versio