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Register a new userEstimating the outcome of spreading processes on networks with incomplete information: a mesoscale approach
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Recent advances in data collection have facilitated the access to time-resolved human proximity data that can conveniently be represented as temporal networks of contacts between individuals. While this type of data is fundamental to investigate how information or diseases propagate in a population, it often suffers from incompleteness, which possibly leads to biased conclusions. A major challenge is thus to estimate the outcome of spreading processes occurring on temporal networks built from partial information. To cope with this problem, we devise an approach based on Non-negative Tensor Factorization (NTF) -- a dimensionality reduction technique from multi-linear algebra. The key idea is to learn a low-dimensional representation of the temporal network built from partial information, to adapt it to take into account temporal and structural heterogeneity properties known to be crucial for spreading processes occurring on networks, and to construct in this way a surrogate network similar to the complete original network. To test our method, we consider several human-proximity networks, on which we simulate a loss of data. Using our approach on the resulting partial networks, we build a surrogate version of the complete network for each. We then compare the outcome of a spreading process on the complete networks (non altered by a loss of data) and on the surrogate networks. We observe that the epidemic sizes obtained using the surrogate networks are in good agreement with those measured on the complete networks. Finally, we propose an extension of our framework when additional data sources are available to cope with the missing data problem.
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There is currently growing interest in modeling the information diffusion on social networks across multi-disciplines. The majority of the corresponding research has focused on information diffusion independently, ignoring the network evolution in the diffusion process. Therefore, it is more reasonable to describe the real diffusion systems by the co-evolution between network topologies and information states. In this work, we propose a mechanism considering the coevolution between information states and network topology simultaneously, in which the information diffusion was executed as an SIS process and network topology evolved based on the adaptive assumption. The theoretical analyses based on the Markov approach were very consistent with simulation. Both simulation results and theoretical analyses indicated that the adaptive process, in which informed individuals would rewire the links between the informed neighbors to a random non-neighbor node, can enhance information diffusion (leading to much broader spreading). In addition, we obtained that two threshold values exist for the information diffusion on adaptive networks, i.e., if the information propagation probability is less than the first threshold, information cannot diffuse and dies out immediately; if the propagation probability is between the first and second threshold, information will spread to a finite range and die out gradually; and if the propagation probability is larger than the second threshold, information will diffuse to a certain size of population in the network. These results may shed some light on understanding the co-evolution between information diffusion and network topology.
Although there is always an interplay between the dynamics of information diffusion and disease spreading, the empirical research on the systemic coevolution mechanisms connecting these two spreading dynamics is still lacking. Here we investigate the coevolution mechanisms and dynamics between information and disease spreading by utilizing real data and a proposed spreading model on multiplex network. Our empirical analysis finds asymmetrical interactions between the information and disease spreading dynamics. Our results obtained from both the theoretical framework and extensive stochastic numerical simulations suggest that an information outbreak can be triggered in a communication network by its own spreading dynamics or by a disease outbreak on a contact network, but that the disease threshold is not affected by information spreading. Our key finding is that there is an optimal information transmission rate that markedly suppresses the disease spreading. We find that the time evolution of the dynamics in the proposed model qualitatively agrees with the real-world spreading processes at the optimal information transmission rate.
We develop a generalized group-based epidemic model (GgroupEM) framework for any compartmental epidemic model (for example; susceptible-infected-susceptible, susceptible-infected-recovered, susceptible-exposed-infected-recovered). Here, a group consists of a collection of individual nodes. This model can be used to understand the important dynamic characteristics of a stochastic epidemic spreading over very large complex networks, being informative about the state of groups. Aggregating nodes by groups, the state space becomes smaller than the individual-based approach at the cost of aggregation error, which is strongly bounded by the isoperimetric inequality. We also develop a mean-field approximation of this framework to further reduce the state-space size. Finally, we extend the GgroupEM to multilayer networks. Since the group-based framework is computationally less expensive and faster than an individual-based framework, then this framework is useful when the simulation time is important.
This paper mainly discusses the diffusion on complex networks with time-varying couplings. We propose a model to describe the adaptive diffusion process of local topological and dynamical information, and find that the Barabasi-Albert scale-free network (BA network) is beneficial to the diffusion and leads nodes to arrive at a larger state value than other networks do. The ability of diffusion for a node is related to its own degree. Specifically, nodes with smaller degrees are more likely to change their states and reach larger values, while those with larger degrees tend to stick to their original states. We introduce state entropy to analyze the thermodynamic mechanism of the diffusion process, and interestingly find that this kind of diffusion process is a minimization process of state entropy. We use the inequality constrained optimization method to reveal the restriction function of the minimization and find that it has the same form as the Gibbs free energy. The thermodynamical concept allows us to understand dynamical processes on complex networks from a brand-new perspective. The result provides a convenient means of optimizing relevant dynamical processes on practical circuits as well as related complex systems.
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.
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