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Register a new userGeneralized individual-based epidemic model for vulnerability assessment of correlated scale-free complex networks
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Many complex networks exhibit vulnerability to spreading of epidemics, and such vulnerability relates to the viral strain as well as to the network characteristics. For instance, the structure of the network plays an important role in spreading of epidemics. Additionally, properties of previous epidemic models require prior knowledge of the complex network structure, which means the models are limited to only well-known network structures. In this paper, we propose a new epidemiological SIR model based on the continuous time Markov chain, which is generalized to any type of network. The new model is capable of evaluating the states of every individual in the network. Through mathematical analysis, we prove an epidemic threshold exists below which an epidemic does not propagate in the network. We also show that the new epidemic threshold is inversely proportional to the spectral radius of the network. In particular, we employ the new epidemic model as a novel measure to assess the vulnerability of networks to the spread of epidemics. The new measure considers all possible effective infection rates that an epidemic might possess. Next, we apply the measure to correlated networks to evaluate the vulnerability of disassortative and assortative scalefree networks. Ultimately, we verify the accuracy of the theoretical epidemic threshold through extensive numerical simulations. Within the set of tested networks, the numerical results show that disassortative scale-free networks are more vulnerable to spreading of epidemics than assortative scale-free networks.
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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.
The study of complex networks sheds light on the relation between the structure and function of complex systems. One remarkable result is the absence of an epidemic threshold in infinite-size scale-free networks, which implies that any infection will perpetually propagate regardless of the spreading rate. The vast majority of current theoretical approaches assumes that infections are transmitted as a reaction process from nodes to all neighbors. Here we adopt a different perspective and show that the epidemic incidence is shaped by traffic flow conditions. Specifically, we consider the scenario in which epidemic pathways are defined and driven by flows. Through extensive numerical simulations and theoretical predictions, it is shown that the value of the epidemic threshold in scale-free networks depends directly on flow conditions, in particular on the first and second moments of the betweenness distribution given a routing protocol. We consider the scenarios in which the delivery capability of the nodes is bounded or unbounded. In both cases, the threshold values depend on the traffic and decrease as flow increases. Bounded delivery provokes the emergence of congestion, slowing down the spreading of the disease and setting a limit for the epidemic incidence. Our results provide a general conceptual framework to understand spreading processes on complex networks.
The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular methods employed in network embedding either rely on implicit approximations of the principle of proximity preservation or implement it by enforcing the geometry of the embedding space, thus hindering geometric properties that networks may spontaneously exhibit. Here, we take advantage of a model-free embedding method explicitly devised for preserving pairwise proximity, and characterize the geometry emerging from the mapping of several networks, both real and synthetic. We show that the learned embedding has simple and intuitive interpretations: the distance of a node from the geometric center is representative for its closeness centrality, and the relative positions of nodes reflect the community structure of the network. Proximity can be preserved in relatively low-dimensional embedding spaces, and the hidden geometry displays optimal performance in guiding greedy navigation regardless of the specific network topology. We finally show that the mapping provides a natural description of contagion processes on networks, with complex spatiotemporal patterns represented by waves propagating from the geometric center to the periphery. The findings deepen our understanding of the model-free hidden geometry of complex networks.
In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.
We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal network with tunable degree correlation, we identify a discontinuous transition that is independent of the degree correlation strength unless the synergy is absent or extremely weak. Regardless of synergy (absent or present), a positive and negative degree correlation in the model reduces and raises the epidemic threshold, respectively. For networks with a strongly positive degree correlation, the mean-field treatment predicts the emergence of two discontinuous jumps in the steady-state infected density. To test the mean-field treatment, we provide approximate master equations of the present model, which accurately describe the synergistic SIS dynamics. We quantitatively confirm all qualitative predictions of the mean-field treatment in numerical evaluations of the approximate master equations.
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