Threshold In Scale-free Networks Research Articles

Traffic dynamics considering packet loss in finite buffer networks**Project supported by the National Key Research and Development Program of China (Grant No. 2016YFC0802508), the National Natural Science Foundation of China (Grant Nos. 11672289 and 61503355), and the support from the Chinese Scholarship Council.

In real complex systems, the limited storage capacity of physical devices often results in the loss of data. We study the effect of buffer size on packet loss threshold in scale-free networks. A new order parameter is proposed to characterize the packet loss threshold. Our results show that the packet loss threshold can be optimized with a relative small buffer size. Meanwhile, a large buffer size will increase the travel time. Furthermore, we propose a Buffered-Shortest-Path-First (BSPF) queuing strategy. Compared to the traditional First-In-First-Out (FIFO) strategy, BSPF can not only increase the packet loss threshold but can also significantly decrease the travel length and travel time in both identical and heterogeneous node capacity cases. Our study will help to improve the traffic performance in finite buffer networks.

Collective versus hub activation of epidemic phases on networks

We consider a general criterion to discern the nature of the threshold in epidemic models on scale-free (SF) networks. Comparing the epidemic lifespan of the nodes with largest degrees with the infection time between them, we propose a general dual scenario, in which the epidemic transition is either ruled by a hub activation process, leading to a null threshold in the thermodynamic limit, or given by a collective activation process, corresponding to a standard phase transition with a finite threshold. We validate the proposed criterion applying it to different epidemic models, with waning immunity or heterogeneous infection rates in both synthetic and real SF networks. In particular, a waning immunity, irrespective of its strength, leads to collective activation with finite threshold in scale-free networks with large degree exponent, at odds with canonical theoretical approaches.

Note on ‘Influences of Resource Limitations and Transmission Costs on Epidemic Simulations and Critical Thresholds in Scale-Free Networks’

In a recent paper entitled ‘Influences of Resource Limitations and Transmission Costs on Epidemic Simulations and Critical Thresholds in Scale-Free Networks’ by Huang et al., the authors attempted to establish a key characteristic of epidemic dynamics in a scale-free network when properly accounting for the cost of transmitting the infection at each node and the resources available for transmission to that node. The main input parameter is the effective rate of spreading the infection, i.e. the instantaneous rate at which the infection is spread to an uninfected node via a single link to an infected node. The primary result is the existence of a positive critical threshold for the infection-spreading rate at or below which the epidemic dies out and above which the epidemic is spread through the network and ultimately reaches a steady-state non-vanishing condition. Some flaws in the authors’ proof of this result are discussed, and an alternative derivation is provided that sheds additional light on the transient and steady-state behavior of the system. The alternative derivation may be adapted to the analysis of other scale-free networks with different features.

Response to Wilson’s note on ‘Influences of resource limitations and transmission costs on epidemic simulations and critical thresholds in scale-free networks’

James R. Wilson points out what he describes as flaws in our proof in ‘Influences of Resource Limitations and Transmission Costs on Epidemic Simulations and Critical Thresholds in Scale-free Networks’ (Simulation 85(3): 205—219) and offers an alternative steady-state behavior derivation based on our epidemic simulation model. In this response we will explain our definitions for the terms used in our paper and the derivation process for our analysis, then compare and contrast our mathematical model with that proposed by Wilson. We suggest that more compartmental models can be used to support our argument that increasing transmission costs or decreasing individual resources increases the critical threshold of a contagion event in a scale-free network.

Traffic-driven epidemic spreading in finite-size scale-free networks

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 for the understanding of spreading processes on complex networks.

Different thresholds of bond percolation in scale-free networks with identical degree sequence

Generally, the threshold of percolation in complex networks depends on the underlying structural characterization. However, what topological property plays a predominant role is still unknown, despite the speculation of some authors that degree distribution is a key ingredient. The purpose of this paper is to show that power-law degree distribution itself is not sufficient to characterize the threshold of bond percolation in scale-free networks. To achieve this goal, we first propose a family of scale-free networks with the same degree sequence and obtain by analytical or numerical means several topological features of the networks. Then, by making use of the renormalization-group technique we determine the threshold of bond percolation in our networks. We find an existence of nonzero thresholds and demonstrate that these thresholds can be quite different, which implies that power-law degree distribution does not suffice to characterize the percolation threshold in scale-free networks.

Influences of Resource Limitations and Transmission Costs on Epidemic Simulations and Critical Thresholds in Scale-Free Networks

Critical thresholds represent one of the most important diffusion indicators of epidemic outbreaks. However, we believe that recent studies have overemphasized ways that the power-law connectivity distribution features of social networks affect epidemic dynamics and critical thresholds. As a result, two important factors have been overlooked: resource limitations and transmission costs associated with social interactions and daily contact. Here we present our results from the simultaneous application of mean-field theory and an agent-based network simulation approach for analyzing the effects of resources and costs on epidemic dynamics and critical thresholds. Our main findings are: (a) a significant critical threshold does exist when resources and costs are taken into consideration, and it has a lower bound whenever contagion events occur in scale-free networks; (b) when transmission costs increase or individual resources decrease, critical contagion thresholds in scale-free networks grow linearly and steady density curves shrink linearly; (c) regardless of whether the resources of individuals obey delta, uniform, or normal distributions, they have the same critical thresholds and epidemic dynamics as long as the average value of usable resources remains the same across different scale-free networks; and (d) the spread of epidemics in scale-free networks remains controllable as long as resources are properly restricted and intervention strategy investments are significantly increased.

Influences of Resource Limitations and Transmission Costs on Epidemic Simulations and Critical Thresholds in Scale-Free Networks

Critical thresholds represent one of the most important diffusion indicators of epidemic outbreaks. However, we believe that recent studies have overemphasized ways that the power-law connectivity distribution features of social networks affect epidemic dynamics and critical thresholds. As a result, two important factors have been overlooked: resource limitations and transmission costs associated with social interactions and daily contact. Here we present our results from the simultaneous application of mean-field theory and an agent-based network simulation approach for analyzing the effects of resources and costs on epidemic dynamics and critical thresholds. Our main findings are: (a) a significant critical threshold does exist when resources and costs are taken into consideration, and it has a lower bound whenever contagion events occur in scale-free networks; (b) when transmission costs increase or individual resources decrease, critical contagion thresholds in scale-free networks grow linearly and steady density curves shrink linearly; (c) regardless of whether the resources of individuals obey delta, uniform, or normal distributions, they have the same critical thresholds and epidemic dynamics as long as the average value of usable resources remains the same across different scale-free networks; and (d) the spread of epidemics in scale-free networks remains controllable as long as resources are properly restricted and intervention strategy investments are significantly increased.

Modelling disease spread and control in networks: implications for plant sciences

Networks are ubiquitous in natural, technological and social systems. They are of increasing relevance for improved understanding and control of infectious diseases of plants, animals and humans, given the interconnectedness of today's world. Recent modelling work on disease development in complex networks shows: the relative rapidity of pathogen spread in scale-free compared with random networks, unless there is high local clustering; the theoretical absence of an epidemic threshold in scale-free networks of infinite size, which implies that diseases with low infection rates can spread in them, but the emergence of a threshold when realistic features are added to networks (e.g. finite size, household structure or deactivation of links); and the influence on epidemic dynamics of asymmetrical interactions. Models suggest that control of pathogens spreading in scale-free networks should focus on highly connected individuals rather than on mass random immunization. A growing number of empirical applications of network theory in human medicine and animal disease ecology confirm the potential of the approach, and suggest that network thinking could also benefit plant epidemiology and forest pathology, particularly in human-modified pathosystems linked by commercial transport of plant and disease propagules. Potential consequences for the study and management of plant and tree diseases are discussed.

Absence of epidemic threshold in scale-free networks with degree correlations.

Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide for the susceptible-infected-susceptible model an exact result showing that a scale-free degree distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or disassortative mixing. Degree correlations result therefore irrelevant for the epidemic spreading picture in these scale-free networks. The present result is related to the divergence of the average nearest neighbor's degree, enforced by the degree detailed balance condition.