The effect of network mixing patterns on epidemic dynamics and the efficacy of disease contact tracing

In networks, nodes may preferentially contact other nodes with similar (assortatively mixed) or dissimilar (disassortatively mixed) numbers of contacts. Different patterns of contact support different epidemic dynamics, potentially affecting the efficacy of control measures such as contact tracing, which aims to identify and isolate nodes with infectious contacts. We used stochastic simulations to investigate the effects of mixing patterns on epidemic dynamics and contact-tracing efficacy. For uncontrolled epidemics, outbreaks occur at lower infection rates for more assortatively mixed networks, with faster initial epidemic growth rate and shorter epidemic duration than for disassortatively mixed networks. Contact tracing performs better for assortative mixing where epidemic size is large and tracing rate low, but it performs better for disassortative mixing at higher contact rates. For assortatively mixed networks, disease spreads first to highly connected nodes, but this is balanced by contact tracing quickly identifying these same nodes. The converse is true for disassortative mixing, where both disease and tracing are less likely to target highly connected nodes. For small epidemics, contact tracing is more effective on disassortative networks due to the greater resilience of assortative networks to link removal. Multi-step contact tracing is more effective than single-step tracing for assortative mixing, but this effect is smaller for disassortatively mixed networks.     

Recent network evolution increases the potential for large epidemics in the British cattle population.

Following the foot and mouth disease epidemic in Great Britain (GB) in 2001, livestock movement bans were replaced with mandatory periods of standstill for livestock moving between premises. It was anticipated that these movement restrictions would limit each individual's contact networks, the extent of livestock movements and thus the spread of future disease outbreaks. However, the effect of behaviour changes on the global network in adapting to these restrictions is currently unknown. Here, we take a novel approach using GB cattle movement data to construct week-by-week contact networks between animal holdings (AH) to explore the evolution of the network since this policy was introduced, the first time network theory has been used for this purpose. We show that the number of AH moving cattle as part of the giant strong component (GSC), representing the region of maximal connectivity, has been increasing linearly over time. This is of epidemiological significance as the size of the GSC indicates the number of holdings potentially exposed to disease, thus giving a lower bound of maximum epidemic size. Therefore, despite restriction of cattle movements, emergent behaviour in this self-organizing system has potentially increased the size of infectious disease epidemics within the cattle industry.     

Infectious disease control using contact tracing in random and scale-free networks.

Contact tracing aims to identify and isolate individuals that have been in contact with infectious individuals. The efficacy of contact tracing and the hierarchy of traced nodes-nodes with higher degree traced first-is investigated and compared on random and scale-free (SF) networks with the same number of nodes N and average connection K. For values of the transmission rate larger than a threshold, the final epidemic size on SF networks is smaller than that on corresponding random networks. While in random networks new infectious and traced nodes from all classes have similar average degrees, in SF networks the average degree of nodes that are in more advanced stages of the disease is higher at any given time. On SF networks tracing removes possible sources of infection with high average degree. However a higher tracing effort is required to control the epidemic than on corresponding random networks due to the high initial velocity of spread towards the highly connected nodes. An increased latency period fails to significantly improve contact tracing efficacy. Contact tracing has a limited effect if the removal rate of susceptible nodes is relatively high, due to the fast local depletion of susceptible nodes.     

Disease control across urban–rural gradients

Controlling the regional re-emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) after its initial spread in ever-changing personal contact networks and disease landscapes is a challenging task. In a landscape context, contact opportunities within and between populations are changing rapidly as lockdown measures are relaxed and a number of social activities re-activated. Using an individual-based metapopulation model, we explored the efficacy of different control strategies across an urban–rural gradient in Wales, UK. Our model shows that isolation of symptomatic cases or regional lockdowns in response to local outbreaks have limited efficacy unless the overall transmission rate is kept persistently low. Additional isolation of non-symptomatic infected individuals, who may be detected by effective test-and-trace strategies, is pivotal to reducing the overall epidemic size over a wider range of transmission scenarios. We define an ‘urban–rural gradient in epidemic size'' as a correlation between regional epidemic size and connectivity within the region, with more highly connected urban populations experiencing relatively larger outbreaks. For interventions focused on regional lockdowns, the strength of such gradients in epidemic size increased with higher travel frequencies, indicating a reduced efficacy of the control measure in the urban regions under these conditions. When both non-symptomatic and symptomatic individuals are isolated or regional lockdown strategies are enforced, we further found the strongest urban–rural epidemic gradients at high transmission rates. This effect was reversed for strategies targeted at symptomatic individuals only. Our results emphasize the importance of test-and-trace strategies and maintaining low transmission rates for efficiently controlling SARS-CoV-2 spread, both at landscape scale and in urban areas.     

Prophet_TD Routing Algorithm Based on Historical Throughput and Encounter Duration

Opportunistic networks are self-organizing networks that do not require a complete path between the source node and the destination node as it uses encounter opportunities brought by nodes movement to achieve network communication. Opportunistic networks routing algorithms are numerous and can be roughly divided into four categories based on different forwarding strategies. The Prophet routing algorithm is an important routing algorithm in opportunistic networks. It forwards messages based on the encounter probability between nodes, and has good innovation significance and optimization potential. However, the Prophet routing algorithm does not consider the impact of the historical throughput of the node on message transmission, nor does it consider the impact of the encounter duration between nodes on message transmission. Therefore, to improve the transmission efficiency of opportunistic networks, this paper based on the Prophet routing algorithm, fuses the impact of the historical throughput of the node and the encounter duration between nodes on message transmission at the same time, and proposes the Prophet_TD routing algorithm based on the historical throughput and the encounter duration. This paper uses the Opportunistic Networks Environment v1.6.0 (the ONE v1.6.0) as the simulation platform, controls the change of running time and the number of nodes respectively, conducts simulation experiments on the Prophet_TD routing algorithm. The simulation results show that compared to the traditional Prophet routing algorithm, on the whole, the Prophet_TD routing algorithm has a higher message delivery rate and a lower network overhead rate, and its average latency is also lower when node density is large.     

An optimal procedure for solving the hierarchical network design problem

The hierarchical network design problem consists of finding a minimum cost bilevel network that connects all the nodes in a set, created by a loopless main path and a forest. The main path is formed by primary (higher cost) arcs, providing a path between an origin node and a destination node. The forest, built using secondary (lower cost) arcs, connects all the nodes not on the main path, to the path itself. We state and prove some properties of the problem, which allow finding good upper bounds to the solution in polynomial time when the primary costs are proportional to secondary costs. We also propose an O(n⁴) procedure to improve on these bounds. In turn, these bounds are used to significantly reduce the number of nodes and arcs of the problem. Once the problem is reduced, large instances can be solved to optimality. At this stage, we use one of two linear integer optimization formulations. The first and preferred one is based on multicommodity flows, which avoids the formation of subtours. The second formulation avoids subtours by iteratively adding ad hoc constraints. We show some examples and provide computational experiments performed on networks with sizes up to 600 nodes and 14 000 arcs.     

Determination of critical network interactions: an augmented Boolean pseudo-dynamics approach

Network theory has established that highly connected nodes in regulatory networks (hubs) show a strong correlation with criticality in network function. Although topological analysis is fully capable of identifying network hubs, it does not provide an objective method for ranking the importance of a particular node by relating its contribution to the overall network response. Towards this end, the authors have developed an augmented Boolean pseudo-dynamics approach to a priori determine the critical network interactions in biological interaction networks. The approach utilises network topology and dynamic state information to determine the set of active pathways. The active pathways are used in conjunction with the key cellular properties of efficiency and robustness, to rank the network interactions based on their importance in the sustenance of network function. To demonstrate the utility of the approach, the authors consider the well characterised guard cell signalling network in plant cells. An integrated analysis of the network revealed the critical mechanisms resulting in stomata closure in the presence and absence of abscisic acid, in excellent agreement with published results.     

无线传感器网络几类拓扑控制及其抗毁性应用简述

无线传感器网络的拓扑结构随着网络中节点的增加、减少和移动实时变化,为保证网络的连通性和覆盖性不被影响,拓扑控制技术所要解决的问题正是传感器节点如何更好地自组织构建全局网络拓扑．本文首先概述了四类拓扑控制算法的理论基础及算法步骤．然后,对提高网络抗毁性的两类拓扑演化算法进行了详细叙述,即无标度网络生长与构建$k$连通网络,分别构建了基于节点位置偏好的移动网络拓扑模型和基于$k$连通的节点调度优化模型．最后,分别从移动节点的引入、折中控制算法的探索、复杂网络理论的应用和传统算法与智能算法的结合这四方面对拓扑控制算法的前景进行了阐述．     

Social embeddedness in an online weight management programme is linked to greater weight loss

The obesity epidemic is heightening chronic disease risk globally. Online weight management (OWM) communities could potentially promote weight loss among large numbers of people at low cost. Because little is known about the impact of these online communities, we examined the relationship between individual and social network variables, and weight loss in a large, international OWM programme. We studied the online activity and weight change of 22 419 members of an OWM system during a six-month period, focusing especially on the 2033 members with at least one friend within the community. Using Heckman''s sample-selection procedure to account for potential selection bias and data censoring, we found that initial body mass index, adherence to self-monitoring and social networking were significantly correlated with weight loss. Remarkably, greater embeddedness in the network was the variable with the highest statistical significance in our model for weight loss. Average per cent weight loss at six months increased in a graded manner from 4.1% for non-networked members, to 5.2% for those with a few (two to nine) friends, to 6.8% for those connected to the giant component of the network, to 8.3% for those with high social embeddedness. Social networking within an OWM community, and particularly when highly embedded, may offer a potent, scalable way to curb the obesity epidemic and other disorders that could benefit from behavioural changes.     

Network model of knowledge diffusion

This paper introduces a diffusion network model: an individual-citation-based directed network model with a time dimension, as a potentially useful approach to capture the diffusion of research topics. The approach combines social network analysis, network visualization and citation analysis to discuss some of the issues concerning the spread of scientific ideas. The process of knowledge diffusion is traced from a network point of view. Using research on the h-index as a case study, we built detailed networks of individual publications and demonstrated the feasibility of applying the diffusion network model to the spread of a research. The model shows the specific paths and associations of individual papers, and potentially complementing issues raised by epidemic models, which primarily deal with average properties of entire scientific communities. Also, based on the citation-based network, the technique of main path analysis identified the articles that influenced the research for some time and linked them into a research tradition that is the backbone of the h-index field.     

On computing the reliability of opportunistic multihop networks with Mobile relays

Opportunistic multihop networks with mobile relays recently have drawn much attention from researchers across the globe due to their wide applications in various challenging environments. However, because of their peculiar intrinsic features like lack of continuous connectivity, network partitioning, highly dynamic behavior, and long delays, it is very arduous to model and effectively capture the temporal variations of such networks with the help of classical graph models. In this work, we utilize an evolving graph to model the dynamic network and propose a matrix‐based algorithm to generate all minimal path sets between every node pair of such network. We show that these time‐stamped‐minimal‐path sets (TS‐MPS) between each given source‐destination node pair can be used, by utilizing the well‐known Sum‐of‐Disjoint Products technique, to generate various reliability metrics of dynamic networks, ie, two‐terminal reliability of dynamic network and its related metrics, ie, two‐terminal reliabilities of the foremost, shortest, and fastest TS‐MPS, and Expected Hop Count. We also introduce and compute a new network performance metric?Expected Slot Count. We use two illustrative examples of dynamic networks, one of four nodes, and the other of five nodes, to show the salient features of our technique to generate TS‐MPS and reliability metrics.     

Shaping the interdisciplinary knowledge network of China: a network analysis based on citation data from 1981 to 2010

This study builds the interdisciplinary knowledge network of China, which is used to catch the knowledge exchange structure of disciplines, and investigates the evolution process from 1981 to 2010. A network analysis was performed to examine the special structure and we compare state of the networks in different periods to determine how the network has got such properties. The dataset are get from the reference relationship in literature on important Chinese academic journals from 1980 to 2010. The analytical results reveal the hidden network structure of interdisciplinary knowledge flows in China and demonstrate that the network is highly connected and has a homogeneous link structure and heterogeneous weight distribution. Through comparing of the network in three periods, that is 1981–1990, 1991–2000 and 2001–2010, we find that the special evolution process, which is limited by the number of nodes, play an important influence on interdisciplinary knowledge flows.     

Dynamics and processing in finite self-similar networks

A common feature of biological networks is the geometrical property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks show self-similar connectivity at multiple scales. We analyse the relationship between topology and signalling in contrasting classes of such topologies. We find that networks differ in their ability to contain or propagate signals between arbitrary nodes in a network depending on whether they possess branching or loop-like features. Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise. Surprisingly, small-world topologies, with diameters logarithmic in system size, have slower dynamical time scales, and may be less integrated (more modular) than networks with longer path lengths. All of these phenomena are essentially mesoscopic, vanishing in the infinite limit but producing strong effects at sizes and time scales relevant to biology.     

Small Worlds in Networks of Inventors and the Role of Academics: An Analysis of France

Using data on patent applications at the European Patent Office, we examine the structural properties of networks of inventors in France in different technologies. We find that the higher the presence of inventors from universities and public research organizations (PROs), the more likely the networks are to exhibit small world properties. University and PRO inventors contribute to reduce average path length insofar they are more mobile (across applicants) than other inventors, thus linking up otherwise disconnected cliques. We achieve these results by implementing an original methodology for detecting small world properties in one-mode projections of two-mode graphs.     

Garfield number: on some characteristics of Eugene Garfield’s first and second order co-authorship networks

In this note we give an overview of the first- and second-order collaboration network reflected by Eugene Garfield’s publications in scientific journals. Although he had only a quite limited number of co-authors and co-publications, his co-authors’ own collaboration networks generate a large world-wide and multidisciplinary coverage. The classical model of co-authorship network is the Erd?s network with the Erd?s Number indicating the shortest co-authorship path through which an author is connected with Paul Erd?s. The two networks, generated by Erd?s and Garfield, respectively, show completely different patterns and characteristics but illustrate the ways how ideas of great scholars and pioneers disseminate and influence the respective scientific communities.     

Patent collaboration networks in Sweden and Spain during the Second Industrial Revolution

ABSTRACT

This article aims to analyse and compare the patent collaboration networks of Spain and Sweden during the Second Industrial Revolution, a key period for technological and industrial development in several economies and the distinct development paths taken by these two countries. The data used are from two new historical patent datasets for Spain and Sweden for the period 1878–1914. To study the structure of collaboration networks in both countries, we applied social network analysis methods and focused on two specific key network properties: connectivity and openness to external nodes. The results demonstrate that collaboration networks were better connected and more open to foreign influence in Sweden than in Spain. This research opens new paths for further multidisciplinary studies both on the evolution of industrial economies and on innovation networks dynamics.     

Preventable H5N1 avian influenza epidemics in the British poultry industry network exhibit characteristic scales

Epidemics are frequently simulated on redundantly wired contact networks, which have many more links between sites than are minimally required to connect all. Consequently, the modelled pathogen can travel numerous alternative routes, complicating effective containment strategies. These networks have moreover been found to exhibit ‘scale-free’ properties and percolation, suggesting resilience to damage. However, realistic H5N1 avian influenza transmission probabilities and containment strategies, here modelled on the British poultry industry network, show that infection dynamics can additionally express characteristic scales. These system-preferred scales constitute small areas within an observed power law distribution that exhibit a lesser slope than the power law itself, indicating a slightly increased relative likelihood. These characteristic scales are here produced by a network-pervading intranet of so-called hotspot sites that propagate large epidemics below the percolation threshold. This intranet is, however, extremely vulnerable; targeted inoculation of a mere 3–6% (depending on incorporated biosecurity measures) of the British poultry industry network prevents large and moderate H5N1 outbreaks completely, offering an order of magnitude improvement over previously advocated strategies affecting the most highly connected ‘hub’ sites. In other words, hotspots and hubs are separate functional entities that do not necessarily coincide, and hotspots can make more effective inoculation targets. Given the ubiquity and relevance of networks (epidemics, Internet, power grids, protein interaction), recognition of this spreading regime elsewhere would suggest a similar disproportionate sensitivity to such surgical interventions.     

Dual networks and self-checking dividers

Methods of establishing dual network pairs and self-checking dividers from a string of 12 nominally equal resistors permanently connected in series using short-circuiting links between nodes are described. Dual networks that can be generated from a string of 11 nominally equal resistors, permanently connected in series with Hamon star junctions by joining one or more nodes together with one or more zero-resistance links, are established. These networks are then coupled together to form all possible three-terminal self-checking divider networks attainable using a total number of resistors from 2 to 12. There are 58269 physically different dual pairs using 11 resistors, comprising 3733 numerically different ratios. Correspondingly there are 79053 self-checking dividers with 4367 numerically different ratios     

Hierarchically assembled titania-cyclodextrin nano-networks

Hierarchically structured TiO₂ β-cyclodextrin nano-networks are created by a simple, eco-friendly self-assembly process. Electron microscopy shows the resulting nano-networks are composed of TiO₂ nanoparticle β-cyclodextrin complexes assembled into 1 μm diameter nanofibers with lengths more than 1 mm. The individual nanofibers are further interconnected into a highly porous, 3D macro-scale network. This assembly process is notable because it creates large 3D networks directly from nanoparticle self-assembly and offers the opportunity to separately optimize both nanoparticle properties and the structure of the resulting composite materials.     

Optimizing surveillance for livestock disease spreading through animal movements

The spatial propagation of many livestock infectious diseases critically depends on the animal movements among premises; so the knowledge of movement data may help us to detect, manage and control an outbreak. The identification of robust spreading features of the system is however hampered by the temporal dimension characterizing population interactions through movements. Traditional centrality measures do not provide relevant information as results strongly fluctuate in time and outbreak properties heavily depend on geotemporal initial conditions. By focusing on the case study of cattle displacements in Italy, we aim at characterizing livestock epidemics in terms of robust features useful for planning and control, to deal with temporal fluctuations, sensitivity to initial conditions and missing information during an outbreak. Through spatial disease simulations, we detect spreading paths that are stable across different initial conditions, allowing the clustering of the seeds and reducing the epidemic variability. Paths also allow us to identify premises, called sentinels, having a large probability of being infected and providing critical information on the outbreak origin, as encoded in the clusters. This novel procedure provides a general framework that can be applied to specific diseases, for aiding risk assessment analysis and informing the design of optimal surveillance systems.