THE SIS MODEL WITH TIME DELAY ON COMPLEX NETWORKS

2009 ◽  
Vol 19 (02) ◽  
pp. 623-628 ◽  
Author(s):  
XIN-JIAN XU ◽  
GUANRONG CHEN
Keyword(s):  
Complex Networks ◽  
Delay Time ◽  
Transmission Rate ◽  
Small World ◽  
Small World Networks ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Exponential Form ◽  
Sis Model ◽  
Scale Free

We present a time-delayed SIS model on complex networks to study epidemic spreading. We found that the existence of delay will affect, and oftentimes enhance, both outbreak and prevalence of infectious diseases in the networks. For small-world networks, we found that the epidemic threshold and the delay time have a power-law relation. For scale-free networks, we found that for a given transmission rate, the epidemic prevalence has an exponential form, which can be analytically obtained, and it decays as the delay time increases. We confirm all results by sufficient numerical simulations.

Epidemic spreading on evolving networks

2019 ◽  
Vol 33 (23) ◽  
pp. 1950266 ◽  
Author(s):  
Jin-Xuan Yang
Keyword(s):  
Preferential Attachment ◽  
Small World ◽  
Network Evolution ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Scale Free ◽  
Evolving Networks ◽  
Power Law Exponent ◽  
Free Network ◽  
Over Time

Network structure will evolve over time, which will lead to changes in the spread of the epidemic. In this work, a network evolution model based on the principle of preferential attachment is proposed. The network will evolve into a scale-free network with a power-law exponent between 2 and 3 by our model, where the exponent is determined by the evolution parameters. We analyze the epidemic spreading process as the network evolves from a small-world one to a scale-free one, including the changes in epidemic threshold over time. The condition of epidemic threshold to increase is given with the evolution processes. The simulated results of real-world networks and synthetic networks show that as the network evolves at a low evolution rate, it is more conducive to preventing epidemic spreading.

scholarly journals STEADY STATES OF EPIDEMIC SPREADING IN SMALL-WORLD NETWORKS

2004 ◽  
Vol 15 (10) ◽  
pp. 1471-1477 ◽  
Author(s):  
XIN-JIAN XU ◽  
ZHI-XI WU ◽  
YONG CHEN ◽  
YING-HAI WANG
Keyword(s):  
Analytical Methods ◽  
Large Scale ◽  
Small World ◽  
Spreading Rate ◽  
Steady States ◽  
Critical Threshold ◽  
Small World Networks ◽  
Epidemic Spreading ◽  
Sis Model ◽  
Large Scale Simulations

We consider a standard susceptible–infected–susceptible (SIS) model to study the behaviors of steady states of epidemic spreading in small-world networks. Using analytical methods and large scale simulations, we recover the usual epidemic behavior with a critical threshold λc below which infectious diseases die out. For the spreading rate λ far above λc, it was found that the density of infected individuals ρ as a function of λ has the property ρ≈f(K)( ln λ- ln λc).

Propagation and stability in software: A complex network perspective

2015 ◽  
Vol 26 (05) ◽  
pp. 1550052 ◽  
Author(s):  
Lei Wang ◽  
Ping Wang
Keyword(s):  
Software Engineering ◽  
Complex Networks ◽  
Large Scale ◽  
Structural Difference ◽  
Small World ◽  
Change Propagation ◽  
Small World Networks ◽  
Typical Structure ◽  
Scale Free ◽  
Scale Free Networks

In this paper, we attempt to understand the propagation and stability feature of large-scale complex software from the perspective of complex networks. Specifically, we introduced the concept of "propagation scope" to investigate the problem of change propagation in complex software. Although many complex software networks exhibit clear "small-world" and "scale-free" features, we found that the propagation scope of complex software networks is much lower than that of small-world networks and scale-free networks. Furthermore, because the design of complex software always obeys the principles of software engineering, we introduced the concept of "edge instability" to quantify the structural difference among complex software networks, small-world networks and scale-free networks. We discovered that the edge instability distribution of complex software networks is different from that of small-world networks and scale-free networks. We also found a typical structure that contributes to the edge instability distribution of complex software networks. Finally, we uncovered the correlation between propagation scope and edge instability in complex networks by eliminating the edges with different instability ranges.

Complex networks

2018 ◽  
Author(s):  
Graziano Vernizzi ◽  
Henri Orland
Keyword(s):  
Complex Networks ◽  
Small World ◽  
Laplacian Matrix ◽  
Square Lattice ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Scale Free Graphs ◽  
Regular Networks

This article deals with complex networks, and in particular small world and scale free networks. Various networks exhibit the small world phenomenon, including social networks and gene expression networks. The local ordering property of small world networks is typically associated with regular networks such as a 2D square lattice. The small world phenomenon can be observed in most scale free networks, but few small world networks are scale free. The article first provides a brief background on small world networks and two models of scale free graphs before describing the replica method and how it can be applied to calculate the spectral densities of the adjacency matrix and Laplacian matrix of a scale free network. It then shows how the effective medium approximation can be used to treat networks with finite mean degree and concludes with a discussion of the local properties of random matrices associated with complex networks.

EFFECTS OF MOTION ON EPIDEMIC SPREADING

2010 ◽  
Vol 20 (03) ◽  
pp. 765-773 ◽  
Author(s):  
ARTURO BUSCARINO ◽  
AGNESE DI STEFANO ◽  
LUIGI FORTUNA ◽  
MATTIA FRASCA ◽  
VITO LATORA
Keyword(s):  
Mobile Agents ◽  
Small World ◽  
Small World Networks ◽  
Epidemic Spreading ◽  
Long Distance ◽  
Dynamical Networks ◽  
Scale Free ◽  
Random Walkers ◽  
Human Movements ◽  
Disease Spreading

The study of social networks, and in particular those aspects related to disease spreading, has recently attracted considerable attention in the scientific community. In this paper, we investigate the effect of motion on the spread of diseases in dynamical networks of mobile agents. In order to simulate the long distance displacements empirically observed in real human movements, we consider different motion rules, such as random walks with the addition of jumps or Lévy flights. We compare the epidemic thresholds found in dynamical networks of mobile agents with the analogous expressions for static networks. We discuss the existing relations between dynamical networks of random walkers with jumps and static small-world networks, and those between systems of Lévy walkers and scale-free networks.

scholarly journals A New Coupled Awareness-Epidemic Spreading Model with Neighbor Behavior on Multiplex Networks

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Chao Zuo ◽  
Anjing Wang ◽  
Fenping Zhu ◽  
Zeyang Meng ◽  
Xueke Zhao
Keyword(s):  
Transmission Rate ◽  
Coupled Model ◽  
Dynamical Evolution ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Final Size ◽  
Scale Free ◽  
Multiplex Networks ◽  
Free Network ◽  
Effective Transmission

In this paper, we propose a nonlinear coupled model to study the two interacting processes of awareness diffusion and epidemic spreading on the same individual who is affected by different neighbor behavior status on multiplex networks. We achieve this topology scenario by two kinds of factors, one is the perception factor that can change interplay between different layers of networks and the other is the neighbors’ behavior status that can change the infection rate in each layer. According to the microscopic Markov chain approach (MMCA), we analyze the dynamical evolution of the system and derive the theoretical epidemic threshold on uncorrelated heterogeneous networks, and then, we validate the analysis by numerical simulation and discuss the final size of awareness diffusion and epidemic spreading on a scale-free network. With the outbreak of COVID-19, the spread of epidemic in China prompted drastic measures for transmission containment. We examine the effects of these interventions based on modeling of the awareness-epidemic and the COVID-19 epidemic case. The results further demonstrate that the epidemic spreading can be affected by the effective transmission rate of the awareness and neighbors’ behavior status.

Research on Edge-Growing Models Related with Scale-Free Small-World Networks

2014 ◽  
Vol 513-517 ◽  
pp. 2444-2448 ◽  
Author(s):  
Bing Yao ◽  
Ming Yao ◽  
Xiang En Chen ◽  
Xia Liu ◽  
Wan Jia Zhang
Keyword(s):  
Complex Networks ◽  
Topological Structure ◽  
Spanning Trees ◽  
Network Models ◽  
Small World ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Growing Network

Understanding the topological structure of scale-free networks or small world networks is required and useful for investigation of complex networks. We will build up a class of edge-growing network models and provide an algorithm for finding spanning trees of edge-growing network models in this article.

TOWARD A HARMONIOUS UNIFYING HYBRID MODEL FOR ANY EVOLVING COMPLEX NETWORKS

2007 ◽  
Vol 10 (02) ◽  
pp. 117-141 ◽  
Author(s):  
JINQING FANG ◽  
QIAO BI ◽  
YONG LI ◽  
XIN-BIAO LU ◽  
QIANG LIU
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Small World ◽  
Current Interest ◽  
Topological Properties ◽  
Small World Networks ◽  
Scale Free ◽  
Evolving Networks ◽  
Scale Free Networks ◽  
Hybrid Mechanisms

The current interest in complex networks is a part of a broader movement towards research on complex systems. Motivation of this work raises the two challenging questions: (i) Are real networks fundamentally random preferential attached without any deterministic attachment for both un-weighted and weighted networks? (ii) Is there a coherent physical idea and model for unifying the study of the formation mechanism of complex networks? To answer these questions, we propose a harmonious unifying hybrid preferential model (HUHPM) to a certain class of complex networks, which is controlled by a hybrid ratio, d/r, and study their behavior both numerically and analytically. As typical examples, we apply the concepts and method of the HUHPM to un-weighted scale-free networks proposed by Barabasi and Albert (BA), weighted evolving networks proposed by Barras, Bartholomew and Vespignani (BBV), and the traffic driven evolution (TDE) networks proposed by Wang et al., to get the so-called HUHPM-BA, HUHPM-BBV and HUHPM-TDE networks. All the findings of topological properties in the above three typical HUHPM networks give certain universal meaningful results which reveal some essential hybrid mechanisms for the formation of nontrivial scale-free and small-world networks.

Epidemic spreading on networks based on stress response

2017 ◽  
Vol 31 (16) ◽  
pp. 1750131 ◽  
Author(s):  
Fuzhong Nian ◽  
Shuanglong Yao
Keyword(s):  
Stress Response ◽  
Infectious Diseases ◽  
Stress Responses ◽  
Epidemic Model ◽  
Small World ◽  
Small World Networks ◽  
Epidemic Spreading ◽  
Spreading Resistance ◽  
Scale Free ◽  
Scale Free Networks

Based on the stress responses of individuals, the susceptible-infected-susceptible epidemic model was improved on the small-world networks and BA scale-free networks and the simulations were implemented and analyzed. Results indicate that the behaviors of individual’s stress responses could induce the epidemic spreading resistance and adaptation at the network level. This phenomenon showed that networks were learning how to adapt to the disease and the evolution process could improve their immunization to future infectious diseases and would effectively prevent the spreading of infectious diseases.

Robustness of complex networks with both unidirectional and bidirectional links against cascading failures

2017 ◽  
Vol 31 (27) ◽  
pp. 1750252 ◽  
Author(s):  
Lin Ding ◽  
Victor C. M. Leung ◽  
Min-Sheng Tan
Keyword(s):  
Complex Networks ◽  
Low Cost ◽  
Small World ◽  
Network Robustness ◽  
Cascading Failures ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Simulation Results ◽  
Direction Determining

The robustness of complex networks against cascading failures has been of great interest, while most of the researchers have considered undirected networks. However, to be more realistic, a part of links of many real systems should be described as unidirectional. In this paper, by applying three link direction-determining (DD) strategies, the tolerance of cascading failures is investigated in various networks with both unidirectional and bidirectional links. By extending the utilization of a classical global betweenness method, we propose a new cascading model, taking into account the weights of nodes and the directions of links. Then, the effects of unidirectional links on the network robustness against cascaded attacks are examined under the global load-based distribution mechanism. The simulation results show that the link-directed methods could not always lead to the decrease of the network robustness as indicated in the previous studies. For small-world networks, these methods certainly make the network weaker. However, for scale-free networks, the network robustness can be significantly improved by the link-directed method, especially for the method with non-random DD strategies. These results are independent of the weight parameter of the nodes. Due to the strongly improved robustness and easy realization with low cost on networks, the method for enforcing proper links to the unidirectional ones may be useful for leading to insights into the control of cascading failures in real-world networks, like communication and transportation networks.

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