The Discrete-Time SIS Model in Small-World Networks

2012 ◽  
Author(s):  
Guangzheng Li ◽  
Dinghua Shi ◽  
Zhongzhi Zhang
Keyword(s):  
Discrete Time ◽  
Small World ◽  
Small World Networks ◽  
Sis Model

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).

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.

Networks

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Phase Diagrams ◽  
Community Detection ◽  
Network Science ◽  
Small World ◽  
Small World Networks ◽  
Multilayer Networks ◽  
Basic Vocabulary

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.

Tracking sinks of atmospheric methane using small world networks

Chemosphere ◽  
2014 ◽  
Vol 117 ◽  
pp. 766-773 ◽  
Author(s):  
Chih-Sheng Lee ◽  
Pei-Jen Su
Keyword(s):  
Small World ◽  
Atmospheric Methane ◽  
Small World Networks

scholarly journals Multifractal analysis of eigenvectors of small-world networks

2021 ◽  
Vol 144 ◽  
pp. 110745
Author(s):  
Ankit Mishra ◽  
Jayendra N. Bandyopadhyay ◽  
Sarika Jalan
Keyword(s):  
Multifractal Analysis ◽  
Small World ◽  
Small World Networks

scholarly journals Critical exponents in coupled phase-oscillator models on small-world networks

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
Ryosuke Yoneda ◽  
Kenji Harada ◽  
Yoshiyuki Y. Yamaguchi
Keyword(s):  
Critical Exponents ◽  
Small World ◽  
Phase Oscillator ◽  
Small World Networks ◽  
Coupled Phase Oscillator ◽  
Oscillator Models

Small‐World Networks Can Provide a New Tool to Study Diverse Systems

Physics Today ◽  
1998 ◽  
Vol 51 (9) ◽  
pp. 17-18 ◽  
Author(s):  
Gloria B. Lubkin
Keyword(s):  
Small World ◽  
Small World Networks
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