Phase Transitions of an Epidemic Spreading Model in Small-World Networks

2011 ◽  
Vol 55 (6) ◽  
pp. 1127-1131 ◽  
Author(s):  
Da-Yin Hua ◽  
Ke Gao
Keyword(s):  
Phase Transitions ◽  
Small World ◽  
Small World Networks ◽  
Epidemic Spreading ◽  
Spreading Model

scholarly journals PHASE TRANSITIONS IN SOME EPIDEMIC MODELS DEFINED ON SMALL-WORLD NETWORKS

2003 ◽  
Vol 14 (06) ◽  
pp. 825-833 ◽  
Author(s):  
H. N. AGIZA ◽  
A. S. ELGAZZAR ◽  
S. A. YOUSSEF
Keyword(s):  
Phase Transitions ◽  
Small World ◽  
Epidemic Models ◽  
Small World Networks ◽  
Inhomogeneous Models ◽  
Sirs Model ◽  
Variable Susceptibility

Some modified versions of susceptible-infected-recovered-susceptible (SIRS) model are defined on small-world networks. Latency, incubation and variable susceptibility are separately included. Phase transitions in these models are studied. Then inhomogeneous models are introduced. In some cases, the application of the models to small-world networks is shown to increase the epidemic region.

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).

scholarly journals Non-equilibrium Phase Transitions in 2D Small-World Networks: Competing Dynamics

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Wei Liu ◽  
Zhengxin Yan ◽  
Gaoliang Zhou
Keyword(s):  
Phase Transitions ◽  
Tricritical Point ◽  
Equilibrium Phase ◽  
Finite Size ◽  
Small World ◽  
Ferromagnetic Phase ◽  
Kawasaki Dynamics ◽  
Small World Networks ◽  
Competing Dynamics ◽  
Non Equilibrium

Abstract This article offers a detailed analysis of the Ising model in 2D small-world networks with competing Glauber and Kawasaki dynamics. The non-equilibrium stationary state phase transitions are obtained in these networks. The phase transitions are discussed, and the phase diagrams are obtained via Monte Carlo simulations and finite-size analyzing. We find that as the addition of links increases the phase transition temperature increases and the transition competing probability of tricritical point decreases. For the competition of the two dynamics, ferromagnetic to anti-ferromagnetic phase transitions and the critical endpoints are found in the small-world 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 AN EPIDEMIC MODEL ON SMALL-WORLD NETWORKS AND RING VACCINATION

2002 ◽  
Vol 13 (02) ◽  
pp. 189-198 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI ◽  
A. S. ELGAZZAR
Keyword(s):  
Epidemic Model ◽  
Vaccination Programme ◽  
Foot And Mouth Disease ◽  
Small World ◽  
Analytical Approximation ◽  
Theoretical Explanation ◽  
Small World Networks ◽  
Epidemic Spreading ◽  
Sirs Model ◽  
Ring Vaccination

A modified version of susceptible-infected-recovered-susceptible (SIRS) model for the outbreaks of foot-and-mouth disease (FMD) is introduced. The model is defined on small-world networks, and a ring vaccination programme is included. This model can be a theoretical explanation for the nonlocal interactions in epidemic spreading. Ring vaccination is capable of eradicating FMD provided that the probability of infection is high enough. Also an analytical approximation for this model is studied.

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.

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.

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