Effect of triangle behavior on topological properties of weighted networks

2019 ◽  
Vol 33 (16) ◽  
pp. 1950170
Author(s):  
Qi An ◽  
Yajing Zhou ◽  
Kehua Chen ◽  
Weilong Chen ◽  
Guan Yan ◽  
...  
Keyword(s):  
Significant Influence ◽  
Transmission Rate ◽  
Strength Distribution ◽  
Topological Properties ◽  
Epidemic Spreading ◽  
The Real ◽  
Scale Free ◽  
Community Model ◽  
New Community ◽  
Theoretical Results

As an essential dynamic evolving mechanism, triangle behavior can be observed ubiquitously in the real world. Combining transfer mechanism with weighted dynamic, in this paper, we propose a new community model and deduce the strength distribution. Consistent with the theoretical results, numerical simulations show decent right-skewed scale-free characters of strength distribution. Moreover, we calculate some important coefficients to analyze the correlations of nodes and demonstrate the disassortative property of this model. Finally, the process of epidemic spreading with different weighted transmission rate is introduced on the weighted community network, and the results indicate that the triangle behavior has a significant influence on the dynamic of the epidemic spreading. Composed with the models proposed already, our model is supposed to be closer to the realistic network and imitate the real system more accurately and exactly.

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.

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.

scholarly journals Epidemic spreading in lattice-embedded scale-free networks

2007 ◽  
Vol 377 (1) ◽  
pp. 125-130 ◽  
Author(s):  
Xin-Jian Xu ◽  
Zhi-Xi Wu ◽  
Guanrong Chen
Keyword(s):  
Epidemic Spreading ◽  
Scale Free ◽  
Scale Free Networks

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

scholarly journals The Global Behavior of a Periodic Epidemic Model with Travel between Patches

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Luosheng Wen ◽  
Bin Long ◽  
Xin Liang ◽  
Fengling Zeng
Keyword(s):  
Epidemic Model ◽  
Transmission Rate ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Periodic Transmission ◽  
Theoretical Results ◽  
Disease Free

We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratioR0and two theorems on the global behavior: ifR0< 1 the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then it is unstable; ifR0> 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.

The analysis of evolutionary prisoner’s dilemma game based on weighting effect

2021 ◽  
pp. 2150066
Author(s):  
Xinting Hu ◽  
Mengyun Wu
Keyword(s):  
Prisoner's Dilemma ◽  
Weighting Function ◽  
Random Network ◽  
Cooperative Behavior ◽  
Equilibrium Points ◽  
Prisoner’S Dilemma ◽  
The Real ◽  
Scale Free ◽  
Cooperative Strategies ◽  
Average Payoff

In this paper, an improved evolutionary prisoner’s dilemma (PD) game model is proposed by considering the weighting effect. Taking into account individual’s perceived payoff (benefits), the evolutionary tendency of the cooperators and three equilibrium points of the proposed model are obtained. We then numerically investigate how different exterior and interior factors influence on individuals’ cooperative behavior and their payoff both in the ER random network and the BA scale-free network. Our results reveal that the heterogeneous network structure is conducive to cooperation. In addition, the existence of leader nodes is an important driving force for promoting individuals’ cooperation. By further analyzing the rationality coefficient which appears in the weighting function, we obtain that a greater of irrationality could lead more people to take cooperative strategies. Finally, two indicators which are used to measure the real average payoff and perceived average payoff are defined. The results show that the real average payoff and perceived average payoff are larger in the heterogeneity network than that in homogeneous network.

scholarly journals Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Wanjun Xia ◽  
Soumen Kundu ◽  
Sarit Maitra
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Center Manifold ◽  
Transmission Rate ◽  
Sufficient Conditions ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Ratio Dependent ◽  
Theoretical Results

A delayed ecoepidemic model with ratio-dependent transmission rate has been proposed in this paper. Effects of the time delay due to the gestation of the predator are the main focus of our work. Sufficient conditions for local stability and existence of a Hopf bifurcation of the model are derived by regarding the time delay as the bifurcation parameter. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out in order to validate our obtained theoretical results.

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