Spreading of Epidemics on Scale-Free Networks with Time Delay

In the SIR model once a node is cured after infection it becomes permanently immune,but we assume this immunity to be temporary. So we obtain an epidemic model with time delay on scale-free networks. Using the mean field theory the spreading threshold and the spreading dynamics is analyzed. Theoretical results indicate that the threshold is significantly dependent on the topology of scale-free networks and time delay. Numerical simulations confirmed the theoretical results.

Download Full-text

Research on SIQRS Spreading Dynamic Model with Feedback Mechanism on Scale-Free Networks

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.989-994.4524 ◽

2014 ◽

Vol 989-994 ◽

pp. 4524-4527

Author(s):

Tao Li ◽

Yuan Mei Wang ◽

You Ping Yang

Keyword(s):

Dynamic Model ◽

Mean Field Theory ◽

Mean Field ◽

Feedback Mechanism ◽

Epidemic Spreading ◽

Scale Free ◽

Spreading Dynamics ◽

Scale Free Networks ◽

The Mean ◽

The Relationship

A modified spreading dynamic model with feedback-mechanism based on scale-free networks is presented in this study. Using the mean field theory, the spreading dynamics of the model is analyzed. The spreading threshold and equilibriums are derived. The relationship between the spreading threshold, the epidemic steady-state and the feedback-mechanism is analyzed in detail. Theoretical results indicate the feedback-mechanism can increase the spreading threshold, resulting in effectively controlling the epidemic spreading.

Download Full-text

Epidemic Spreading with Feedback Mechanism and Time Delay under Migration in Scale-Free Networks

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.378.655 ◽

2013 ◽

Vol 378 ◽

pp. 655-661

Author(s):

Tao Li ◽

Yuan Mei Wang

Keyword(s):

Time Delay ◽

Mean Field Theory ◽

Mean Field ◽

Feedback Mechanism ◽

Critical Threshold ◽

Epidemic Spreading ◽

Scale Free ◽

Epidemic Dynamics ◽

Scale Free Networks ◽

The Mean

Taking into account the heterogeneity of the underlying networks, an epidemic model with feedback-mechanism, time delay and migrations of individuals on scale-free networks is presented. First, the epidemic dynamics is analyzed via the mean field theory. The spreading critical threshold and equilibriums are derived. The existence of endemic equilibrium is determined by the spreading threshold. Then, the influences of feedback-mechanism, time delay, migrations of individuals and the heterogeneity of the scale-free networks on the spreading threshold and the epidemic steady-state are studied in detail. Numerical simulations are presented to illustrate the results with the theoretical analysis.

Download Full-text

Associated Credit Risk Contagion with Incubatory Period: A Network-Based Perspective

Complexity ◽

10.1155/2020/5642730 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

Kai Xu ◽

Jianming Mo ◽

Qian Qian ◽

Fengying Zhang ◽

Xiaofeng Xie ◽

...

Keyword(s):

Field Theory ◽

Credit Risk ◽

Mean Field Theory ◽

Mean Field ◽

Stable State ◽

Scale Free Network ◽

Scale Free ◽

Free Network ◽

The Mean ◽

Credit Risk Contagion

Associated credit risk is a kind of credit risk among the associated credit entities formed by credit-related entities. Focusing on this hot topic of associated credit risk and the relevant contagion and considering the latent entities and their incubatory period, this paper builds an infectious dynamic model to describe the associated credit risk contagion of associated credit entities based on the mean-field theory of complex networks. Firstly, this paper analyzes the stable state of the associated credit risk contagion in the associated entity network, considering the latent entities and their incubatory period. Secondly, from the perspective of complex network and considering the incubatory period, a SHIS model is built to reveal how the incubatory period influences associated credit risk contagion. Finally, the sensitivity of some parameters is analyzed in the Barabási–Albert (BA) scale-free network. The results show the following: (i) the contagion threshold of associated credit risk is related to the incubatory period of latent entities, the recovery rate and infectivity of infected entities, and the newborn rate of credit entities; (ii) the infectious rate of infected entities, the mortality rate of credit entities, and the important factors stated in (i) are all significantly correlated with the density of infected entities.

Download Full-text

Six Susceptible-Infected-Susceptible Models on Scale-free Networks

Scientific Reports ◽

10.1038/srep22506 ◽

2016 ◽

Vol 6 (1) ◽

Cited By ~ 12

Author(s):

Satoru Morita

Keyword(s):

Field Theory ◽

Mean Field Theory ◽

Mean Field ◽

Information Networks ◽

Propagation Mechanism ◽

Contact Rate ◽

Scale Free ◽

Scale Free Networks ◽

Information Spread ◽

Nature And Society

Abstract Spreading phenomena are ubiquitous in nature and society. For example, disease and information spread over underlying social and information networks. It is well known that there is no threshold for spreading models on scale-free networks; this suggests that spread can occur on such networks, regardless of how low the contact rate may be. In this paper, I consider six models with different contact and propagation mechanisms, which include models studied so far, but are apt to be confused. To compare these six models, I analyze them by degree-based mean-field theory. I find that the result depends on the details of contact and propagation mechanism.

Download Full-text

Spreading Dynamics Analysis of a Novel SEAIRS Epidemic Model with Protection and Hospital Quarantine under Government Pre-warning

10.21203/rs.3.rs-576348/v1 ◽

2021 ◽

Author(s):

Bingchuan Xue ◽

Tao Li ◽

Xinming Cheng ◽

Yumiao Li ◽

Yuanyuan Wu ◽

...

Keyword(s):

Epidemic Model ◽

Mean Field Theory ◽

Mean Field ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Epidemic Spreading ◽

Scale Free ◽

Spreading Dynamics ◽

The Mean ◽

The Impact

Abstract To study the impact of protection and hospital quarantine measure, government pre-warning mechanism and heterogeneity of underlying networks on epidemic spreading, a novel SEAIRS epidemic model is proposed on scale-free networks. The spreading dynamics of the model is studied by means of the mean-field theory. Two equilibriums and the basic reproductive number R0 of the model is analyzed in detail. The global asymptotic stability of the disease-free equilibrium, the permanence of the epidemic spreading and the global attractivity of the endemic equilibrium are proved. Sensitivity analysis shows that the basic reproductive number R0 is dependent on the coverage rate of home quarantine (ωQ,ηA ,ηS ), hospitalization rate η1 and government pre-warning intensity δ . Finally, the theoretical analysis results are confirmed by means of numerical simulations.

Download Full-text

THE COMPLEX NETWORKS WITH RANDOM INITIALIZING AND PREFERENTIAL LINKING

International Journal of Modern Physics B ◽

10.1142/s0217979210056724 ◽

2010 ◽

Vol 24 (24) ◽

pp. 4753-4759 ◽

Cited By ~ 1

Author(s):

TIELI SUN ◽

JINGWEI DENG ◽

KAIYING DENG ◽

SHUANGLIANG TIAN

Keyword(s):

Field Theory ◽

Theoretical Analysis ◽

Computer Simulations ◽

Mean Field Theory ◽

Mean Field ◽

Scale Free ◽

Proposed Model ◽

Free Behavior ◽

Analytical Expressions ◽

Theoretical Results

In this paper, we first derive the analytical expressions of the degree distributions for the network with random initializing attractiveness and preferential linking by using the approach of mean-field theory. Then we discuss the justification of the scale-free behavior and give a remark about the proposed model. Finally, a series of theoretical analysis and numerical simulations for the network model are conducted. The computer simulations and the theoretical results are consistent, and display the effectiveness of the model.

Download Full-text

EPIDEMICS OF SIRS MODEL WITH NONUNIFORM TRANSMISSION ON SCALE-FREE NETWORKS

International Journal of Modern Physics B ◽

10.1142/s021797920905211x ◽

2009 ◽

Vol 23 (09) ◽

pp. 2203-2213 ◽

Cited By ~ 30

Author(s):

C. Y. XIA ◽

S. W. SUN ◽

Z. X. LIU ◽

Z. Q. CHEN ◽

Z. Z. YUAN

Keyword(s):

Disease Transmission ◽

Mean Field Theory ◽

Mean Field ◽

Critical Threshold ◽

Epidemic Threshold ◽

Scale Free ◽

Sirs Epidemic Model ◽

Sirs Model ◽

Scale Free Networks ◽

The Mean

We investigate the effect of nonuniform transmission on the critical threshold of susceptible–infected–recovered–susceptible (SIRS) epidemic model on scale-free networks. Based on the mean-field theory, it is observed that the epidemic threshold is not only correlated with the topology of underlying networks, but also with the disease transmission mechanism (e.g., nonuniform transmission). The current findings will significantly help us to further understand the real epidemics taking place on social and technological networks.

Download Full-text

COEXISTENCE OF FERROMAGNETISM AND SUPERCONDUCTIVITY IN THE TWO-DIMENSIONAL FERROMAGNETIC t–J MODEL

Modern Physics Letters B ◽

10.1142/s0217984903006438 ◽

2003 ◽

Vol 17 (27n28) ◽

pp. 1417-1424

Author(s):

FAN YANG ◽

YUPENG WANG ◽

RUSHAN HAN

Keyword(s):

Field Theory ◽

Mean Field Theory ◽

Mean Field ◽

P Wave ◽

Hole Doping ◽

Cooper Pairs ◽

Two Dimensional ◽

Self Consistent ◽

The Mean ◽

Theoretical Results

The two-dimensional ferromagnetic t–J model is studied in the framework of slave-boson mean field theory. After solving the mean field self-consistent equations, we find that there exists a hole-doping region δ1<δ<δ2 in which p-wave superconductivity and ferromagnetism coexist. There also exists a T* line, under which pre-paired p-wave cooper pairs appear. The similarity and differences between our theoretical results and the experimental ones made for UGe 2 are compared.

Download Full-text