The analysis of epidemic spreading on clique-overlapping growth network

In this paper, we propose a new clique-overlapping growth network and study the epidemic spreading on it. We verify by simulation and theoretical analysis that the degree distribution follows a power-law form. Then, we have simulated the epidemic dynamics in this clique-overlapping growth network. Based on the mean-field theory, we have obtained the theoretical epidemic threshold. We find that the epidemic threshold is related to the evolution mechanism of the network model. The theoretical analysis is well consistent with the simulation results. The results in this model can help people understand the epidemic spreading of various processes, such as infectious diseases, computer viruses, gossips, and so on in real complex networks. Moreover, the appropriate immunization strategies can also be designed based on our results, to hold back the trend of epidemic outbreak.

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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.

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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.

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Analysis of the susceptible-infected-susceptible epidemic dynamics in networks via the non-backtracking matrix

IMA Journal of Applied Mathematics ◽

10.1093/imamat/hxaa003 ◽

2020 ◽

Vol 85 (2) ◽

pp. 214-230 ◽

Cited By ~ 1

Author(s):

Naoki Masuda ◽

Victor M Preciado ◽

Masaki Ogura

Keyword(s):

Lower Bound ◽

Line Graph ◽

Mean Field Theory ◽

Mean Field ◽

Moment Closure ◽

Order Moment ◽

Epidemic Threshold ◽

Incidence Matrices ◽

Epidemic Dynamics ◽

The Given

Abstract We study the stochastic susceptible-infected-susceptible model of epidemic processes on finite directed and weighted networks with arbitrary structure. We present a new lower bound on the exponential rate at which the probabilities of nodes being infected decay over time. This bound is directly related to the leading eigenvalue of a matrix that depends on the non-backtracking and incidence matrices of the network. The dimension of this matrix is $N+M$, where $N$ and $M$ are the number of nodes and edges, respectively. We show that this new lower bound improves on an existing bound corresponding to the so-called quenched mean-field theory. Although the bound obtained from a recently developed second-order moment-closure technique requires the computation of the leading eigenvalue of an $N^2\times N^2$ matrix, we illustrate in our numerical simulations that the new bound is tighter, while being computationally less expensive for sparse networks. We also present the expression for the corresponding epidemic threshold in terms of the adjacency matrix of the line graph and the non-backtracking matrix of the given network.

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Epidemic Spreading with Heterogeneous Awareness on Human Networks

Mathematical Problems in Engineering ◽

10.1155/2017/1979468 ◽

2017 ◽

Vol 2017 ◽

pp. 1-7

Author(s):

Yanling Lu ◽

Guoping Jiang ◽

Zhengxin Wang

Keyword(s):

Theoretical Analysis ◽

Epidemic Model ◽

Arrival Time ◽

Behavioral Responses ◽

Epidemic Spreading ◽

Epidemic Threshold ◽

Epidemic Dynamics ◽

Awareness Information ◽

The Impact ◽

Human Networks

The spontaneous awareness behavioral responses of individuals have a significant impact on epidemic spreading. In this paper, a modified Susceptible-Alert-Infected-Susceptible (SAIS) epidemic model with heterogeneous awareness is presented to study epidemic spreading in human networks and the impact of heterogeneous awareness on epidemic dynamics. In this model, when susceptible individuals receive awareness information about the presence of epidemic from their infected neighbor nodes, they will become alert individuals with heterogeneous awareness rate. Theoretical analysis and numerical simulations show that heterogeneous awareness can enhance the epidemic threshold with certain conditions and reduce the scale of virus outbreaks compared with no awareness. What is more, for the same awareness parameter, it also shows that heterogeneous awareness can slow effectively the spreading size and does not delay the arrival time of epidemic spreading peak compared with homogeneous awareness.

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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.

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Exploring the Epidemic Spreading in a Multilayer Metapopulation Network by considering Individuals’ Periodic Travelling

Complexity ◽

10.1155/2020/6782018 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Dun Han ◽

Qi Shao ◽

Dandan Li

Keyword(s):

Diffusion Model ◽

Mean Field ◽

Field Method ◽

Epidemic Spreading ◽

Epidemic Threshold ◽

Mobility Rate ◽

Frobenius Theorem ◽

Fluctuation Range ◽

The Mean ◽

New Perspective

The convenience of transportation brings the diversity of individuals’ travelling modes; in this paper, we present an improved epidemic diffusion model in a multilayer metapopulation network. Firstly, we construct the metapopulation network with different travelling ways, and then, the epidemic spreading threshold is calculated by means of the mean-field method. Taking the periodicity of individuals’ travelling into account, we further explore the epidemic diffusion model with individuals’ periodic travelling and deduce the epidemic spreading threshold using the Perron–Frobenius theorem. Our results show that if all individuals in each area decide to move, the epidemic threshold can be effectively raised while each individual chooses an unbiased region to arrive. In addition, with the increase of individuals’ mobility rate or regional heterogeneous infection coefficient, the fluctuation range of the density of infected becomes larger, while the fluctuation period is almost unchanged. However, the change of individuals’ periodic motion could cause the change of the fluctuation period of infected density. We try to provide a new perspective for the research of metapopulation.

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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.

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Containing Epidemic Spreading on Networks with Neighbor Resource Supporting

Complexity ◽

10.1155/2020/5409401 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Chengcheng Song ◽

Yanyan Chen ◽

Ning Chen ◽

Zhuo Liu ◽

Xuzhen Zhu ◽

...

Keyword(s):

Field Theory ◽

Complex Networks ◽

Numerical Simulations ◽

Mean Field Theory ◽

Mean Field ◽

Limited Resources ◽

Epidemic Outbreak ◽

Epidemic Spreading ◽

Spreading Model ◽

Outbreak Size

Previous studies revealed that the susceptibility, contacting preference, and recovery probability markedly alter the epidemic outbreak size and threshold. The recovery probability of an infected node is closely related to its obtained resources. How to allocate limited resources to infected neighbors is extremely important for containing the epidemic spreading on complex networks. In this paper, we proposed an epidemic spreading model on complex networks, in which we assume that the node has heterogeneous susceptibility and contacting preference, and susceptible nodes are willing to share their resources to neighbors. Through a developed heterogeneous mean-field theory and a large number of numerical simulations, we find that the recovered nodes provide resources uniformly to their infected neighbor nodes, and the epidemic spreading can be suppressed optimally on homogeneous and heterogeneous networks. Besides, altering the susceptibility and contacting preference does not qualitatively change the results. The susceptibility of the node decreases, which makes the outbreak threshold of epidemic spreading increase, and the outbreak size decreases. Our theory agrees well with the numerical simulations.

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