Immunization and epidemic threshold of an SIS model in complex networks

2016 ◽  
Vol 444 ◽  
pp. 576-581 ◽  
Author(s):  
Qingchu Wu ◽  
Xinchu Fu
Keyword(s):  
Complex Networks ◽  
Epidemic Threshold ◽  
Sis Model

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 Secure the IoT Networks as Epidemic Containment Game

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 156
Author(s):  
Juntao Zhu ◽  
Hong Ding ◽  
Yuchen Tao ◽  
Zhen Wang ◽  
Lanping Yu
Keyword(s):  
Heuristic Algorithms ◽  
Heuristic Method ◽  
Exact Algorithms ◽  
Epidemic Threshold ◽  
Solution Quality ◽  
Sis Model ◽  
Linear Programming Formulation ◽  
Iot Devices ◽  
General Graphs ◽  
The Internet Of Things

The spread of a computer virus among the Internet of Things (IoT) devices can be modeled as an Epidemic Containment (EC) game, where each owner decides the strategy, e.g., installing anti-virus software, to maximize his utility against the susceptible-infected-susceptible (SIS) model of the epidemics on graphs. The EC game’s canonical solution concepts are the Minimum/Maximum Nash Equilibria (MinNE/MaxNE). However, computing the exact MinNE/MaxNE is NP-hard, and only several heuristic algorithms are proposed to approximate the MinNE/MaxNE. To calculate the exact MinNE/MaxNE, we provide a thorough analysis of some special graphs and propose scalable and exact algorithms for general graphs. Especially, our contributions are four-fold. First, we analytically give the MinNE/MaxNE for EC on special graphs based on spectral radius. Second, we provide an integer linear programming formulation (ILP) to determine MinNE/MaxNE for the general graphs with the small epidemic threshold. Third, we propose a branch-and-bound (BnB) framework to compute the exact MinNE/MaxNE in the general graphs with several heuristic methods to branch the variables. Fourth, we adopt NetShiled (NetS) method to approximate the MinNE to improve the scalability. Extensive experiments demonstrate that our BnB algorithm can outperform the naive enumeration method in scalability, and the NetS can improve the scalability significantly and outperform the previous heuristic method in solution quality.

scholarly journals Epidemic threshold of the susceptible-infected-susceptible model on complex networks

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
Hyun Keun Lee ◽  
Pyoung-Seop Shim ◽  
Jae Dong Noh
Keyword(s):  
Complex Networks ◽  
Epidemic Threshold

Structure optimization based on memetic algorithm for adjusting epidemic threshold on complex networks

2016 ◽  
Vol 49 ◽  
pp. 224-237 ◽  
Author(s):  
Jianan Yan ◽  
Maoguo Gong ◽  
Lijia Ma ◽  
Shanfeng Wang ◽  
Bo Shen
Keyword(s):  
Complex Networks ◽  
Memetic Algorithm ◽  
Structure Optimization ◽  
Epidemic Threshold

Global analysis of an SIS model with an infective vector on complex networks

2012 ◽  
Vol 13 (2) ◽  
pp. 543-557 ◽  
Author(s):  
Yi Wang ◽  
Zhen Jin ◽  
Zimo Yang ◽  
Zi-Ke Zhang ◽  
Tao Zhou ◽  
...  
Keyword(s):  
Complex Networks ◽  
Global Analysis ◽  
Sis Model

scholarly journals Group-Based Susceptible-Infectious-Susceptible Model in Large-Scale Directed Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Xu Wang ◽  
Bo Song ◽  
Wei Ni ◽  
Ren Ping Liu ◽  
Y. Jay Guo ◽  
...  
Keyword(s):  
Adjacency Matrix ◽  
Continuous Time ◽  
Large Scale ◽  
Directed Graphs ◽  
Epidemic Models ◽  
Model Complexity ◽  
Mean Field Approximation ◽  
Epidemic Threshold ◽  
Sis Model ◽  
Modeling Accuracy

Epidemic models trade the modeling accuracy for complexity reduction. This paper proposes to group vertices in directed graphs based on connectivity and carries out epidemic spread analysis on the group basis, thereby substantially reducing the modeling complexity while preserving the modeling accuracy. A group-based continuous-time Markov SIS model is developed. The adjacency matrix of the network is also collapsed according to the grouping, to evaluate the Jacobian matrix of the group-based continuous-time Markov model. By adopting the mean-field approximation on the groups of nodes and links, the model complexity is significantly reduced as compared with previous topological epidemic models. An epidemic threshold is deduced based on the spectral radius of the collapsed adjacency matrix. The epidemic threshold is proved to be dependent on network structure and interdependent of the network scale. Simulation results validate the analytical epidemic threshold and confirm the asymptotical accuracy of the proposed epidemic model.

Toward a generalized theory of epidemic awareness in social networks

2017 ◽  
Vol 28 (05) ◽  
pp. 1750070 ◽  
Author(s):  
Qingchu Wu ◽  
Wenfang Zhu
Keyword(s):  
Infectious Disease ◽  
Social Networks ◽  
Approximate Equation ◽  
High Accuracy ◽  
General Function ◽  
Epidemic Threshold ◽  
Sis Model ◽  
Spreading Dynamics ◽  
Local Awareness ◽  
Infinite Networks

We discuss the dynamics of a susceptible-infected-susceptible (SIS) model with local awareness in networks. Individual awareness to the infectious disease is characterized by a general function of epidemic information in its neighborhood. We build a high-accuracy approximate equation governing the spreading dynamics and derive an approximate epidemic threshold above which the epidemic spreads over the whole network. Our results extend the previous work and show that the epidemic threshold is dependent on the awareness function in terms of one infectious neighbor. Interestingly, when a pow-law awareness function is chosen, the epidemic threshold can emerge in infinite networks.

scholarly journals MODELING INFORMATION SPREADING ON COMPLEX NETWORKS

2017 ◽  
Vol 33 (1-2) ◽  
Author(s):  
Daniel Trpevski ◽  
Kire Stamenov ◽  
Ljupčo Kocarev
Keyword(s):  
Complex Networks ◽  
Stable State ◽  
Natural Generalization ◽  
Time Step ◽  
Spreading Process ◽  
Sis Model ◽  
Simultaneous Existence ◽  
Information Type ◽  
Types Of Information ◽  
High Degree

A b s t r a c t: In this article we propose a model for the spread of two types of information in networks. The model is a natural generalization of the epidemic susceptible-infective-susceptible(SIS) model. The two information types have different attractiveness, which affects the nodes' decision on which information type to adopt when both arrive at a node in the same time step. At difference with results from other authors, the model shows simultaneous existence of the two information types in the stable state. We give approximations for the average number of nodes informed with each information type at the end of the spreading process when nodes have high degree.

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