scholarly journals Epidemic Threshold of an SIS Model in Dynamic Switching Networks

2016 ◽  
Vol 46 (3) ◽  
pp. 345-355 ◽  
Author(s):  
Mohammad Reza Sanatkar ◽  
Warren N. White ◽  
Balasubramaniam Natarajan ◽  
Caterina M. Scoglio ◽  
Karen A. Garrett
Keyword(s):  
Switching Networks ◽  
Epidemic Threshold ◽  
Sis Model ◽  
Dynamic Switching

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 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.

A study of epidemic spreading on activity-driven networks

2016 ◽  
Vol 27 (08) ◽  
pp. 1650090 ◽  
Author(s):  
Yijiang Zou ◽  
Weibing Deng ◽  
Wei Li ◽  
Xu Cai
Keyword(s):  
Infection Rate ◽  
Temporal Structure ◽  
Constant Number ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Sis Model ◽  
Outbreak Size

The epidemic spreading was explored on activity-driven networks (ADNs), accounting for the study of dynamics both on and of the ADN. By employing the susceptible-infected-susceptible (SIS) model, two aspects were considered: (1) the infection rate of susceptible agent (depending on the number of its infected neighbors) evolves due to the temporal structure of ADN, rather than being a constant number; (2) the susceptible and infected agents generate unequal links while being activated, namely, the susceptible agent gets few contacts with others in order to protect itself. Results show that, in both cases, the larger epidemic threshold and smaller outbreak size were obtained.

Epidemic Threshold in Temporally-Switching Networks

2017 ◽  
pp. 161-177 ◽  
Author(s):  
Leo Speidel ◽  
Konstantin Klemm ◽  
Víctor M. Eguíluz ◽  
Naoki Masuda
Keyword(s):  
Switching Networks ◽  
Epidemic Threshold

Dynamic Switching Networks

2019 ◽  
Vol 28 (1) ◽  
pp. 77-96
Author(s):  
A. M. Khalili ◽  
Keyword(s):  
Switching Networks ◽  
Dynamic Switching

EPIDEMIC SPREADING AND GLOBAL STABILITY OF A NEW SIS MODEL WITH DELAY ON HETEROGENEOUS NETWORKS

2015 ◽  
Vol 23 (04) ◽  
pp. 1550029 ◽  
Author(s):  
HUIYAN KANG ◽  
YIJUN LOU ◽  
GUANRONG CHEN ◽  
SEN CHU ◽  
XINCHU FU
Keyword(s):  
Global Stability ◽  
Heterogeneous Networks ◽  
Lyapunov Functional ◽  
Functional Differential Equations ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Sis Model ◽  
Vector Population ◽  
Functional Differential ◽  
Disease Free

In this paper, we study a susceptible-infected-susceptible (SIS) model with time delay on complex heterogeneous networks. Here, the delay describes the incubation period in the vector population. We calculate the epidemic threshold by using a Lyapunov functional and some analytical methods, and find that adding delay increases the epidemic threshold. Then, we prove the global stability of disease-free and endemic equilibria by using the theory of functional differential equations. Furthermore, we show numerically that the epidemic threshold of the new model may change along with other factors, such as the infectivity function, the heterogeneity of the network, and the degrees of nodes. Finally, we find numerically that the delay can affect the convergence speed at which the disease reaches equilibria.

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