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

Abstract

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.

A Mobility-Based Epidemic Model for IoT Malware Spread

“…Link type Mobility Malware type Infection timing SI [9], [26], SIS [12], [27], SIR [15], [25], [28], SISV [29], SDIR [19], SEIRS [7], [18], SCIRAS [30], SEIQVS [31]…”

“…Although individual groups have different numbers and categories of devices, the authors in [26] assume that the infection rate is homogeneous. In [12], [27], the authors propose SIS model for malware propagation. In [27], the authors calculate immunization and infection probability based on the Markov chain.…”

“…Moreover, infection rates are heterogeneous due to different link weights. Authors in [12] suggest that there is a relationship between the sender and the receiver, and thus the links between the nodes are bidirectional and have the same infection rate. SIR propagation model is studied in [15], [25].…”

A New Simple Epidemic Discrete-Time Model Describing the Dissemination of Information with Optimal Control Strategy

“…In 1927, Kermack and McKendrick devised the Susceptible-Infected-Removed (SIR) model which can be considered as an interesting contribution in the mathematical theory of epidemics [8]. In recent decades, epidemic modeling approaches have extended the field of epidemiology and various mathematical models have been designed to analyze the evolution of an epidemic according to population systems [9][10][11][12][13]. Such a kind of models divides the studied population (humans, animals, etc.)…”

Game Theoretic Suppression of Forged Messages in Online Social Networks

“…With no verification on user-generated content, OSNs are vulnerable to forged messages that intentionally mislead or deceive the recipients. There are a variety of forged messages, such as e-mail spams [4], fake views, e.g., in Amazon [5], [6], and diffusing rumors [7]- [9]. The publishers of forged messages can use social bots [10] or employ water army [11] to propagate forged messages and avoid sanction.…”