The Dynamical Modeling Analysis of the Spreading of Passive Worms in P2P Networks

Shujuan Zhang,Juan Zhang,Zhen Jin

doi:10.1155/2018/1656907

Shujuan Zhang, Juan Zhang + Show 1 more

Open Access

https://doi.org/10.1155/2018/1656907

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Abstract

Passive worms are prone to spreading through Peer-to-Peer networks, and they pose a great threat to the security of the network. In this paper, considering network heterogeneity and the number of hops a search can reach, we propose a novel mathematical model to study the dynamics of the propagation of passive worms. For the proposed model, the basic reproduction number R0 is derived by employing the existence of the positive equilibrium. And the stabilities of the worm-free equilibrium and positive equilibrium are analyzed. Moreover, we verify the rationality of the model established by comparing the stochastic simulation with the numerical simulation. Finally, we examine the effect of the number of hops on the spread of passive worms and discuss the various immunization strategies. We find that if R0>1, the propagation speed of passive worms is accelerated with the increase of hop count d; if R0<1, the number of infected peers decreases rapidly with the increase of the value of d and drops to zero eventually. Results show that the network topology and the number of hops can affect the spread of passive worms.

Highlights

Peer-to-Peer (P2P) networks are composed of connected computers, which can function as both clients and servers
The basic reproduction number R0 is derived by employing the existence of the positive equilibrium
We verify the rationality of the model established by comparing the stochastic simulation with the numerical simulation

Summary

Introduction

Peer-to-Peer (P2P) networks are composed of connected computers, which can function as both clients and servers. In 2018, Rguibi et al [13] presented a propagation model of passive worms in P2P networks. In this proposed model, the hesitation to open a new downloaded file was considered. We take the above two aspects into account and propose a novel dynamical model to study the dynamics of passive worm propagation in P2P networks. We verify the rationality of the proposed model by comparing the stochastic simulation with the numerical simulation and investigate the effects of network topology and hop count on passive worm propagation.

The Model Formulation

Basic Reproduction Number

Global Stability of Equilibria

Simulation Results

Discussions and Conclusions

I20 I30