State-Based Switching for Optimal Control of Computer Virus Propagation with External Device Blocking

Qingyi Zhu,Seng W Loke,Ye Zhang

doi:10.1155/2018/4982523

Abstract

The rapid propagation of computer virus is one of the greatest threats to current cybersecurity. This work deals with the optimal control problem of virus propagation among computers and external devices. To formulate this problem, two control strategies are introduced: (a) external device blocking, which means prohibiting a fraction of connections between external devices and computers, and (b) computer reconstruction, which includes updating or reinstalling of some infected computers. Then the combination of both the impact of infection and the cost of controls is minimized. In contrast with previous works, this paper takes into account a state-based cost weight index in the objection function instead of a fixed one. By using Pontryagin’s minimum principle and a modified forward-backward difference approximation algorithm, the optimal solution of the system is investigated and numerically solved. Then numerical results show the flexibility of proposed approach compared to the regular optimal control. More numerical results are also given to evaluate the performance of our approach with respect to various weight indexes.

Highlights

Computer virus, ranging from Morris worms in 1988 to WannaCry last year, can spread to every corner of our world via Internet in a very short time
Model by Dong et al [6], SIP model proposed by Abazari et al [7], SVEIR model proposed by Upadhyay et al [8], and SLBS model proposed by Yang et al [9, 10]
To formulate the optimal control problem of system (1), we introduce two types of countermeasures for inhibiting virus propagation: (a) external device blocking, which means prohibiting a fraction of connections between external devices and computers, and (b) computer reconstruction, which includes updating or reinstalling of some infected computers

Summary

Introduction

Computer virus, ranging from Morris worms in 1988 to WannaCry last year, can spread to every corner of our world via Internet in a very short time. A better understanding of the behaviors of virus propagation and predicting its outbreak are of crucial importance to thwart its wide spread. In this scenario, more and more attentions from worldwide scholars have been paid to the dynamical modeling of computer virus propagation through the classical epidemiology approach. Depending on the topology of propagation networks, all current dynamical models of computer virus fall into two categories: homogeneous models and heterogeneous models [2]. In [14], both the topology of networks and the interaction between computer viruses and honeynet potency are considered Both homogeneous and heterogeneous models provide significant insights into a detailed and qualitative understanding of how and when computer viruses break out

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Results

Conclusion