Research On Propagation And Control Of Computer Virus

Network technology has evolved by leaps and bounds nowadays,and the growing popularity of the Internet has greatly changed the way we work and live.However,since the emergence of the Internet,cyber security has become an unavoidable issue,and now it has risen to the national strategic height.The attacks of computer viruses(viruses,for short)are the most typical kind of cyber security incidents.Antivirus software,patches and firewall are the main technical means of defending against viruses,which can weed out all viruses they can recognize that stay in individual electronic devices(nodes,for short).Unfortunately,these techniques seem powerless to the outbreak of a new virus.In order to effectively contain virus diffusion,it is necessary to understand the propagation laws of viruses,which may provide a theoretical basis for decision-making,as well as to use technical measures.The propagation dynamics of computer viruses is aimed at establishing dynamical models capturing the propagation behaviors of viruses by taking into full account the characteristics of viruses and various factors,especially countermeasures,that have significant impacts on viral spread,analyzing the propagation laws of viruses and working out effective strategies to suppress virus prevalence.This thesis is dedicated to the understanding of propagation laws of computer viruses and the decision-making of low-cost and high-efficiency virus-containing strategies.The major contributions are listed below.(1)In order to investigate the effects of both external infection source(i.e.offline infected nodes)and infected removable storage media on virus propagation,an SLBRS(susceptible-latent-breaking-recovered-susceptible)model based on fully-connected network is proposed.Studies show that the unique viral equilibrium of the model is globally stable,and the result is examined by some numerical experiments.Besides,the experiments reveal that 1)both external infection source and infected removable storage media can accelerate virus diffusion,and 2)infected removable storage media can pose a greater threat to online nodes than infected external source.(2)To better understand the effects of nonlinear infection and countermeasure rates on viral spread,an SICS(susceptible-infected-countermeasured-susceptible)model based on fully-connected network is formulated.Studies show that the unique viral equilibrium of the model is globally stable,and the result is examined by some numerical and simulation experiments.The results predicted by the model are in good agreement with the simulated results obtained probabilistically,which implies the validity of the model.Additionally,the experiments exhibit that viruses on the network always persist and do not tend to extinction.(3)In the presence of external infection source,an SICS model based on scale-free network is presented.Theoretical analysis shows that the unique viral equilibrium of the model is globally attractive.The results predicted by the model are in good accordance with the simulated results obtained probabilistically,which demonstrates that the main result and the model are both valid.Besides,the experiments display that 1)countermeasure dissemination to higher-degree nodes is more effective in suppressing viral spread than that to lower-degree nodes,and 2)decreasing the power-law exponent is conducive to the containment of virus prevalence.(4)In order to distribute countermeasures dynamically on scale-free network and try to reduce virus diffusion at lower cost,an optimal control problem is formulated based on a controlled SICS model and a given objective function.Theoretical analysis shows the existence of an optimal control for the problem,and the optimality system for the problem is also derived.The numerical experiments reveal that 1)the optimal control strategy can indeed minimize the objective function and reduce the proportion of infected nodes to a low level simultaneously,and 2)higher-degree nodes need less cost than lower-degree nodes.As higher-degree nodes play a critical role in the network,it is suggested that a higher priority be assigned to higher-degree nodes at the time of countermeasure dissemination.(5)In order to disseminate countermeasures flexibly on arbitrary network and attempt to reduce virus prevalence at lower cost,an optimal control problem is proposed based on a controlled SICS model with nonlinear infection rate and a given objective function.The existence of an optimal control for the problem is proved,and the optimality system for the problem is also derived.The numerical experiments demonstrate the effectiveness of the optimal control strategy.Moreover,the experiments exhibit that 1)linear infection rate overestimates the prevalence of viruses when compared to the nonlinear infection rate,2)decreasing the tradeoff factor is beneficial to the suppression of virus spread,and 3)the structure of network has a certain impact on the virus propagation and the control cost.(6)In order to distribute countermeasures dynamically on arbitrary network and attempt to decrease viral spread at lower cost,and to explore how the action mode of surfing the Internet(such as keeping online or offline all the time,or sometimes online and sometimes offline)affects virus propagation,an optimal control problem is presented based on a controlled SICES(susceptible-infected-countermeasured-externalsusceptible)model and a given objective function.The existence of an optimal control and the optimality system for the problem are both shown.The numerical experiments indicate the effectiveness of the optimal control strategy.Furthermore,in order to obtain a lower objective function and diminish the proportion of infected nodes to a lower level,users can choose the corresponding action mode of surfing the Internet according to the structure of network.For example,it is better either to disconnect the Internet frequently or to stay online all the while on WS(Watts-Strogatz)small-world network,or to disconnect the Internet frequently on BA(Barabási-Albert)scale-free network,or to maintain online all through on Facebook network.