Seeking Best-Balanced Patch-Injecting Strategies through Optimal Control Approach

To restrain escalating computer viruses, new virus patches must be constantly injected into networks. In this scenario, the patch-developing cost should be balanced against the negative impact of virus. This article focuses on seeking best-balanced patch-injecting strategies. First, based on a novel virus-patch interactive model, the original problem is reduced to an optimal control problem, in which (a) each admissible control stands for a feasible patch-injecting strategy and (b) the objective functional measures the balance of a feasible patch-injecting strategy. Second, the solvability of the optimal control problem is proved, and the optimality system for solving the problem is derived. Next, a few best-balanced patch-injecting strategies are presented by solving the corresponding optimality systems. Finally, the effects of some factors on the best balance of a patch-injecting strategy are examined. Our results will be helpful in defending against virus attacks in a cost-effective way.

[1]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[2]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[3]  Yuan Yan Tang,et al.  On the Optimal Dynamic Control Strategy of Disruptive Computer Virus , 2017 .

[4]  P. Van Mieghem,et al.  Virus Spread in Networks , 2009, IEEE/ACM Transactions on Networking.

[5]  Shouhuai Xu,et al.  A Stochastic Model of Multivirus Dynamics , 2012, IEEE Transactions on Dependable and Secure Computing.

[6]  Wanlei Zhou,et al.  A Differential Game Approach to Patch Injection , 2018, IEEE Access.

[7]  Lu-Xing Yang,et al.  Heterogeneous virus propagation in networks: a theoretical study , 2017 .

[8]  Yuan Yan Tang,et al.  A Bi-Virus Competing Spreading Model with Generic Infection Rates , 2018, IEEE Transactions on Network Science and Engineering.

[9]  Kakali Chatterjee,et al.  Cloud security issues and challenges: A survey , 2017, J. Netw. Comput. Appl..

[10]  Lu-Xing Yang,et al.  The optimal dynamic immunization under a controlled heterogeneous node-based SIRS model , 2016 .

[11]  Kathleen M. Carley,et al.  The impact of countermeasure propagation on the prevalence of computer viruses , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  Yuan Yan Tang,et al.  Towards understanding the effectiveness of patch injection , 2019 .

[13]  Wanlei Zhou,et al.  Effective Repair Strategy Against Advanced Persistent Threat: A Differential Game Approach , 2019, IEEE Transactions on Information Forensics and Security.

[14]  Lu-Xing Yang,et al.  A Novel Virus-Patch Dynamic Model , 2015, PloS one.

[15]  Chuandong Li,et al.  A New Virus-Antivirus Spreading Model , 2015, ISNN.

[16]  Xiaofan Yang,et al.  The effect of infected external computers on the spread of viruses: A compartment modeling study , 2013 .

[17]  Xiaofan Yang,et al.  The impact of patch forwarding on the prevalence of computer virus: A theoretical assessment approach , 2017 .

[18]  Yuan Yan Tang,et al.  A Risk Management Approach to Defending Against the Advanced Persistent Threat , 2020, IEEE Transactions on Dependable and Secure Computing.

[19]  Vladimir Batagelj,et al.  Exploratory Social Network Analysis with Pajek , 2005 .

[20]  Mark E. J. Newman,et al.  Technological Networks and the Spread of Computer Viruses , 2004, Science.

[21]  Jacob Goldenberg,et al.  Distributive immunization of networks against viruses using the ‘honey-pot’ architecture , 2005 .

[22]  Yuan Yan Tang,et al.  Dynamic malware containment under an epidemic model with alert , 2017 .

[23]  Piet Van Mieghem,et al.  The N-intertwined SIS epidemic network model , 2011, Computing.

[24]  Minhaj Ahmad Khan,et al.  A survey of security issues for cloud computing , 2016, J. Netw. Comput. Appl..

[25]  Shouhuai Xu,et al.  Push- and pull-based epidemic spreading in networks: Thresholds and deeper insights , 2012, TAAS.

[26]  Mazliza Othman,et al.  Internet of Things security: A survey , 2017, J. Netw. Comput. Appl..

[27]  Shouhuai Xu,et al.  Adaptive Epidemic Dynamics in Networks , 2013, ACM Trans. Auton. Adapt. Syst..

[28]  Anupama Sharma,et al.  Capturing the interplay between malware and anti-malware in a computer network , 2014, Appl. Math. Comput..

[29]  Lu-Xing Yang,et al.  The Impact of the Network Topology on the Viral Prevalence: A Node-Based Approach , 2015, PloS one.

[30]  Lijuan Chen,et al.  Optimal control of a delayed SLBS computer virus model , 2015 .