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Optimal control of computer virus under a delayed model. (English) Zbl 1278.49045
Summary: This paper addresses the issue of how to suppress the spread of a computer virus by means of the optimal control method. First, a controlled delayed computer virus spread model is established. Second, an optimal control problem is formulated by making a tradeoff between the control cost and the control effect. Third, the optimal control strategies are theoretically investigated. Finally, it is experimentally shown that the spread of infected nodes can be suppressed effectively by adopting an optimal control strategy.

MSC:
49N90 Applications of optimal control and differential games
68M11 Internet topics
93A30 Mathematical modelling of systems (MSC2010)
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[1] J.O. Kephart, S.R. White, Directed-graph epidemiological models of computer viruses, in: 1991 IEEE Symposium on Security and Privacy, 1991, pp. 343-359.
[2] J.O. Kephart, S.R. White, Measuring and modeling computer virus prevalence, in: 1993 IEEE symposium on Security and Privacy, 1993, pp. 2-15.
[3] Wierman, J.C.; Marchette, D.J., Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction, Comput. stat. data anal., 45, 3-23, (2004) · Zbl 1429.68037
[4] Billings, L.; Spears, W.M.; Schwartz, I.B., A unified prediction of computer virus spread in connected networks, Phys. lett. A, 297, 261-266, (2002) · Zbl 0995.68007
[5] Yuan, H.; Chen, G., Network virus-epidemic model with the point-to-group information propagation, Appl. math. comput., 206, 357-367, (2008) · Zbl 1162.68404
[6] Piqueira, J.R.C.; de Vasconcelos, A.A.; Gabriel, C.E.C.J.; Araujo, V.O., Dynamic models for computer viruses, Comput. security, 27, 355-359, (2008)
[7] Piqueira, J.R.C.; Araujo, V.O., A modified epidemiological model for computer viruses, Appl. math. comput., 213, 355-360, (2009) · Zbl 1185.68133
[8] Mishra, B.; Jha, N., Fixed period of temporary immunity after run of anti-malicious software on computer nodes, Appl. math. comput., 190, 1207-1212, (2007) · Zbl 1117.92052
[9] Han, X.; Tan, Q., Dynamical behavior of computer virus on Internet, Appl. math. comput., 217, 2520-2526, (2010) · Zbl 1209.68139
[10] Zaman, G.; Kang, Y.H.; Jung, I.H., Optimal vaccination and treatment in the SIR epidemic model, Proc. KSIAM, 3, 31-33, (2007)
[11] Zaman, G.; Kang, Y.H.; Jung, I.H., Stability analysis and optimal vaccination of an SIR epidemic model, Biosystems, 93, 240-249, (2008)
[12] Zaman, G.; Kang, Y.H.; Jung, I.H., Optimal treatment of an SIR epidemic model with time delay, Biosystems, 98, 43-50, (2009)
[13] Fleming, W.H.; Rishel, R.W., Deterministic and stochastic, (1975), Springer Verlag New York · Zbl 0323.49001
[14] Kamien, M.I.; Schwartz, N.L., Dynamics optimization: the calculus of variations and optimal control in economics and management, (2000), Elsevier Science The Netherlands · Zbl 0709.90001
[15] Fister, K.R.; Lenhart, S.; Mc Nally, J.S., Optimizing chemotherapy in an HIV model, Electron. J. diff. eqns., 32, 1-12, (1998)
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