Zhu, Qingyi; Yang, Xiaofan; Yang, Lu-Xing; Zhang, Chunming Optimal control of computer virus under a delayed model. (English) Zbl 1278.49045 Appl. Math. Comput. 218, No. 23, 11613-11619 (2012). 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. Cited in 40 Documents MSC: 49N90 Applications of optimal control and differential games 68M11 Internet topics 93A30 Mathematical modelling of systems (MSC2010) Keywords:computer virus; delayed model; controlled system; optimal control problem; objective functional; control strategy PDF BibTeX XML Cite \textit{Q. Zhu} et al., Appl. Math. Comput. 218, No. 23, 11613--11619 (2012; Zbl 1278.49045) Full Text: DOI References: [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: 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: 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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.