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Types of Nodes and Centrality Measures in Networks Read chapter Read first chapter

2019 | OriginalPaper | Chapter

8. Optimal Impulse Control of SIR Epidemics Over Scale-Free Networks

Authors : Vladislav Taynitskiy, Elena Gubar, Quanyan Zhu

Published in: Game Theory for Networking Applications

Publisher: Springer International Publishing

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Abstract

Recent wide spreading of Ransomware has created new challenges for cybersecurity over large-scale networks. The densely connected networks can exacerbate the spreading and makes the containment and control of the malware more challenging. In this work, we propose an impulse optimal control framework for epidemics over networks. The hybrid nature of discrete-time control policy of continuous-time epidemic dynamics together with the network structure poses a challenging optimal control problem. We leverage the Pontryagin’s minimum principle for impulsive systems to obtain an optimal structure of the controller and use numerical experiments to corroborate our results.

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previous chapter Enhanced Design of Stochastic Defense System with Mixed Game Strategies
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Literature
1.
Agur, Z., Cojocaru, L., Mazor, G., Anderson, R.M., Danon, Y.L.: Pulse mass measles vaccination across age cohorts. Proc. Natl. Acad. Sci. USA 90, 11698–11702 (1993)CrossRef
2.
3.
Blaquière, A.: Impulsive optimal control with finite or infinite time horizon. J. Optim. Theory Appl. 46, 431–439 (1985)MathSciNetCrossRef
4.
Chahim, M., Harti, R., Kort, P.: A tutorial on the deterministic impulse control maximum principle: necessary and sufficient optimality conditions. Eur. J. Oper. Res. 219, 18–26 (2012)MathSciNetCrossRef
5.
Dykhta, V.A., Samsonyuk, O.N.: A maximum principle for smooth optimal impulsive control problems with multipoint state constraints. Comput. Math. Math. Phys. 49, 942–957 (2009)MathSciNetCrossRef
6.
Fu, X., Small, M., Walker, D.M., Zhang, H.: Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. Phys. Rev. E. 77(3), 036113 (2008)MathSciNetCrossRef
7.
Gubar, E., Zhu, Q.: Optimal control of influenza epidemic model with virus mutations. In: Proceedings 12th Biannual European Control Conference, pp. 3125–3130. IEEE Control Systems Society, New York (2013)
8.
Gubar, E., Kumacheva, S., Zhitkova, E., Porokhnyavaya, O.: Impact of propagation information in the model of tax audit. In: Recent Advances in Game Theory and Applications. Static and Dynamic Game Theory: Foundations and Applications, Switzerland, pp. 91–110 (2015)
9.
Gubar, E., Zhu, Q., Taynitskiy, V.: Optimal control of multi-strain epidemic processes in complex networks. In: Game Theory for Networks. GameNets 2017. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol. 212, pp. 108–117. Springer, Cham (2017)
10.
Kharraz, A., Robertson, W., Balzarotti, D., Bilge, L., Kirda, E.: Cutting the gordian knot: a look under the hood of ransomware attacks. In: International Conference on Detection of Intrusions and Malware, and Vulnerability Assessment, pp. 3–24. Springer, Berlin (2015)
11.
Luo, X., Liao, Q.: Ransomware: a new cyber hijacking threat to enterprises. In: Handbook of Research on Information Security and Assurance, pp. 1–6. IGI Global, Hershey (2009)
12.
Pastor-Satorras, R., Vespignani A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86(14), 3200 (2001)CrossRef
13.
Sethi, S.P., Thompson, G.L.: Optimal Control Theory: Applications to Management Science and Economics. Springer, Berlin (2006)MATH
14.
Taynitskiy, V.A., Gubar, E.A., Zhitkova, E.M.: Optimization of protection of computer networks against malicious software. In: Proceedings of International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference) (2016)
15.
Taynitskiy, V., Gubar, E., Zhu Q.: Optimal impulse control of bi-virus SIR epidemics with application to heterogeneous internet of things. In: Constructive Nonsmooth Analysis and Related Topics. Abstracts of the International Conference. Dedicated to the Memory of Professor V.F. Demyanov, pp. 113–116 (2017)
Metadata
Title
Optimal Impulse Control of SIR Epidemics Over Scale-Free Networks
Authors
Vladislav Taynitskiy
Elena Gubar
Quanyan Zhu
Copyright Year
2019
Book
Game Theory for Networking Applications

Print ISBN: 978-3-319-93057-2

Electronic ISBN: 978-3-319-93058-9

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-93058-9_8