The impact of quarantine strategies on malware dynamics in a network with heterogeneous immunity
Abstract
In this paper, we investigate the influence of two types of isolation on malware propagation within a computer network. Model 1 proposes the network quarantine strategy, where infected computers are fully disconnected from the network. As for model 2, the control strategy is the anti-virus software quarantine, where infected files in a computer are contained in an isolation folder. Both models consider the aspect of heterogeneous immunity, that is, weak and strong immunization of computers in a network. Analytical examinations produced a virus-free equilibrium and an endemic equilibrium for each model. It has been observed that the quarantine reproduction number Rq plays an essential role in the existence and stability of the equilibrium points. Furthermore, numerical simulations are accomplished to substantiate the qualitative results. Finally, a sensitivity analysis is executed to specify the dominant parameters on Rq. It is found that the performance of network quarantine is better than anti-virus software quarantine in controlling malware propagation.
Keyword : computer malware, propagation model, quarantine, heterogeneous immunity, stability
How to Cite
Al-Tuwairqi, S. M., & Bahashwan, W. S. (2022). The impact of quarantine strategies on malware dynamics in a network with heterogeneous immunity. Mathematical Modelling and Analysis, 27(2), 282–302. https://doi.org/10.3846/mma.2022.14391
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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C. Gan, X. Yang and Q. Zhu. Global stability of a computer virus propagation model with two kinds of generic nonlinear probabilities. Abstract and Applied Analysis, 2014, 2014. https://doi.org/10.1155/2014/735327
C. Gan, X. Yang, Q. Zhu and W. Liu. A propagation model of computer virus with nonlinear vaccination probability. Commun Nonlinear Sci Numer Simulat, 19:92–100, 2014. https://doi.org/10.1016/j.cnsns.2013.06.018
Z. Hu, H. Wang, F. Liao and W. Ma. Stability analysis of a computer virus model in latent period. Chaos, Solitons & Fractals, 75:20–28, 2015. https://doi.org/10.1016/j.chaos.2015.02.001
J. O. Kephart and S. R. White. Directed-graph epidemiological models of computer viruses. IEEE Symposium on Security and Privacy, pp. 343–358, 1991.
N.H. Khanh. Dynamical analysis and approximate iterative solutions of an antidotal computer virus model. Int. J. Appl. Comput. Math, 3:S829–S841, 2017. https://doi.org/10.1007/s40819-017-0385-6
S. Koonprasert and N. Channgam. Global stability and sensitivity analysis of SEIQR worm virus propagation model with quarantined state in mobile internet. Global Journal of Pure and Applied Mathematics, 13:3833–3850, 2017.
M. Kumar, B.K. Mishra and T.C. Panda. Stability analysis of a quarantined epidemic model with latent and breaking-out over the internet. International Journal of Hybrid Information Technology, 8(7):133–148, 2015. https://doi.org/10.14257/ijhit.2015.8.7.12
A. Lanz, D. Rogers and T.L. Alford. An epidemic model of malware virus with quarantine. Journal of Advances in Mathematics and Computer Science, 33(4):1–10, 2019. https://doi.org/10.9734/jamcs/2019/v33i430182
D. Li, J. Chen, B.L. Jianwei, B. Qianhong Wu and Weiran Liu. Modeling and hopf bifurcation analysis of benign worms with quarantine strategy. Springer International Publishing, 2:103–118, 2017.
W. Liu, C. Liu, X. Liu, S. Cui and X. Huang. Modeling the spread of malware with the influence of heterogeneous immunization. Applied Mathematical Modelling, 40:3141–3152, 2016. https://doi.org/10.1016/j.apm.2015.09.105
M. Martcheva. An Introduction to Mathematical Epidemiology. Springer, 2015. https://doi.org/10.1007/978-1-4899-7612-3
B. K. Mishra and D. K. Saini. SEIRS epidemic model with delay for transmission of malicious objects in computer network. Applied Mathematics and Computation, 188(2):1476–1482, 2007. https://doi.org/10.1016/j.amc.2006.11.012
B.K. Mishra and N. Jha. SEIQRS model for the transmission of malicious objects in computer network. Applied Mathematical Modelling, 34(3):710–715, 2010. https://doi.org/10.1016/j.apm.2009.06.011
M.R. Parsaei, R. Javidan, N. Shayegh Kargar and H. Saberi Nik. On the global stability of an epidemic model of computer viruses. Theory in Biosciences, 136(34):169–178, 2017. https://doi.org/10.1007/s12064-017-0253-2
L. Perko. Differential Equations and Dynamic Systems. Springer Verlag, 1991. https://doi.org/10.1007/978-1-4684-0392-3
J. Piqueira and C. Batistela. Considering quarantine in the SIRA malware propagation model. Mathematical Problems in Engineering, 2019, 2019. https://doi.org/10.1155/2019/6467104
J. Piqueira, A. deVasconcelos, C. Gabriel and V. Araujo. Dynamic models for computer viruses. Computers and Security, 27(7-8):355–359, 2008. https://doi.org/10.1016/j.cose.2008.07.006
Y.S. Rao, P.K. Nayak, H. Saini and T.C. Panda. Behavioral modeling of malicious objects in a highly infected network under quarantine defence. International Journal of Information Security and Privacy, 13(1):17–29, 2019. https://doi.org/10.4018/IJISP.2019010102
R. Upadhyay, S. Kumari and A. Misra. Modeling the virus dynamics in computer network with SVEIR model and nonlinear incident rate. Journal of Applied Mathematics and Computing, 54(1-2):485–509, 2017. https://doi.org/10.1007/s12190-016-1020-0
R. Upadhyay and P. Singh. Modeling and control of computer virus attack on a targeted network. Physica A: Statistical Mechanics and its Applications, 538:122617, 2020. https://doi.org/10.1016/j.physa.2019.122617
F. Wang, Y. Zhang, C. Wang, J. Ma and S.J. Moon. Stability analysis of a SEIQV epidemic model for rapid spreading worms. Computers and Security, 29(4):410–418, 2010. https://doi.org/10.1016/j.cose.2009.10.002
J. Watmough and P. van den Driessche. Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180:29–48, 2002. https://doi.org/10.1016/S00255564(02)00108-6
L. Yang and X. Yang. An epidemic model of computer viruses with vaccination and generalized nonlinear incidence rate. Physica A, 392:6523–6535, 2013.
L. Yang and X. Yang. The impact of nonlinear infection rate on the spread of computer virus. Nonlinear Dynamics, 82(1-2):85–95, 2015. https://doi.org/10.1007/s11071-015-2140-z
L. Yang, X. Yang, Q. Zhu and L. Wen. A computer virus model with graded cure rates. Nonlinear Analysis: Real World Applications, 14:414–422, 2013. https://doi.org/10.1016/j.nonrwa.2012.07.005
Y. Yao, X. w. Xie, H. Guo, F. x. Gao and G. Fu. The worm propagation model with dual dynamic quarantine strategy. Communications in Computer and Information Science, 135(PART 2):497–502, 2011. https://doi.org/10.1007/9783-642-18134-4_79
C.C. Zou, W. Gong and D. Towsley. Worm propagation modeling and analysis under dynamic quarantine defense. In Proceedings of the 2003 ACM Workshop on Rapid Malcode, WORM 03, pp. 51–60, New York, NY, USA, 2003. Association for Computing Machinery.