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Journal of Information and Optimization Sciences

(Since 1980)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

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Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

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Journal of Information and Optimization Sciences
Open Access Research Article

Computer virus propagation models: A mathematical review

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pp. 1043–1055Vol. 44Issue 6September 2023DOI: 10.47974/JIOS-1426XML
Published Online:
11 Nov 2023
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1426
Pages:
1043–1055

Abstract

The physical world has come together by the connection of devices on an extra ordinary level through internet of things. This forms a very complex and dynamic network system and number of heterogeneous device are connected with each other. Physical objects connected in a network, interchange data with other connected devices via communication networks. The data interchange is very helpful in a number of domains in day-to-day life of human beings. Security of connection and data is one of the major challenges for this connection and communication. A computer virus is a potential threat resulting into the damage of connected devices into a network and the data. Epidemic models, similar with biological virus spread models, are widely studied to investigate the behaviour of computer viruses. The primary objective of the article is to categorize a number of computer virus propagation model, so that their comparative studies becomes easier. This article contains a qualitative review and categorization of computer virus propagation models into three categories, namely, compartment model, network model and stochastic model. The study is helpful to further investigate the virus propagation mechanism and to control them optimally.

Keywords

Delay differential equationEpidemic modelNetwork modelSIR modelSIS modelStochastic model

Subject Classifications

68M25 Computer security

References

[1] A. Lohachab & B. Karambir, “Critical Analysis of DDoS; An Emerging Security Threat Over IoT Networks”, J. Commun. Inf. Netw. vol. 3, pp. 57-78, (2018).
[2] A. Singh, A. K. Awasthi, K. Singh & P. K. Srivastava, “Modeling and Analysis of Worm Propagation in Wireless Sensor Networks”, Wireless Pers Commun,, vol. 98, pp. 2535-2551, (2018).
[3] A. Raza, M. S. Arif, M. Rafiq, M. Bibi, M. Naveed, M. U. Iqbal, Z. Butt, H. A. Naseem and J. N. Abbasi, “Numerical Treatment for Stochastic Computer Virus Model”, Computer Modeling in Engineering & Sciences, vol. 120, no. 2, pp. 445-465, (2019).
[4] B. K. Mishra and G. M. Ansri, “Differential Epidemic Model of Virus and Worms in Computer Network”, International Journal of Network Security, vol. 14, no. 3, pp. 149-155, (2012).
[5] B. Zhu, S. Deng, Y. Xu, X. Yuan & Z. Zhang, “Information Security Risk Propagation Model Based on the SEIR Infectious Disease Model for Smart Grid”, information, vol. 10, pp. 1-17, (2019).
[6] C. Gan, X. Yang, W. Liu & Q. Zhu, “A Propagation Model of Computer Virus with Nonlinear Vaccination Probability”, “Communications in Nonlinear Science and Numerical Simulation”, vol. 19, pp. 92-100, (2014).
[7] C. Gan, X. Yang, W. Liu & Q. Zhu, “Propagation of Computer Virus both Across the Internet and External Computers: A Complex-Network Approach”, “Communications in Nonlinear Science and Numerical Simulation”, vol. 19, pp. 2785-2792, (2014).
[8] C. Li, W. Hu and T. Huang, “Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses”, Mathematical Problems in Engineering, vol. 2014, ID. 784684, pp. 1-14, (2014).
[9] C. Zhang, Y. Zhao, Y. Wu and S. Deng, “A Stochastic Dynamic Model of Computer Viruses”, Discrete Dynamics in Nature and Society, vol. 2012, article ID. 264874, pp. 1-16, (2012).
[10] H. Chen and Y. Huang, “Study of Computer Virus Propagation Models in Networks based on the Stability and Control”, Bio-Technology: An Indian Journal, vol. 10, issue: 13, pp. 7417-7421, (2014).
[11] J. Amador and J. R. Artalejo, “Stochastic Modeling of Computer Virus Spreading with Warning Signals”, Journal of the Franklin Institute, vol. 350, pp. 1112-1138, vol. (2013).
[12] J. C. Wierman and D. Marchette, “Modeling Computer Virus Prevalence with a Susceptible-Infected-Susceptible Model with Reintroduction”, Computational Statistics & Data Analysis, vol. 45, pp. 3-23, (2004).
[13] J. N. C. Goncalves, H. S. Rodrigues, M T. T. Monterio, “Optimal Control Measures for a Susceptible-Carrier-Infectious-Recovered-Susceptible Malware Propagation Model”, Optimal Control Applications and Methods, vol. 40, no. 4, pp. 691-702,(2019).
[14] J. Ren, X.Yang, Q. Zhu, L.X. Yang and C. Zhang, “A Novel Computer Virus and Its Dynamics”, Nonlinear Analysis:: Real World Applications, vol. 13, pp. 376-384, (2012).
[15] J. Zhou, X. Hua & Chen, “Analysis and Simulation of Computer Virus Propagation Models in the Network Environment”, Advanced Materials Research, vol. 204, pp. 433-436, (2011).
[16] K. Sha, W. T. Wei, A. Yang, Z. Wang & W. Shi, “On Security Challenges and Open Issues in Internet of Thing”, Future Generation Computer Systems, vol. 83, pp. 326-337, (2018).
[17] L. X. Yang & X. Yang, “A New Epidemic Model of Computer Viruses”, “Communications in Nonlinear Science and Numerical Simulation”, vol. 19.pp. 1935-1944, (2014).
[18] L. X. Yang, X. Yang, L. Wen and J. Liu, “A Novel Computer Virus Propagation Model and Its Dynamics”, International Journal of Computer Mathematics, vol. 89, no. 17, pp. 2307-2314, (2013).
[19] M. Peng, X. He, J. Huang and T. Dong, “Modeling Computer Virus and its Dynamics”, Mathematical Problems in Engineering, vol. 2013, ID. 842614, pp. 1-5, (2013).
[20] M. S. S. Khan, “A Computer Virus Propagation Model Using Delay Differential Equations with Probabilistic Contagion and Immunity”, International Journal of Computer Networks & Communications, vol. 6, no. 5, pp. 111-128, (2014).
[21] P. K. Srivastava, R. P. Ojha, K. Sharma, S. Awasthi and G. Sanyal, “Effect of Quarantine and Recovery on Infectious Nodes in Wireless Sensor Network”, International Journal of Sensors, Wireless Communications and Control, vol. 2018, no. 8, pp. 26-36, (2018).
[22] P. Shahrear, A. K. Chakraborty, M. A. Islam and U. Habiba, “Analysis of Computer Virus Propagation Based on Compartmental Model”, Applied and Computational Mathematics, vol. 12, no. 1-2, pp. 12-21, (2018).
[23] R. Zarin, H. Khaliq, A. Khan, D. Khan, A. Agkul and U. W. Humphries, “Deterministic and Fractional Modeling of a Computer Virus Propagation ”, Results in Physics, vol.33, ID. 105130, pp. 1-13, (2022).
[24] S. K. Choudhary, “Emergence of Power Law Behavior in Threshold based Neuron Model with Stochastic Membrane Constant”, International Journal of Applied Mathematics and Informatics, vol. 12, pp. 21-28, (2018).
[25] S. K. Choudhary, K. Singh and V. K. Solanki, “Spiking Activity of a LIF Neuron in Distributed Delay Framework”, International Journal of Interactive Multimedia and Artificial Intelligence, vol. 3, no. 7, pp. 70-76, (2016).
[26] S. K. Choudhary and K. Singh, “Temporal Information Processing and Stability Analysis of the MSHN Neuron Model in DDF”, International Journal of Interactive Multimedia and Artificial Intelligence, vol. 4, no. 2, pp. 39-45, (2016).
[27] S. K. Choudhary and V. K. Solanki, “LIF Neuron with Hypo-exponential Distributed Delay: Emergence of Unimodal, Bimodal, Multimodal ISI Distribution with Long Tail”, Recent Patent on Engineering, vol. 12, pp. 21-28, (2020). 
[28] T. Korkiatsakul, S. Koonprasert and N. Neamprem, “Analytical Solutions of Computer Virus Propagation Model with Anti-virus Software and Time Dependent Connecting Network in Caputo Fractional Derivative Sense”, International Journal of Engineering Research and Technology, vol. 12, no. 12, pp. 3006-3017, (2019).
[29] W. C. Yen, E. Lin and C. L. Huang, “Predicting Spread Probability of Learning-Effect Computer Virus”, Coevolving Spreading Dynamics of Complex Networks, vol. 2021, ID. 6672630, pp. 1-17, (2021).
[30] W. Liu & S. Zhong, “Web Malware Spread Modelling and Optimal Control Strategies”, Sci Rep, vol. 7, no. 42308, pp. 1-19, (2017).
[31] Y. Chu, W. Xia and Z. Wang, “A Delay Computer Virus Model with Nonlinear Incidence Rate”, Systems Science & Control Engineering, vol. 7, no. 1, pp. 389-406, (2019).
[32] Z. Zhang, S. Kumari and R. K. Upadhyay, “A delayed e-Epidemic SLBS Model for Computer Virus”, Adv Differ Equ, vol. 2019, ID. 414, pp. 1-24, (2019).
[33] C. Gan, Q. Feng, Q. Zhu, Z. Zhang, Y. Zhang and Y. Xiang, “Analysis of Computer Virus Propagation Behaviors over Complex Networks: A Case Study of Oregon Routing Network,,” Nonlinear Dyn, vol. 100, pp. 1725-1740, (2020).
[34] Kar, A. K., & Aswani, R. (2021). How to differentiate propagators of information and misinformation–Insights from social media analytics based on bio-inspired computing. Journal of Information and Optimization Sciences, 42(6), 1307-1335.
[35] Kumar, A., Singh, K., & Khan, T. (2021). L-RTAM: Logarithm based reliable trust assessment model for WBSNs. Journal of Discrete Mathematical Sciences and Cryptography, 24(6), 1701-1716.
[36] Kumar, A., Singh, K., Khan, T., Ahmadian, A., Saad, M. H. M., & Manjul, M. (2021). ETAS: An efficient trust assessment scheme for BANs. IEEE Access, 9, 83214-83233.
[37] Shariq, M., Singh, K., Lal, C., Conti, M., & Khan, T. (2022). ESRAS: An efficient and secure ultra-lightweight RFID authentication scheme for low-cost tags. Computer Networks, 217, 109360.
[38] Khan, T., & Singh, K. (2019). Resource management based secure trust model for WSN. Journal of Discrete Mathematical Sciences and Cryptography, 22(8), 1453-1462.
[39] Singh, A., & Bist, A. S. (2020). OSX malware detection: Challenges and solutions. Journal of Information and Optimization Sciences, 41(2), 379-385.

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