HD-SEIRS Malware Propagation Model in Heterogeneous Complex Networks

Document Type : Computer Article

Authors

1 PhD Student, Department of Computer Science, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

2 Associate Professor, Department of Computer Science, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In recent years, the Internet has become part of the requirements of human life. With the widespread use of the Internet, the Web, and online social networks, the number of vulnerabilities and security threats has increased significantly. Various types of malwares (worms and viruses) have become a major threat to the security of systems and networks. In this regard, researchers are looking for ways to identify malware and fight against them. One of the methods used in this field is to model the malware propagation in order to identify and combat malware by modeling its behavior. In this article, a malware propagation model based on the propagation of epidemic diseases in a heterogeneous network structure, considering the devices connected to the network and the Internet, is introduced. Modeling is done based on the Susceptible-Exposed-Infected-Recovered epidemic model for devices and Internet networks. The results show that the speed of malware propagation in the proposed HD-SEIRS model is significantly reduced compared to the SEIR model. Also, in this article, the basic reproduction ratio (R_0 )  is calculated for the proposed model and the effect of parameter changes on the proposed model is investigated.

Keywords

Main Subjects

References

[1] Y. Ye, T. Li, D. Adjeroh, and S.S. Iyengar. “A survey on malware detection using data mining techniques.” ACM Computing Surveys (CSUR) 50, no. 3 (2017): 1-40.
[2] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.U. Hwang. “Complex networks: Structure and dynamics.” Physics Reports 424, no. 4-5 (2006): 175-308.
[3] A. M. del Rey. “Mathematical modeling of the propagation of malware: a review.” Security and Communication Networks 8, no. 15 (2015): 2561-2579.
[4] L. Zhao, Q. Wang, J. Cheng, Y. Chen, J. Wang, and W. Huang. “Rumor spreading model with consideration of forgetting mechanism: A case of online blogging LiveJournal.” Physica A: Statistical Mechanics and its Applications 390, no. 13 (2011): 2619-2625.
[5] K. Sznajd-Weron, and J. Sznajd. “Opinion evolution in closed community.” International Journal of Modern Physics C 11, no. 06 (2000): 1157-1165.
[6] J. Yang, C. Yao, W. Ma, and G. Chen. “A study of the spreading scheme for viral marketing based on a complex network model.” Physica A: Statistical Mechanics and its Applications 389, no. 4 (2010): 859-870.
[7] M.T. Signes-Pont, A. Cortés-Castillo, H. Mora-Mora, and J. Szymanski. “Modelling the malware propagation in mobile computer devices.” Computers & Security 79 (2018): 80-93.
[8] W.O. Kermack, and A.G. McKendrick. “A contribution to the mathematical theory of epidemics.” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 115, no. 772 (1927): 700-721.
[9] E. Kuhl, and E. Kuhl. “The classical SIR model.” Computational Epidemiology: Data-Driven Modeling of COVID-19 (2021): 41-59.
[10] R. Almeida. “Analysis of a fractional SEIR model with treatment.” Applied Mathematics Letters, 84 (2018): 56-62.
[11] S. Hosseini. “Defense against malware propagation in complex heterogeneous networks.” Cluster Computing,  24 (2021): 1199-1215.
[12] J.R.C. Piqueira, M.A. Cabrera, and C.M. Batistela. “Malware propagation in clustered computer networks.” Physica A: Statistical Mechanics and its Applications, 573 (2021): 125958.
[13] B.K. Mishra, A.K. Keshri, D.K. Mallick, and B.K. Mishra. “Mathematical model on distributed denial of service attack through Internet of things in a network.” Nonlinear Engineering 8, no. 1 (2019): 486-495.
[14] X. Zhu, and J. Huang. “Malware propagation model for cluster-based wireless sensor networks using epidemiological theory.” PeerJ Computer Science 7 (2021): 728-738.
[15] C. Nwokoye, and I.I. Umeh. “The SEIQR–V model: On a more accurate analytical characterization of malicious threat defense.” Int. J. Inf. Technol. Comput. Sci 9, no. 12 (2017): 28-37.
[16] P. Van den Driessche. "Reproduction numbers of infectious disease models." Infectious Disease Modelling 2, no. 3 (2017): 288-303.
[17] J.A. Wattis. “An introduction to mathematical models of coagulation–fragmentation processes: a discrete deterministic mean-field approach.” Physica D: Nonlinear Phenomena 222, no. 1-2 (2006): 1-20.
 
Journal of Modeling in Engineering
Volume 22, Issue 79
November 2024
Pages 17-28

Files

History

  • Receive Date: 13 January 2023
  • Revise Date: 10 April 2023
  • Accept Date: 03 April 2024

Share

How to cite

Statistics