Propagation of Computer Virus via a Modified Sira Model

  • Peter M. Achuba
  • Bamidele Oluwade Department of Mathematical Science, Kogi State University, Kogi state
Keywords: Computer virus, SIS, SIR, SIRA model, Antivirus Software, First Order ODE, Basal Reproduction

Abstract

Computer viruses are capable of unleashing their effects (payloads) in two ways: either by means of the system users’ action (e.g. Trojan horses) or by means of the encoded destructive sequence which enable it to infect systems without the aid of a system user (a typical example is a computer viral worm). The implication of the above is that computer systems can be latent infected before they become infectious. In this paper, the aim is to determine the behavior of computer viruses in a computer network which has fully functioning computer antivirus software installed on it. The model proposed is a modification of the SIRA (Susceptible, Infected, Recovered and Antidotal) model to include latent infected computers in the network which leads to the SLIRA (Susceptible, Latent infected, Infected, Recovered and Antidotal) model. In the model, some particular behaviors which some computer viruses exhibit (which lead to latent infection of computers by viruses) are considered. Thereafter, the disease-free, endemic equilibrium points, basal reproduction rate and stability conditions are sought. It can be inferred that every networked organization should have computer antivirus software installed on its system since whenever the total population of computers on the network is antidotal we achieve asymptotic stability.

References

[1] Cohen, Frederick B. (1990), A Short Course on Computer Viruses, ASP
Press, Pittsburgh, USA.
[2] Denning, P.J., (1990), Computer Under Attack, Addison-Wesley,
Reading, Mass.
[3] Kephart, J.O., and White, S.R. (1991), Directed Graph Epidemiological
models of computer viruses. In: IEEE Symposium on Security and
Privacy. pg343-361.
[4] Li, Chuandong; Hu, Wenfeng and Huang, Tingwen (2014), Stability
and Bifurcation Analysis of a Modified Epidemic Model for Computer
Viruses, Mathematical Problems in Engineering;
https://www.hindawi.com/journals/mpe/2014/784684
(http://dx.doi.org/10.1155/2014/784684)
[5] Zhang, Chunming; Yang, Xiaofan and Zhu, Qingy (2011), An Optimal
Control Model for Computer Viruses, Journal of Information &
Computational Science, 8:13, 2587 – 2596
[ 6] Han, X and Tan, Q. L. (2010), Dynamical Behaviour of Computer
Virus on Internet, Applied Mathematics and Computation, 217, no.6, 2520
– 2526
[7] Serazzi, Giuseppe and Zanero, Stefano (2004), Computer Virus
Propagation Models, Dipartmento di Elettronica e Informazione,
Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy
[8] Piqueira, J.R.C.; Navarro, B.F.; Monteiro, L.H.A.(2005),
Epidemiological Models Applied to Viruses in Computer
Networks, Journal of Computer Science, 1(1),31–34
Published
2020-05-03
How to Cite
Achuba, P. M., & Oluwade, B. (2020). Propagation of Computer Virus via a Modified Sira Model. Ilorin Journal of Computer Science and Information Technology, 2(1), 95 - 107. Retrieved from https://iljcsit.com.ng/index.php/ILJCSIT/article/view/21