DYNAMICAL ASPECTS OF A DELAYED COMPUTER VIRUSES MODEL WITH HORIZONTAL AND VERTICAL DISSEMINATION OVER INTERNET

Jian Ding, Nadia Gul, Guiyun Liu and Tareq Saeed
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Jian Ding: School of Control Technology, Wuxi Institute of Technology, Wuxi 214121, P. R. China
Nadia Gul: ��Department of Mathematics, Shaheed Benazir Bhutto Women University, Peshawar 25000, Khyber Pakhtunkhwa, Pakistan
Guiyun Liu: ��School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, P. R. China
Tareq Saeed: �Financial Mathematics and Actuarial Science, (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-14

Abstract: In this paper, to explore propagation dynamics of computer viruses over the Internet, a delayed SLBRS (susceptible–latent–breaking-out–recovering–susceptible) model of computer viruses considering horizontal and vertical dissemination over Internet is studied. The basic reproduction number at which computer viruses are prone to be extinct or continue to exist is calculated with the help of the next generation matrix method. By choosing the time delay because of processing time consumed to recover the breaking-out computers as bifurcation parameter, a series of sufficient criteria for experience of Hopf bifurcation are derived. Specially, optimal strategies to control dissemination of computer viruses over Internet are established. Finally, numerical simulations for certificating correctness of our theoretical findings are carried out. The findings show that the exhibition of Hopf bifurcation has an important impact on prediction and control of the propagation of computer viruses over the Internet.

Keywords: Delay; Hopf Bifurcation; Optimal Strategies; SLBRS Model; Stability (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400923

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