INVESTIGATING VIRUS SPREAD ANALYSIS IN COMPUTER NETWORKS WITH ATANGANA–BALEANU FRACTIONAL DERIVATIVE MODELS

Imtiaz Ahmad, Asmidar Abu Bakar, Hijaz Ahmad, Aziz Khan and Thabet Abdeljawad
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Imtiaz Ahmad: Institute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional, Kajang, Selangor, Malaysia
Asmidar Abu Bakar: Institute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional, Kajang, Selangor, Malaysia†Department of Computing, College of Computing and Informatics (CCI), Universiti Tenaga Nasional (UNITEN), Kajang, Selangor 43000, Malaysia
Hijaz Ahmad: ��Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Aziz Khan: �Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia
Thabet Abdeljawad: �Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia¶Department of Medical Research, China Medical University, Taichung 40402, Taiwan∥Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, South Korea**Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Garankuwa, Medusa 0204, South Africa

FRACTALS (fractals), 2024, vol. 32, issue 07n08, 1-17

Abstract: This paper proposes a mathematical model to investigate the dynamic behaviors of a modified computer virus model using the Atangana–Baleanu fractional derivative in the Caputo sense, aiming to elucidate the connection between its parameters and network attributes. By introducing a relatively new numerical method, we address the memory-dependent and nonlocal features of the system. The existence and uniqueness of the model’s solution are confirmed. To explore solution trajectories and assess the impact of various input factors on computer virus dynamics, we employ an efficient numerical technique. Our simulations provide insights into the consequences of fractional order, anti-virus measures, asymptotic fraction, damage rate, and removal rate in the system. These findings illuminate the relationships between model parameters, facilitating the design of networks that minimize the risk of virus outbreaks and prevent future cyber threats. By identifying critical factors involved in the progression of viruses, these results enable the development of more effective defense mechanisms.

Keywords: Atangana–Baleanu Fractional Mathematical Model; Computer Virus; Efficient Energy Usage; Sustainable Network Environments; Anti-Virus Measures (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400437

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