A Fractional Mathematical Model for Controlling and Understanding Transmission Dynamics in Computer Virus Management Systems

Akeem Olarewaju Yunus, Morufu Oyedunsi Olayiwola, Adewole Mukaila Ajileye

Abstract


The constant danger of computer viruses and malware makes it difficult to safely simulate the management of computer systems over time for both networks and individual users. The present study proposes a novel six-compartment fractional model that builds on existing classical frameworks and examines the existence and uniqueness of its solution, indicating that it is both mathematically and biologically well-posed. Additionally, we compute the fundamental reproduction number R0 and use sensitivity analysis to investigate the impact of various factors on the model's behavior. The Laplace Adomian Decomposition Method is employed for numerical analysis, and its findings have the potential to transform computer security and network management by providing robust countermeasures and eradication tactics. The complex properties of the fractional-order model are further explored by examining the memory effect of fractional order on system dynamics. The research findings offer valuable insights for virus managers in developing and implementing effective management methods and can successfully prevent the spread of computer viruses by leveraging these discoveries. In conclusion, this study provides significant insights and solutions for protecting the integrity of digital domains and network infrastructure.


Keywords


Computer viruses; Malware; Caputo fractional order derivative; Mathematical modeling; Laplace-Adomian decomposition method; Simulation analysis

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References


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DOI: https://doi.org/10.37905/jjbm.v5i2.25956

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