Stochastic fractional order model for the computational analysis of computer virus

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dc.contributor.authorAyaz, Armughan
dc.contributor.authorRehamn, Muhammad Aziz Ur
dc.contributor.authorRafiq, Muhammad
dc.contributor.authorIqbal, Zafar
dc.contributor.authorAhmed, Nauman
dc.contributor.authorAkgul, Ali
dc.contributor.authorCeesay, Baboucarr
dc.date.accessioned2026-03-14T11:48:51Z
dc.date.available2026-03-14T11:48:51Z
dc.date.issued2025
dc.departmentSiirt Üniversitesi
dc.description.abstractThis work presents a novel mathematical framework for analyzing the propagation dynamics of computer viruses by formulating a fractional-order model. The classical integer-order differential model of computer virus spread is reformulated using Caputo fractional derivatives, yielding a fractional computer virus model that captures the inherent memory and persistence characteristics of digital infection processes. A comprehensive analytical investigation is conducted, including the verification of fundamental properties such as positivity and boundedness of the system. The existence and uniqueness of the solutions are rigorously established using the Banach fixed-point theorem. The model exhibits two equilibrium states whose global stability is thoroughly analyzed. To incorporate the stochastic behavior of networked systems, such as fluctuating traffic, random user activity, and unpredictable system responses, the fractional computer virus model is extended into a stochastic fractional computer virus model by introducing white noise terms. Unlike previous studies, which often neglect the combined impact of stochasticity and memory, this research provides a rigorous treatment of both, ensuring the unique solvability of the stochastic fractional computer virus model. A Grunwald-Letnikov-based nonstandard finite difference scheme is developed to obtain reliable numerical approximations of the model while preserving essential qualitative features such as solution positivity and boundedness. Numerical simulations, based on realistic test scenarios, support the theoretical findings and illustrate the complex dynamics introduced by both fractional-order behavior and stochastic influences. This study provides a robust and realistic framework for understanding and predicting the spread of computer viruses in complex digital environments.
dc.identifier.doi10.1038/s41598-025-10330-5
dc.identifier.issn2045-2322
dc.identifier.issue1
dc.identifier.pmid41028801
dc.identifier.scopus2-s2.0-105017771801
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1038/s41598-025-10330-5
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8986
dc.identifier.volume15
dc.identifier.wosWOS:001586155000020
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.indekslendigikaynakPubMed
dc.language.isoen
dc.publisherNature Portfolio
dc.relation.ispartofScientific Reports
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260310
dc.subjectFractional Differential Equation
dc.subjectComputer Virus
dc.subjectLyapunov Function
dc.subjectGl Nsfd Scheme
dc.subjectStochastic Process
dc.subjectLocal And Global Stability
dc.titleStochastic fractional order model for the computational analysis of computer virus
dc.typeArticle

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