A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model

A computer network can detect potential viruses through the use of kill signals, thereby minimizing the risk of virus propagation. In the realm of computer security and defensive strategies, computer viruses play a significant role. Understanding of their spread and extension is a crucial component....

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 2; pp. 3195 - 3210
Main Authors Singh, Jagdev, Kumar, Jitendra, kumar, Devendra, Baleanu, Dumitru
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
collocation method
epidemiological model
jacobi polynomial
operational matrix of differentiation
sira
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Summary:A computer network can detect potential viruses through the use of kill signals, thereby minimizing the risk of virus propagation. In the realm of computer security and defensive strategies, computer viruses play a significant role. Understanding of their spread and extension is a crucial component. To address this issue of computer virus spread, we employ a fractional epidemiological SIRA model by utilizing the Caputo derivative. To solve the fractional-order computer virus model, we employ a computational technique known as the Jacobi collocation operational matrix method. This operational matrix transforms the problem of arbitrary order into a system of nonlinear algebraic equations. To analyze this system of arbitrary order, we derive an approximate solution for the fractional computer virus model, also considering the Vieta Lucas polynomials. Numerical simulations are performed and graphical representations are provided to illustrate the impact of order of the fractional derivative on different profiles.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024155