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An Investigation Through Stochastic Procedures for Solving the Fractional Order Computer Virus Propagation Mathematical Model with Kill Signals

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Abstract

In this study, the numerical investigations through the stochastic procedures for solving a class of fractional order (FO) computer virus propagation (CVP) mathematical model with kill signals (KS), i.e., CVP-KS is presented. The KS gets alert about those viruses, which can be infected through the computer system to decrease the virus propagation danger. The mathematical model of the CVP-KS is based on the SEIR-KS model. The focus of these investigations is to present the numerical solutions of the FO-SEIR-KS model using the sense of Levenberg–Marquardt backpropagation scheme (LMBS) together with the neural networks (NNs), i.e., LMBS-NNs. The use of the one dynamic of the other makes the model nonlinear. Three different FO values have been used to check the performances of the designed scheme for this FO-SEIR-KS nonlinear mathematical model. The statics used in this study is 80%, 10% and 10% for training, testing and certification for solving the FO-SEIR-KS nonlinear mathematical model. The numerical simulations are performed through the stochastic LMBS-NNs scheme for solving the FO-SEIR-KS nonlinear mathematical model. The obtained results will be compared with the design of database reference solutions based on the Adams–Bashforth–Moulton. In order to accomplish the validity, capability, consistency, competence and accuracy of the LMBS-NNs, the numerical results using the error histograms, regression, mean square error, state transitions and correlation have been provided.

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Acknowledgements

The first author thanks the Faculty of Sciences and Liberal Arts, Rajamangala University of Technology Isan, Thailand.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan

    Zulqurnain Sabir

  2. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, 64002, Yunlin, Taiwan, ROC

    Muhammad Asif Zahoor Raja

  3. Department of Computer Science, Iqra University Islamabad Campus, Islamabad, Karachi, Pakistan

    Nadia Mumtaz

  4. Department of Islamic Educational Management, Institute Agama Islam Negeri Curup, Rejang Lebong, Indonesia

    Irwan Fathurrochman

  5. Department of Mathematics, Zagazig Faculty of Engineering, Zagazig University, Zagazig, Egypt

    R. Sadat

  6. Faculty of Engineering and Technology, Future University, Cairo, Egypt

    Mohamed R. Ali

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  1. Zulqurnain Sabir
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  2. Muhammad Asif Zahoor Raja
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  3. Nadia Mumtaz
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  4. Irwan Fathurrochman
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Correspondence to R. Sadat.

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Sabir, Z., Raja, M.A.Z., Mumtaz, N. et al. An Investigation Through Stochastic Procedures for Solving the Fractional Order Computer Virus Propagation Mathematical Model with Kill Signals. Neural Process Lett 55, 1783–1797 (2023). https://doi.org/10.1007/s11063-022-10963-x

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