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A Spectral Collocation Method for Computer Virus Spread Case of Delayed Optimal Control Problem

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Abstract

In this essay, a method is presented for approximating the optimal control problem (OCP) with nonlinear delay differential equations using global collocation at Legendre–Gauss–Radau points. This OCP models the spread of the computer virus. The operational matrices and collocation method together with hybrid Legendre polynomials and block-pulse functions are applied to discretize the model and convert it into a large-scale finite-dimensional nonlinear programming that can be solved by the existing well-developed methods in Matlab software. The numerical simulations show that the proposed collocation method leads to high precision solutions. Finally, the effects of the parameters that appeared in the model are analyzed. The experimental results demonstrate that the strategy for increasing the failure and the retrieval rates and decreasing the epidemic rate and the number of new computers gives a considerable influence on controlling and restraining the propagation of computer viruses.

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Acknowledgements

The first and third authors would like to thank Gonbad Kavous University for supporting this research work. The second author would like to appreciate the research council of Farhangian University for supporting this research.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Gonbad Kavous University, Gonbad Kavous, Iran

    Mehdi Shahini & Raheleh Khanduzi

  2. Department of Educational Mathematics, Farhangian University, Tehran, Iran

    Asyieh Ebrahimzadeh

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  1. Mehdi Shahini
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  2. Asyieh Ebrahimzadeh
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  3. Raheleh Khanduzi
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Correspondence to Asyieh Ebrahimzadeh.

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Communicated by Davoud Mirzaei.

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Shahini, M., Ebrahimzadeh, A. & Khanduzi, R. A Spectral Collocation Method for Computer Virus Spread Case of Delayed Optimal Control Problem. Bull. Iran. Math. Soc. 48, 507–535 (2022). https://doi.org/10.1007/s41980-021-00530-w

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  • DOI: https://doi.org/10.1007/s41980-021-00530-w

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