https://doi.org/10.1140/epjp/s13360-023-04475-3
Regular Article
Dynamical analysis and optimal control of a stochastic SIAR model for computer viruses
School of Mathematics and Statistics, Xinyang Normal University, 464000, Xinyang, Henan, People’s Republic of China
Received:
5
June
2023
Accepted:
12
September
2023
Published online:
1
October
2023
Mathematical formulation of a stochastic computer viruses model with the application of optimal control and randomly noise transmission has been focused in this paper. For the ease of understanding, the model is divided into four different classes of susceptible, infected, antidotal and removed population. All four cases have been perturbed by the white noise. The existence and uniqueness for the global positive solution of the model are proved. The existence of the ergodicity of the stationary distribution is discussed by using the Lyapunov function and Has'minskii theory. The sufficient conditions for the extinction of the computer virus are presented. The optimal control strategies based on the least cost of prevention and control of computer viruses are carried out by using the stochastic maximum principle. The validity of the theoretical analysis results are verified by numerical simulation.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
