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<p>This paper considers a two-dimensional, non-local-in-time diffusive mathematical model of the epidemiological dynamics of computer viruses, which generalizes the SIES model. The model system with Caputo derivatives of piecewise-constant order consists of equations for three unknown functions, two of which are expressed in closed form as solutions to the corresponding linear boundary value problems. A qualitative analysis of the nonlinear boundary value problem with respect to the third unknown function, representing the number of infected nodes, is performed. A numerical solution method and some results of computer modeling of the fractional-order virus propagation dynamics in a network are presented.</p>

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Modeling Fractional-Differential Dynamics of Computer Virus Propagation Based on a Diffusive Epidemiological Model

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • V. M. Bulavatsky,
  • V. O. Bohaienko

摘要

This paper considers a two-dimensional, non-local-in-time diffusive mathematical model of the epidemiological dynamics of computer viruses, which generalizes the SIES model. The model system with Caputo derivatives of piecewise-constant order consists of equations for three unknown functions, two of which are expressed in closed form as solutions to the corresponding linear boundary value problems. A qualitative analysis of the nonlinear boundary value problem with respect to the third unknown function, representing the number of infected nodes, is performed. A numerical solution method and some results of computer modeling of the fractional-order virus propagation dynamics in a network are presented.