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Dynamics of a fractional-order epidemiological model for computer viruses

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Abstract

In this work, we consider a fractional-order epidemiological model for computer viruses to study memory effects on population dynamics. This model is derived from a well-known integer-order epidemiological model and the Caputo fractional derivative. Our objective is to provide a rigorous mathematical analysis for dynamics of the fractional-order model. Here, positivity, linear invariant, asymptotic stability properties including local and global asymptotic stability, uniform and Mittag-Leffler stability are established. It is worth noting that the stability properties are investigated by a simple approach, which is based on stability theory for fractional-order dynamical systems and an appropriate linear Lyapunov function. As an important consequence, dynamical properties of the fractional-order model are determined fully. Additionally, a set of numerical experiments is conducted to support the theoretical findings. As we expect, the numerical results are consistent with the theoretical ones.

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Acknowledgements

We would like to thank the editor and anonymous referees for useful and valuable comments that led to a great improvement of the paper.

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  1. Department of Mathematics, FPT University, Hoa Lac Hi-Tech Park, Km29 Thang Long Blvd, Hanoi, Vietnam

    Manh Tuan Hoang

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  1. Manh Tuan Hoang
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Hoang, M.T. Dynamics of a fractional-order epidemiological model for computer viruses. São Paulo J. Math. Sci. (2023). https://doi.org/10.1007/s40863-023-00382-8

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