A fractional calculus model for worm propagation in computer network

Mohd Khalid; Anjali Sang; Jyoti Mishra; Vijay Kumar Gupta; Ali Akgül

doi:10.5269/bspm.75430

Mohd Khalid Maulana Azad National Urdu University, Hyderabad-500032, India.
Anjali Sang
Jyoti Mishra
Vijay Kumar Gupta
Ali Akgül

Abstract

Fractional Calculus emerges as a new field with wide applications in the fields of science and engineering. There is an increasing trend to find fractional calculus applications in various real-life non-linear and non-local problems, to develop new models for existing problems. Various results reported by the researchers, and many more are on the way to be discovered. Among all these problems is a computer science problem, worm propagation over various networks. This paper aims to present some short summaries of the work by distinguished researchers in modeling virus and worm propagation problems using fractional calculus. We believe this incomplete, but important, information will guide many researchers and help them to see some of the main real-world applications and gain an understanding of this powerful mathematical tool. We expect this collection will also benefit our community. Along with this a fractional SEIR model of virus propagation with the help of Caputo derivative is taken in this work. Its equilibrium point and asymptotic stability are discussed.

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References

Ucar, E., Ucar, S., Evirgen, F., Ozdemir, N., A fractional SAIDR Model in the Frame of Atangana?Baleanu Derivative, Fractal Fract., 5(2) (2021), 32. https://doi.org/10.3390/fractalfract5020032

Yuan, H., Chen, G., Network virus-epidemic model with the point-to-group information propagation, Appl. Math. Comput., 206 (2008), 357-367. https://doi.org/10.1016/j.amc.2008.09.025

Gao, Q., Zhuang, J., Stability analysis and control strategies for worm attack in mobile networks via a VEIQS propagation model, Appl. Math. Comput., 368 (2020), 124584. https://doi.org/10.1016/j.amc.2019.124584

Xiao, X.X., Fua, P., Lia, Q., Hua, G., Jiang, G., Modeling and Validation of SMS Worm Propagation over Social Networks, J. Comput. Sci., (2017). https://doi.org/10.1016/j.jocs.2017.05.011

Pinto, C.M.A., Machado, J.A.T., Fractional Dynamics of Computer Virus Propagation, Math. Probl. Eng., 2014, Article ID 476502, 7 pages. https://doi.org/10.1155/2014/476502

Mishra, B.K., Pandey, S.K., Dynamic model of worm propagation in computer network, Appl. Math. Model., 38 (2014), 1459-1467. https://doi.org/10.1016/j.apm.2013.10.046

Feng, L., Liao, X., Han, Q., Li, H., Dynamical analysis and control strategies on malware propagation model, Appl. Math. Model., (2013). https://doi.org/10.1016/j.apm.2013.03.051

Yang, F., Zhang, Z., Zeb, A., Hopf bifurcation of a VEIQS worm propagation model in mobile networks with two delays, Alexandria Eng. J., (2021). https://doi.org/10.1016/j.aej.2021.03.055

Dong, N.P., Long, H.V., Giang, N.L., The fuzzy fractional SIQR model of computer virus propagation in wireless sensor network using Caputo Atangana?Baleanu derivatives, Fuzzy Sets Syst., (2021).

Ebenezer, B., Farai, N., Kwesi, A.A.S., Fractional Dynamics of Computer Virus Propagation, Sci. J. Appl. Math. Stat., 3(3) (2015), 63-69. https://doi.org/10.11648/j.sjams.20150303.11

Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives: Theory and Applications, Gordon & Breach, Philadelphia, (1993).

Mishra, J., A Study on the spread of COVID 19 outbreak by using mathematical modeling, Results Phys., 19 (2020), 103482.

Mishra, J., Fractional hyper-chaotic model with no equilibrium, Chaos Solitons Fractals, 116 (2018), 43-53.

Akgul, A., Fatima, U., Iqbal, M.S., Ahmed, N., Raza, A., Iqbal, Z., Rafiq, M., A fractal fractional model for computer virus dynamics, Chaos Solitons Fractals, 147 (2021), 110947.

Dong, N.P., Long, H.V., Giang, N.L., The fuzzy fractional SIQR model of computer virus propagation in wireless sensor network using Caputo Atangana-Baleanu derivatives, Fuzzy Sets Syst., 429 (2022), 28-59.

Dong, N.P., Long, H.V., Giang, N.L., The fuzzy fractional SIQR model of computer virus propagation in wireless sensor network using Caputo Atangana?Baleanu derivatives, Fuzzy Sets Syst., 429 (2021). https://doi.org/10.1016/j.fss.2021.04.012

Pinto, C., Tenreiro Machado, J.A., Fractional Dynamics of Computer Virus Propagation, Math. Probl. Eng., (2014). https://doi.org/10.1155/2014/476502

Mishra, J., Telegraph model with fractional differential operators: Nonsingular kernels, Results Phys., 39 (2022), 105743.

Ahmed, N., Macias-Diaz, J.E., Shahid, N., Raza, A., Rafiq, M., On the computational simulation of a temporally nonlocal and nonlinear diffusive epidemic model of disease transmission, Int. J. Mod. Phys. C, 2550031 (2025).

Rafique, M., Rehamn, M.A.U., Alqahtani, A.M., et al., A new epidemic model of sexually transmittable diseases: a fractional numerical approach, Sci. Rep., 15 (2025), 3784. https://doi.org/10.1038/s41598-025-01234-w

Iqbal, Z., Ahmed, N., Macas-Diaz, J.E., Theoretical Analysis and Simulation of a Fractional-Order Compartmental Model with Time Delay for the Propagation of Leprosy, Fractal Fract., 7 (2023), 79.