Transmission Dynamics of Malware in Networks Using Caputo Fractional Order Derivative

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Jyoti Kumari Gupta 1 Bimal Kumar Mishra 2,*

1. Department of Computer Science, Vinoba Bhave University, Hazaribag, India

2. Principal, Adarsh College, Rajdhanwar, Vinoba Bhave University, Hazaribag, India

* Corresponding author.


Received: 18 Nov. 2023 / Revised: 12 Dec. 2023 / Accepted: 8 Mar. 2024 / Published: 8 Jun. 2024

Index Terms

Fractional calculus, Caputo-fractional order derivative, Basic reproduction number, Sensitivity analysis, Fractional forward Euler method


Fractional calculus plays a crucial role in the representation of various natural and physical phenomena by incorporating the inherent non-locality and long-term memory effect of fractional operators. These models offer a more precise and systematic depiction of the underlying phenomena. The focus of this research paper is on the utilization of fractional calculus in the context of the epidemic model. Specifically, the model considers a fractional order ρ, where 0<ρ≤1, and employs the Caputo fractional order derivative to describe the transmission of malware in both wireless and wired networks. The basic reproduction number, along with the fractional order ρ, is identified as the threshold parameter in this model. The stability of the system is analysed at different stages of the reproduction number, considering both local and global asymptotic stability. Additionally, sensitivity analysis is conducted on the model parameters to determine the direction of change in the reproduction number. This analysis aids in understanding whether the reproduction number will increase or decrease under different scenarios. To obtain numerical results, the Fractional Forward Euler Method is utilized for simulation purposes. This method enables the computation of the model's dynamics and offers insights into the behaviour of the system. While the Caputo fractional order derivative offers a promising framework for modelling epidemic dynamics, they often entail significant computational overhead, limiting the scalability and practical utility of fractional calculus-based epidemic models, especially in real-time simulation and forecasting scenarios.

Cite This Paper

Jyoti Kumari Gupta, Bimal Kumar Mishra, "Transmission Dynamics of Malware in Networks Using Caputo Fractional Order Derivative", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.10, No.2, pp. 1-12, 2024. DOI: 10.5815/ijmsc.2024.02.01


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