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A fractional epidemiological model for computer viruses pertaining to a new fractional derivative

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  • Singh, Jagdev
  • Kumar, Devendra
  • Hammouch, Zakia
  • Atangana, Abdon

Abstract

In the computer security and for any defensive strategy, computer viruses are very significant aspect. To understand their expansion and extension is very important component. In order to deal with this issue, we consider a fractional epidemiological model. In this article, we analyze moderate epidemiological model to describe computer viruses with an arbitrary order derivative having non-singular kernel. We obtain the solution of the problem by using an iterative method. By using the fixed-point theorem the existence of the solution is discussed. The uniqueness of the solution is verified. We perform some numerical simulations and show graphically to observe the impact of the arbitrary order derivative.

Suggested Citation

  • Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:504-515
    DOI: 10.1016/j.amc.2017.08.048
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    References listed on IDEAS

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    1. Wierman, John C. & Marchette, David J., 2004. "Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction," Computational Statistics & Data Analysis, Elsevier, vol. 45(1), pages 3-23, February.
    2. Alkahtani, Badr Saad T. & Atangana, Abdon, 2016. "Analysis of non-homogeneous heat model with new trend of derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 566-571.
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