A fractional epidemiological model for computer viruses pertaining to a new fractional derivative
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 epide...
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| Vydáno v: | Applied mathematics and computation Ročník 316; s. 504 - 515 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Inc
01.01.2018
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| ISSN: | 0096-3003, 1873-5649 |
| On-line přístup: | Získat plný text |
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| 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. |
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| AbstractList | 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. |
| Author | Atangana, Abdon Kumar, Devendra Hammouch, Zakia Singh, Jagdev |
| Author_xml | – sequence: 1 givenname: Jagdev surname: Singh fullname: Singh, Jagdev email: jagdevsinghrathore@gmail.com organization: Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India – sequence: 2 givenname: Devendra orcidid: 0000-0003-4249-6326 surname: Kumar fullname: Kumar, Devendra email: devendra.maths@gmail.com, dev.ku15@gmail.com organization: Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India – sequence: 3 givenname: Zakia surname: Hammouch fullname: Hammouch, Zakia email: hammouch.zakia@gmail.com organization: E3MI, Departement de Mathematiques, FST Errachidia Universite Moulay Ismail BP.509 Boutalamine 52000 Errachidia, Morocco – sequence: 4 givenname: Abdon surname: Atangana fullname: Atangana, Abdon email: abdonatangana@yahoo.fr organization: Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa |
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| Keywords | Caputo-Fabrizio derivative Fixed point theorem Computer viruses Fractional differential equations Epidemiological model |
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