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Entropy 2016, 18(2), 40; doi:10.3390/e18020040

Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative

1
Institute for Groundwater Studies, University of the Free State, Bloemfontein 9301, South Africa
2
Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Received: 17 September 2015 / Revised: 3 November 2015 / Accepted: 5 November 2015 / Published: 26 January 2016
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory)
View Full-Text   |   Download PDF [1572 KB, uploaded 26 January 2016]   |  

Abstract

Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a mathematical equation for prediction. In this work, a model of the well-known river blindness disease is created via the Caputo and beta derivatives. A partial study of stability analysis was presented. The extended system describing the spread of this disease was solved via two analytical techniques: the Laplace perturbation and the homotopy decomposition methods. Summaries of the iteration methods used were provided to derive special solutions to the extended systems. Employing some theoretical parameters, we present some numerical simulations. View Full-Text
Keywords: river blindness disease; Caputo fractional derivative; beta-derivative; special solutions river blindness disease; Caputo fractional derivative; beta-derivative; special solutions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Atangana, A.; Alqahtani, R.T. Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative. Entropy 2016, 18, 40.

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