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BioMed Research International
Volume 2014 (2014), Article ID 523159, 10 pages
http://dx.doi.org/10.1155/2014/523159
Research Article

Model of Break-Bone Fever via Beta-Derivatives

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Ma SIM Focus Area, North-West University, Mafikeng 2735, South Africa

Received 14 August 2014; Revised 21 August 2014; Accepted 21 August 2014; Published 11 September 2014

Academic Editor: TEWA Jean Jules

Copyright © 2014 Abdon Atangana and Suares Clovis Oukouomi Noutchie. 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.

Abstract

Using the new derivative called beta-derivative, we modelled the well-known infectious disease called break-bone fever or the dengue fever. We presented the endemic equilibrium points under certain conditions of the physical parameters included in the model. We made use of an iteration method to solve the extended model. To show the efficiency of the method used, we have presented in detail the stability and the convergence of the method for solving the system (2). We presented the uniqueness of the special solution of system (2) and finally the numerical simulations were presented for various values of beta.