Modeling the spread of Rubella disease using the concept of with local derivative with fractional parameter |
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| Authors: | Abdon Atangana Badr Saad T. Alkahtani |
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| Affiliation: | 1. Faculty of Natural and Agricultural Sciences, Institute for Groundwater Studies, University of the Free State, Bloemfontein, South Africa;2. Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia |
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| Abstract: | Our aim in this work was to examine the model underpinning the spread of the Rubella virus using the novel derivative called beta‐derivative. The study of the equilibrium points together with the analysis of the disease free equilibrium points was presented. Due to the complexity of the modified equation, we introduced a new operator based on the Sumudu transform. The properties of this operator were proposed and proved in detail. We made used of this operator together with the idea of perturbation method to derive a special solution of the extended model. The stability of the method for solving this model was presented. The uniqueness of the special solution was presented, and numerical simulations were done. The graphical representations show that the model depends on both parameters and the fractional order. © 2015 Wiley Periodicals, Inc. Complexity 21: 442–451, 2016 |
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| Keywords: | model of Rubella disease beta‐derivative novel operator stability analysis numerical simulations |
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