Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators

Volume 10, Issue 6, pp 3191--3200 http://dx.doi.org/10.22436/jnsa.010.06.32

Publication Date: June 25, 2017 Submission Date: February 17, 2017

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Authors

Badr Saad T. Alkahtani - Department of mathematics, colle of science, King Saud University, P. O. Box 1142, Riyadh 11989, Saudi Arabia. Abdon Atangana - Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa. Ilknur Koca - Department of Mathematics, Faculty of Sciences, Mehmet Akif Ersoy University, 15100, Burdur, Turkey.

Abstract

A mathematical system of equations using the concept of fractional differentiation with non-local and non-singular kernel has been analysed in this work. The developed mathematical model is designed to portray the spread of Zika virus within a given population. We presented the equilibrium point and also the reproductive number. The model was solving analytically using the Adams type predictor-corrector rule for Atangana-Baleanu fractional integral. The existence and uniqueness exact solution was presented under some conditions. The numerical replications were also presented.

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Keywords

• Zika virus
• reproduction number
• numerical approximation.

MSC

•  34A34
•  34A08
•  74G15

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