Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators
Badr Saad T. Alkahtani
- Department of mathematics, colle of science, King Saud University, P. O. Box 1142, Riyadh 11989, Saudi Arabia.
- Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa.
- Department of Mathematics, Faculty of Sciences, Mehmet Akif Ersoy University, 15100, Burdur, Turkey.
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.
Share and Cite
Badr Saad T. Alkahtani, Abdon Atangana, Ilknur Koca, Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 6, 3191--3200
Alkahtani Badr Saad T., Atangana Abdon, Koca Ilknur, Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators. J. Nonlinear Sci. Appl. (2017); 10(6):3191--3200
Alkahtani, Badr Saad T., Atangana, Abdon, Koca, Ilknur. "Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators." Journal of Nonlinear Sciences and Applications, 10, no. 6 (2017): 3191--3200
- Zika virus
- reproduction number
- numerical approximation.
O. J. J. Algahtani, Comparing the Atangana-Baleanu and Caputo-Fabrizio derivative with fractional order: Allen Cahn model, Chaos Solitons Fractals, 89 (2016), 552–559.
B. S. T. Alkahtani, Chua’s circuit model with Atangana-Baleanu derivative with fractional order, Chaos Solitons Fractals, 89 (2016), 547–551.
A. Atangana, D. Baleanu, New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer model, Therm. Sci., 20 (2016), 763–769.
A. Atangana, D. Baleanu, Caputo-Fabrizio derivative applied to groundwater flow within confined aquifer, J. Eng. Mech., 143 (2017), D4016005-01–D4016005-05.
A. Atangana, I. Koca, Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order, Chaos Solitons Fractals, 89 (2016), 447–454.
E. Bonyah, K. O. Okosun, Mathematical modeling of Zika virus, Asian Pac. J. Trop. Dis., 6 (2016), 673–679.
L.-P. Chen, J.-F. Qu, Y. Chai, R.-C. Wu, G.-Y. Qi, Synchronization of a class of fractional-order chaotic neural networks, Entropy, 15 (2013), 3265–3276.
J. Hadamard, Essai sur l’étude des fonctions données par leur développement de Taylor, J. Mat. Pure Appl. Ser., 4 (1892), 101–186.
U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput., 218 (2011), 860–865.
J. Lessler, L. H. Chaisson, L. M. Kucirka, Q.-F. Bi, K. Grantz, H. Salje, A. C. Carcelen, C. T. Ott, J. S. Sheffield, N. M. Ferguson, D. A. Cummings, Assessing the global threat from Zika virus, Science, 353 (2016), 663–673.
F. Mainardi, Y. Luchko, G. Pagnini, The fundamental solution of the space-time fractional diffusion equation, Fract. Calc. Appl. Anal., 4 (2001), 153–192.
O. O. Makinde, K. O. Okosun, Impact of chemo-therapy on optimal control of malaria disease with infected immigrants, Biosyst, 104 (2011), 32–41.
O. O. Makinde, K. O. Okosun, Modelling the impact of drug resistance in malaria transmission and its optimal control analysis, Int. J. Phys. Sci., 6 (2011), 6479–6487.