Figure 1.
Approximate solution for $ \alpha = 0.3 $
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Analysis of a Lymphatic filariasis-schistosomiasis coinfection with public health dynamics: Model obtained through Mittag-Leffler function
| 1. | Department of Mathematics Education Kumasi Campus, University of Education Winneba, Ghana, Kumasi Ashanti Region, Box 1277, Ghana |
| 2. | Department of Mathematics Education, University of Education Winneba, Winneba, Central region, Box 25, Ghana |
In this paper, Lymphatic filariasis-schistosomiasis coinfected model is studied within the context of fractional derivative order based on Mittag-Leffler function of ABC in the Caputo sense. The existence and uniqueness of system model solution is derived by employing a well- known Banach fixed point theorem. The numerical solution based on the Mittag-Leffler function suggests that the dynamics of the coinfected model is well explored using fractional derivative order because of non-singularity.
Keywords:
Banach fixed point theorem,
Mittag-Leffler function,
Atangana-Beleanu,
Lymphatic filariasis-schistosomiasis,
Caputo.
Mathematics Subject Classification:
Primary: 34D20, 34D23; Secondary: 34Kxx, 34A08.
Citation:
Ebenezer Bonyah, Samuel Kwesi Asiedu.
Analysis of a Lymphatic filariasis-schistosomiasis coinfection with public health dynamics: Model obtained through Mittag-Leffler function. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020029
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References:
| [1] |
A. Atangana and I. Koca,
On the new fractional derivative and application to nonlinear Baggs and Freedman model, J. Nonlin. Sci. Appl., 9 (2016), 2467-2480.
doi: 10.22436/jnsa.009.05.46. |
| [2] |
A. Atangana and D. Baleanu, New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer model, Therm. Sci., 89 (2016), 763-769. Google Scholar |
| [3] |
A. Atangana and I. Koca,
Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order, Chaos Solitons Fract., 89 (2016), 447-454.
doi: 10.1016/j.chaos.2016.02.012. |
| [4] |
A. Atangana and J. F. Gomez-Aguilar,
Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena, Eur. Phys. J. Plus., 133 (2018), 166.
doi: 10.1140/epjp/i2018-12021-3. |
| [5] |
H. M. Baskonus, T. Mekkaoui, H. Hammouch and H. Bulut,
Active control of a Chaotic fractional order economic system, Abstr. Appl. Anal., 17 (2015), 5771-5783.
doi: 10.3390/e17085771. |
| [6] |
A. H. Bhrawy, S. S. Ezz-Eldien, E. H. Abdelkawy, M. A. Doha and D. Baleanu,
Solving fractional optimal control problems within a Chebyshev- Legendre operational technique, Int. J. Cont., 90 (2017), 1230-1244.
doi: 10.1080/00207179.2016.1278267. |
| [7] |
E. Bonyah, K. O. Okosun, O. O. Okosun and L. Ossei, Mathematical modeling of Lymphatic filariasis-schistosomiasis co-infection dynamics:Insight through public education, Int. Jour. Eco. Devel., 33 (2017). Google Scholar |
| [8] |
H. Bulut, H. M. Baskonus and F. B. M. Belgacem, The analytical solutions of some fractional ordinary differential equations by Sumudu transform method, Abstr. Appl. Anal., 2013 (2013), Art. ID 203875, 6 pp.
doi: 10.1155/2013/203875. |
| [9] |
K. M. Owolabi,
Numerical solution of diffusive HBV model in a fractional medium, Spr. Plus., 5 (2016), 1643.
doi: 10.1186/s40064-016-3295-x. |
| [10] |
K. M. Owolabi and A. Atangana,
Numerical approximation of nonlinear fractional parabolic differential equations with Caputo abrizio derivative in Riemann Liouville sense, Spr. Plus., 99 (2017), 171-179.
doi: 10.1016/j.chaos.2017.04.008. |
| [11] |
K. M. Owolabi,
Mathematical modelling and analysis of two-component system with Caputo fractional derivative order, Spr. Plus., 103 (2017), 544-554.
doi: 10.1016/j.chaos.2017.07.013. |
| [12] |
N. Ozalp and I. Koca,
A fractional order nonlinear dynamical model of interpersonal relationships, Adv. Diff. Equ., 189 (2012), 1-7.
doi: 10.1186/1687-1847-2012-189. |
| [13] |
A. Paparao and K. L. Narayan, Solving fractional optimal control problems within a Chebyshev- Legendre operational technique, Int. J. Cont., 32 (2017), 75-86. Google Scholar |
| [14] |
A. V. Paparao, V. S. Kalesha and A. Paparao, Dynamics of directly transmitted viral micro parasite model, Int. J. Ecol. Devel., 32 (2017), 88-97. Google Scholar |
| [15] |
C. M. A. Pinto and A. R. M. Carvalho,
New findings on the dynamics of HIV and TB coinfection models, Appl. math. comp., 242 (2014), 36-46.
doi: 10.1016/j.amc.2014.05.061. |
| [16] |
J. Singh, D. Kumar, M. A. Qurashi and D. Baleanu,
A new fractional model for giving up smoking dynamics, Adv. Diff. Equ., 88 (2017), 1-16.
doi: 10.1186/s13662-017-1139-9. |
| [17] |
B. S. TAlkahtani, I. Koca and A. Atangana, Analysis of a new model of H1N1 spread: Model obtained via Mittag-Leffler function, Adv. Mech. Eng., 9 (2017), 1-8. Google Scholar |
show all references
References:
| [1] |
A. Atangana and I. Koca,
On the new fractional derivative and application to nonlinear Baggs and Freedman model, J. Nonlin. Sci. Appl., 9 (2016), 2467-2480.
doi: 10.22436/jnsa.009.05.46. |
| [2] |
A. Atangana and D. Baleanu, New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer model, Therm. Sci., 89 (2016), 763-769. Google Scholar |
| [3] |
A. Atangana and I. Koca,
Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order, Chaos Solitons Fract., 89 (2016), 447-454.
doi: 10.1016/j.chaos.2016.02.012. |
| [4] |
A. Atangana and J. F. Gomez-Aguilar,
Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena, Eur. Phys. J. Plus., 133 (2018), 166.
doi: 10.1140/epjp/i2018-12021-3. |
| [5] |
H. M. Baskonus, T. Mekkaoui, H. Hammouch and H. Bulut,
Active control of a Chaotic fractional order economic system, Abstr. Appl. Anal., 17 (2015), 5771-5783.
doi: 10.3390/e17085771. |
| [6] |
A. H. Bhrawy, S. S. Ezz-Eldien, E. H. Abdelkawy, M. A. Doha and D. Baleanu,
Solving fractional optimal control problems within a Chebyshev- Legendre operational technique, Int. J. Cont., 90 (2017), 1230-1244.
doi: 10.1080/00207179.2016.1278267. |
| [7] |
E. Bonyah, K. O. Okosun, O. O. Okosun and L. Ossei, Mathematical modeling of Lymphatic filariasis-schistosomiasis co-infection dynamics:Insight through public education, Int. Jour. Eco. Devel., 33 (2017). Google Scholar |
| [8] |
H. Bulut, H. M. Baskonus and F. B. M. Belgacem, The analytical solutions of some fractional ordinary differential equations by Sumudu transform method, Abstr. Appl. Anal., 2013 (2013), Art. ID 203875, 6 pp.
doi: 10.1155/2013/203875. |
| [9] |
K. M. Owolabi,
Numerical solution of diffusive HBV model in a fractional medium, Spr. Plus., 5 (2016), 1643.
doi: 10.1186/s40064-016-3295-x. |
| [10] |
K. M. Owolabi and A. Atangana,
Numerical approximation of nonlinear fractional parabolic differential equations with Caputo abrizio derivative in Riemann Liouville sense, Spr. Plus., 99 (2017), 171-179.
doi: 10.1016/j.chaos.2017.04.008. |
| [11] |
K. M. Owolabi,
Mathematical modelling and analysis of two-component system with Caputo fractional derivative order, Spr. Plus., 103 (2017), 544-554.
doi: 10.1016/j.chaos.2017.07.013. |
| [12] |
N. Ozalp and I. Koca,
A fractional order nonlinear dynamical model of interpersonal relationships, Adv. Diff. Equ., 189 (2012), 1-7.
doi: 10.1186/1687-1847-2012-189. |
| [13] |
A. Paparao and K. L. Narayan, Solving fractional optimal control problems within a Chebyshev- Legendre operational technique, Int. J. Cont., 32 (2017), 75-86. Google Scholar |
| [14] |
A. V. Paparao, V. S. Kalesha and A. Paparao, Dynamics of directly transmitted viral micro parasite model, Int. J. Ecol. Devel., 32 (2017), 88-97. Google Scholar |
| [15] |
C. M. A. Pinto and A. R. M. Carvalho,
New findings on the dynamics of HIV and TB coinfection models, Appl. math. comp., 242 (2014), 36-46.
doi: 10.1016/j.amc.2014.05.061. |
| [16] |
J. Singh, D. Kumar, M. A. Qurashi and D. Baleanu,
A new fractional model for giving up smoking dynamics, Adv. Diff. Equ., 88 (2017), 1-16.
doi: 10.1186/s13662-017-1139-9. |
| [17] |
B. S. TAlkahtani, I. Koca and A. Atangana, Analysis of a new model of H1N1 spread: Model obtained via Mittag-Leffler function, Adv. Mech. Eng., 9 (2017), 1-8. Google Scholar |
Figure 2.
Approximate solution for $\alpha = 0.5$
Figure 3.
Approximate solution for $\alpha = 0.65$
Figure 4.
Approximate solution for $\alpha = 0.75$
Figure 5.
Approximate solution for $ \alpha = 0.95 $
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