Multi-step Homotopy Analysis Method for Solving Malaria Model

Peter Olumuyiwa, Adebisi Ajimot Folasade, Oguntolu Festus Abiodun, Bitrus Sambo, Akpan Collins Emmanuel


In this paper, we consider the modified epidemiological malaria model proposed by Abadi and Harald. The multi-step homotopy analysis method (MHAM) is employed to compute an approximation to the solution of the model of fractional order. The fractional derivatives are described in the Caputo sense. We illustrated the profiles of the solutions of each of the compartments. Figurative comparisons between the MHAM and the classical fourth-order reveal that this method is very effective


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Abbasbandy, E. & Shivanian E. (2009). Application of the variational iteration method for system of nonlinear Volterrasintegro-differential equations. Mathematical and Comp. Applic., 14(2), 147-158.

Abdallah, I. A. (2009). Homotopy analytical solution on MHD fluid flow and heat transfer problem. Appl. Math. Inf. Sci., 3(2), 223-233.

Alomari, A. K., Noorani, M. S. & Nazar, M. R. (2009). Adaptation of homotopy analysis method for the numeric–analytic solution of Chen system. Communications in Nonlinear Science and Numerical Simulation, 14(5), 2336-2346.

Baird, J. K. (2007). “Resurgent malaria at the millennium: control strategies in crisis,”. Drugs, 59(4), 719–743.

Cang, J., Tan, Y., Xu, H. & Liao, S. (2009). Series solutions of non-linear Riccati differential equations with fractional order. Chaos, Solitons & Fractals, 40(1), 1-9.

Edward, S, Raymond., K. E Gabriel., K. T, Nestory, F. Godfrey. & M. G., Arbogast, M. P. (2015). A Mathematical Model for Control and Elimination of the Transmission Dynamics of Measles. Appl. and Comp Maths., 4(6), 396-408.

Ertürk, V. S. & Momani,O. Z. (2011). An approximate solution of a fractional order differential equation model of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells. Comput. Mathe. Appl.,62, 992–1002.

Gebremeskel, A. A. & Krogstad, H. E. (2015) Mathematical Modelling of Endemic Malaria Transmission. American Journal of Applied Mathematics, 3(2),36-46. doi.10.11648/j.ajam.20150302.12

Ibrahim, M. O., Peter, O. J, Ogwumu, O. D. & Akinduko, O. B. (2017). On the Homotopy Analysis Method for PSTIR Typhoid Model Transactions of the Nigerian. Association of Mathematical Physics, 4(2), 51-56.

Liao, S. J. (1992). The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University.

Lin, W. (2007). Global existence theory and chaos control of fractional differential equations. JMAA,332, 709– 726. doi.10.1515/fca-2016-0040.

Miller, S. R. (1993). An introduction to the fractional calculus and fractional differential equations. Wiley, USA

Nedelman, J. (1983). Inoculation and recovery rate in the malaria mode1 of Dietz, Molineaux, and Thomas. Math. Biosci., 69, 209-233.

Ngwa, G. A. (2004). “Modelling the dynamics of endemic malaria in growing populations”. Discrete Contin. Dyn. Syst. Ser. B, 4, 1173-1202.

Peters, W. (1998). “Drug resistance in malaria parasites of animals and man”. Advances in Parasitology, 41–58. doi.10.13140/2.1.4175.776

Peter, O. J.& Akinduko O. B. (2018). Semi Analytic Method for Solving HIV/AIDS Epidemic Model. Int. J. Modern Biol., Med., 9(1), 1-8

Peter, O. J. & Ibrahim. M. O. (2017). Application of Differential Transform Method in Solving a Typhoid Fever Model. International Journal of Mathematical Analysis and Optimization, 1(1), 250-260.

Ridley, R. G. (2002). “Medical need, scientific opportunity and the drive for antimalarial drugs”. Nature, 415, 686–693. doi.10.1038/415686a

Zurigat, M., Momani, S. & Alawneh, A. (2010). Analytical approximate solutions of systems of fractional algebraic-differential equations by homotopy analysis method. Computers and Mathematics with Applications, 59(3), 1227-1235

Zurigat, M., Momani, S, odibat, Z. & Alawneh, A. (2010). The homotopy analysis method for handling systems of fractional differential equations. Applied Mathematical Modeling, 34(1), 24-35.


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