Differential Transform Method for Solving Mathematical Model of SEIR and SEI Spread of Malaria

Abioye Adesoye Idowu, Ibrahim Mohammed Olanrewaju, Peter Olumuyiwa James, Amadiegwu Sylvanus, Oguntolu Festus Abiodun


In this paper, we use Differential Transformation Method (DTM) to solve two dimensional mathematical model of malaria human variable and the other variable for mosquito. Next generation matrix method was used to solve for the basic reproduction number  and we use it to test for the stability that whenever  the disease-free equilibrium is globally asymptotically stable otherwise unstable. We also compare the DTM solution of the model with Fourth order Runge-Kutta method (R-K 4) which is embedded in maple 18 to see the behaviour of the parameters used in the model. The solutions of the two methods follow the same pattern which was found to be efficient and accurate.


Malaria; SEIR; SEI; Differential Transformation Method; Runge-Kutta method; Reproduction number.

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M. Z. Ahmad., D. Alsarayreh, A. Alsarayreh & I. Qaralleh (2017, February). “Differential Transformation Method (DTM) for solving SIS and SI epidemic models”, Sains Malaysiana, 46(10), pp. 2007-2017, http://dx.doi.org/10.17576/jsm-2017-4610-40

R. M. Anderson & R. M. May (1991). "Infectious diseases of Humans: Dynamics and Control”, illus, New York, NY, Oxford University Press, December, 1992.ISBN 0-19-854599-1.

F. S. Akinboro, S. Alao & F. O. Akinpelu (2014, March). “Numerical Solution of SIR Model using Differential Transformation Method and Variational Iteration Method”,Gen. Math. Notes, 22(2), 82-92.

H.-F. Huo & Q.-M. Qui (2014, February). “Stability of a Mathematical Model of Malaria Trans- mission with Relapse”, Hindawi Publishing Corporation Abstract and Applied analysis, 2014(1) Article ID 289349, 9 pages, http://dx.doi.org/10.1155/2014/289349.

B. Ibis, M. Bayram & G. Agargun. (2011). “Applications of Fractional Differential Transform Method to Fractional Differential-Algebraic Equations”, European Journal of Pure and Applied Mathematics, 4(2), 129-141, ISSN 1307-5543.

T. Julius, D.-M. Senelani & N. Farai (2014, April). “A mathematical model for the transmission and spread of drug sensitive and resistant malaria strains within a human population”, Hindawi Publishing Corporation, ISRN Biomathematics, Article ID 636973, pp. 1-12, http://dx.doi.org/10.1155/2014/636973.

W. O. Kermack, W. O & A. G. McKendrick. (1927, August), “A contribution to the mathematical theory of epidemics”, Proceeding of the Royal Society of London. Series A, Containing papers of a Mathematical and Physical Character, 115 (772): 700-721.

G. Macdonald.. The Epidemiology and control of malaria, Oxford University press, London, 1957.

G. Methi (2016, June). “Solution of Differential Equation Using Differential Transform Method”, Asian Journal of Mathematics & Statistics, 9(13), pp 1-5

F. Mirzaee (2011, April). “Differential Transform Method for Solving Linear and Nonlinear Systems of Ordinary Differential Equations”, Applied Mathematical Sciences, 5(70), 3465 - 3472.

D. Nazari & S. Shahmorad (2010, January). “Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions”, Journal of Computational and Applied Mathematics, 234, 883-891.

K. O. Okosun & O. D. Makinde (2011, September). “Modelling the impact of drug resistance in malaria”, Available online at http://www.academicjournals.org/IJPS, DOI: 10.5897/IJPS 10.542, ISSN 1992 - 1950.

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

S. Olaniyi & O. S. Olabiyi (2013, August). “Mathematical Model for Malaria Transmission Dynamics in Human and Mosquito Populations with Nonlinear Forces of Infection”, International Journal of Pure and Applied Mathematics 88(1), 125-156, doi: http://dx.doi.org/10.12732/ijpam.v88i1.10.

M. A. E. Osman, K. K. Adu & C. Yang (2017, November). “A Simple SEIR Mathematical Model of Malaria Transmission”, Asian Research Journal of Mathematics 7(3): 1-22, Article no.ARJOM.37471, ISSN: 2456-477X.

B. Soltanalizadeh (2012). “Application of Differential Transformation Method for Solving a Fourth-order Parabolic Partial Differential Equations”, International Journal of Pure and Applied Mathematics, Vol. 78(3), 299-308, ISSN: 1311-8080 (printed version).

J. K. Zhou Differential Transformation and its Applications for Electrical Circuits. Huazhong University Press, Wuhan, China. (1986).

M. Altaf Khan., A. Wahid., S. Islam., I. Khan., S. Shafie, & T. Gul. (2015). Stability analysis of an SEIR epidemic model with non-linear saturated incidence and temporary immunity. Int. J. Adv. Appl. Math. and Mech. 2(3), 1 – 14.

O. J. Peter .,M. O. Ibrahim ., F. A. Oguntolu.,O. B. Akinduko., S. T. Akinyemi.(2018) Direct and Indirect Transmission Dynamics of Typhoid Fever Model by Differential Transform Method. ATBU, Journal of Science, Technology & Education (JOSTE); 6 (1), 167-177


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