The APPROXIMATE SOLUTIONS OF MALARIA DISEASE TRANSMISSION MODEL: USING MUTI-STEP DIFFERENTIAL TRANSFORMATION METHOD

Authors

Keywords:

Malaria disease, Fourth order Runge-Kutta method, Multi-Step Differential Transform Methods, Maple21, SPEIR-SEI

Abstract

In this paper, numerical solutions to the SPEIR-SEI Malaria disease model were obtained using the Multi-Step Differential Transformation Method (MS-DTM). MS-DTM is a semi-analytical method for solving a system of a non-linear differential equation where its exact solution is difficult to obtain. The analytical solution of MS-DTM was compared with the solution of Maple21’s in-built classical fourth-order Runge-Kutta method. The results demonstrate the reliability and efficiency of the method and the graphs show that the solutions from both methods agreed well with each other.

Dimensions

Abioye, A. I., Ibrahim, M. O., Peter, O. J., Amadiegwu, S. and Oguntolu, F. A. (2018). Differential Transform Method for Solving Mathematical Model of SEIR and SEI Spread of Malaria, International Journal of Sciences: Basic and Applied Research (IJSBAR). Vol. 40, No 1, pp 197-219.

Adewale, S.O, Ajao, S.O. Olapade, I. A. Adeniran, G.A. and Oyewumi, A. A. (2016). Effect of Chemoprophylaxi treatment on the dynamic of spread of Malaria. International Journal of Scientific and Engineering Research, Vol 7(1). ISSN:2229-5518.

Agada, D. O., Omale, D. Nurudeen, R. and Abimbola, O .M. (2021). Solution To Mathematical Model On Malaria Transmission Dynamics Using Homotopy Perturbation Method (HPM). International Journal of Science and Advanced Innovative Research, Vol. 6(3). ISSN: 2536-7315.

Akogwu, B. O. (2022). The Solution of a Mathematical Model for Covid-19 Transmission and Vaccination in Nigeria by using a Differential Transformation Method,FUDMA Journal of Sciences (FJS) Vol. 6 No. 5, October 2022, pp 50 – 56.

Anderson, R. M. andMay, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control.Oxford University Press, Oxford.

Arikoglu, A. and Ozkol, I. (2006). Solution of differential-difference equations by using differential transform method, Appl. Math. Comput., Vol 181(1) (2006), 153-162.

Astuti F., Suryanto A. and Darti I. (2019). Multi-step differential transform method for solving the influenza virus model with disease resistance, 9th Annual Basic Science International Conference (BaSIC2019). IOP Conf. Series: Materials Science and Engineering,546. DOI:10.1088/1757-899X/546/5/052013.

Bakare, E.A. and Nwozo, C.R. (2015) Mathematical Analysis of the Dynamics of Malaria Disease Transmission Model. International Journal of Pure and Applied Mathematics, 99, 411-437. https://doi.org/10.12732/ijpam.v99i4.3.

Bervillier C. (2012). Status of the differential transformation method, Applied Mathematics and Computation, vol. 218, pp. 10158- 10170.

Bildik, N., Konuralp, A., Bek, F. and Kucukarslan, S. (2006) Solution of different types of the partial differential equation by differential transform method and Adomian's decomposition method, Appl. Math. Comput., 127 (2006), 551-567.

CDC. (2021). Malaria's Impact Worldwide, https://www.cdc/gov/malaria/malaria_worldwide/impact.html

Chitnis, N., Cushing, J. M. and Hyman, J. M. (2006). Bifurcation Analysis of a Mathematical Model for Malaria Transmission, SIAM Journal on Applied Mathematics.Vol. 67, (1), Pp.24-45.

El-Zahar, E. R. (2015). Applications of Adaptive Multi-Step Differential Transform Method to Singular Perturbation Problems Arising in Science and Engineering, Appl. Math. Inf. Sci. 9, No. 1, 223-232. http://dx.doi.org/10.12785/amis/090128

Fact sheet on the World Malaria Report (2014) Available at https://www.who.int/malaria/media/world_malaria_report_2014/en/

Forouzannia, F., Gumel, A. B. (2014). Mathematical analysis of an age-structured model for malaria transmission dynamics, Math. Biosci. 247, 80–94.

Ghazala, N. and Shaista, G. (2019). Comparative Study Of Mathematical Model Of Ebola Virus Disease Via Using Differential Transform Method And Variation Of Iteration Method. Matrix Science Mathematics, 3(1), 17-19.

Gokdogan A., Merdan M. and Yildirim A. (2012). A multistage differential transformation method for approximate solution of Hantavirus infection model, Mathematical and Computer Modelling, vol. 55, pp. 761-769.

Hyun, M. Y. (2000). Malaria transmission model for different levels of acquired immunity and temperature dependent parameters vector. Rev. SaudePublica., 34(3): 223-231.

Isao, K., Akira, S. and Motoyoshi, M. (2004). Combining Zooprophylaxis and insecticide spraying, a malaria-control strategy limiting the development of insecticide resistance in vector mosquitoes. Proc. R. Soc. Lond., 271: 301-309.

Jia Li (2011). Modelling of transgenic mosquitoes and impact on malaria transmission, Journal of Biological Dynamics, 5:5, pp. 474-494, DOI: 10.1080/17513758.2010.523122

Jang M. J., Chen C. L. and Lilly. C. (2000). On solving the initial-value problems using the differential transformation method, Applied Mathematics a, and Computation, vol. 115, pp. 145-160.

Killeen, G. F., Mckenzie, F. E., Foy, B. D., Schieffelin, C., Billingslay, P. F., and Beier, J. C., (2000). A simplified model for predicting malaria entomologic inoculation rates based on entomologic parameters relevant to control, m. J. Trop. Hyg., vol. 62, pp. 535-544.

Macdonald, G. (1957). The Epidemiology and Control of Malaria. London, New York, Oxford University Press, Toronto.

Mandal, S., Rup Sarker, R., and Somdatta, S. (2011), Mathematical Model of malaria- a review. Malaria Journal, Vol 10, pp. 202.

Makinde, O. D and Okosun, K. O. (2011). Impact of chemo-therapy on optimal control of malaria disease with infected immigrants. BioSystems. 104:32-41.

Merdan, M., Gokdogan, A. andYildirim, A. (2013). On numerical solution to fraction non-linear oscillator equations, Meccanica, 48:1201-1213. DOI: 10.1007/s11012-012-966.

Odibat, Z. M., Bertelle,C., Aziz-Alaoui, M.A. and Duchamp, G.H.E. (2010), A Multi-Step Differential Transform Method and application to non-chaotic or chaotic systems, Comput. Math. Appl.,59, 1462–1472.

Okosun, K.O. and Makinde, O.D. (2011) Modeling the Impact of Drug Resistance in Malaria Transmission and Its Optimal Control Analysis. International Journal of the Physical Science, 28, 6479-6487.

Okosun, K. O. (2010). Mathematical epidemiology of Malaria Disease Transmission and its Optimal Control Analyses, Ph.D. thesis, University of the Western Cape, South Africa

Olaniyi S., and Obabiyi O. S. (2013). Mathematical Model for Malaria Transmission Dynamics In Human and Mosquito Populations with Nonlinear Forces of Infection, International Journal of Pure and Applied Mathematics, Volume 88 No. 1, 125-156. ISSN: 1314-3395 (online version), URL: http://www.ijpam.eu.

Omoloye, M.A, Udokang, A.E. Sanusi, A.O. and Emiola, O.K.S. (2022).Analytical Solution of Dynamical Transmission of Malaria Disease Model using Differential Transform Method. Internal Journal of Novel Research in Physics, Chemistry and Mathematics, Vol. 9 (1), Pp. 1-13.

Ortiz-Ruiz, A.,Postigo, N., Gil-casanova, S., Cuadrado,D., Bautista, J. M., Rubio, J. M., Luengo-Oroz, M. and Linares, M. (2018). Plasmodium Species Differentiation by Non-expert on-line volunteers for Remote Malaria field Diagnosis, BMC Malaria Journal 17(54).

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

Puntani, P. and I-ming, T. (2010). Impact of cross-border migration on disease epidemics: the case of the P. falciparum and P. vivaxmalaria epidemic along the Thai-Myanmar border. J. Bio. Sys., 18(1): 55-73

Rafikov, M., Bevilacqua, L. and Wyse, A. A. P. (2011). Optimal control strategy of malaria vector using genetically modified mosquitoes. J. Theor. Bio., 258: 418-425.

Ross, R., Howard, L. O. and Gorgas, W. C. (1910).The prevention of malaria, John Murray, London.

World Health Organization. 10 facts on malaria, WHO online; 2011.

https://www.who.int/malaria/world_malaria_report_2011/en/

Usman I.G., AbubakarT.U. Muhammad A.H.,Usman B.T. and NagwariA.U.(2020). Mathematical Model for the Transmission Dynamics and Control of Malaria by Incorporating Behavioural Change, Dutse Journal of Pure and Applied Sciences (DUJOPAS),Vol. 6 No. 3.258-271.

Yildirim, A.,Gokdogan, A. and Merdan, M. (2012).On Chaotic systems via multi-step differential transformation method.Can.J. Phys., 90, 391-406. https://doi.org/10.1139/p2012-032.

Published

10-01-2023

How to Cite

The APPROXIMATE SOLUTIONS OF MALARIA DISEASE TRANSMISSION MODEL: USING MUTI-STEP DIFFERENTIAL TRANSFORMATION METHOD. (2023). FUDMA JOURNAL OF SCIENCES, 6(6), 182-194. https://doi.org/10.33003/fjs-2022-0606-1112

Issue

Vol. 6 No. 6 (2022): FUDMA Journal of Sciences - Vol. 6 No. 6

Section

Research Articles
Copyright & Licensing

How to Cite

The APPROXIMATE SOLUTIONS OF MALARIA DISEASE TRANSMISSION MODEL: USING MUTI-STEP DIFFERENTIAL TRANSFORMATION METHOD. (2023). FUDMA JOURNAL OF SCIENCES, 6(6), 182-194. https://doi.org/10.33003/fjs-2022-0606-1112

Most read articles by the same author(s)