Application of Differential Transformation Method for Solving Dynamical Transmission of Lassa Fever Model

Authors: M. A. Omoloye, M. I. Yusuff, O. K. S. Emiola

Abstract:

The use of mathematical models for solving biological problems varies from simple to complex analyses, depending on the nature of the research problems and applicability of the models. The method is more common nowadays. Many complex models become impractical when transmitted analytically. However, alternative approach such as numerical method can be employed. It appropriateness in solving linear and non-linear model equation in Differential Transformation Method (DTM) which depends on Taylor series make it applicable. Hence this study investigates the application of DTM to solve dynamic transmission of Lassa fever model in a population. The mathematical model was formulated using first order differential equation. Firstly, existence and uniqueness of the solution was determined to establish that the model is mathematically well posed for the application of DTM. Numerically, simulations were conducted to compare the results obtained by DTM and that of fourth-order Runge-Kutta method. As shown, DTM is very effective in predicting the solution of epidemics of Lassa fever model.

Keywords: Differential Transform Method, Existence and uniqueness, Lassa fever, Runge-Kutta Method.

References:

[1] Akinpelu, F.O. and Akinwande, R. (2018). “Mathematical model for Lassa fever and sensitivity analysis”. Journal of Scientific and Engineering Research, vol. 5(6): Pp.1-9.
[2] Centers for Disease Control and Prevention (2013). “Lassa fever fact sheet”.
[3] Centers for Disease Control and Prevention (2004). “Imported Lassa fever”. MMWR Morb . Mortality Wkly Rep., vol. 53(38), Pp. 894-897
[4] Central Intelligence Agency. “World fact book for the year 2014. January, 2015.
[5] Fichet-Calvet E., Becker-Ziaja B., Koivogui, L. and Gunther, S. (2014). “Lassa Serology in Natural Populations of Rodents and Horizontal Transmission”. Vector Borne and Zoonotic Diseases. Vol. 14(9): Pp. 665674.
[6] James, T. O., Abdulrahman, S., Akinyemi S. and Akinwade, N. I. (2015). “Dynamics Transmission of Lassa fever Disease”. International Journal and Research in Education Science. Vol 2, Issue 1, Pp:2349-5219.
[7] Meksianis Z. Ndii, Nursanti Anggriani & Asep K. Supriatna (2018). “Application of differential transformation method for solving dengue transmission mathematical model”. Conference Paper in AIP Conference Proceedings • March 2018. DOI: 10.1063/1.5026084. https://www.researchgate.net/publication/323608890
[8] Ogbu, O. E., Ajuluchukwu, C. J. and Uneke, C. J. (2007). “Lassa fever in West Africa sub- region. An Overview”. Journal of Vector Borne Diseases.Vol.44, Pp.1-11.
[9] Omilabu, S. A, Badaru, S. O., Okokhere, P., Asogun, D., Drosten, C., and Emmerich, P. (2005). “Lassa fever Nigeria, 2003 and 2004”. Emerging Infectious Diseases.Vol.11, Pp. 1642–4.
[10] Pukhov, G. E. (1980). “Differential Transformations of Functions and Equations”. Naukova Dumka Publication, Kiev.
[11] World Health Organization (2014). “Lassa Fever: Factsheets”. Available at http:who.int/mediacenter/factsheets/fs179/en/Accessed on 24/06/2016.
[12] World Health Organization (2005). “Strengthening health security by implementing the international health regulations”. Available from: http://www.who.int/ihr/publications/9789241580496/en/.
[13] World Health Organization (2016). “Lassa fever-Sweden”. Available from: http://www.who.int/csr/don/8-april-2016-lassa-fever-sweden/en/. Accessed May 21, 2020.
[14] World Fact Book for the year (2017), retrieved Feb 2016. World Health Organization, Disease outbreak news 19 February 2016: http://www.who.int/crs/don/27- may-016-lassa-fever-nigeria/en/.