# The Solution of a Mathematical Model for Dengue Fever Transmission Using Differential Transformation Method

Keywords:
Dengue Fever, Mathematical Model, Differential Transformation Method, Ordinary Differential Equations

### Abstract

Differential Transformation Method (DTM) is a very effective tool for solving linear and non-linear ordinary differential equations. This paper uses DTM to solve the mathematical model for the dynamics of Dengue fever in a population. The graphical profiles for human population are obtained using Maple software. The solution profiles give the long term behavior of Dengue fever model which shows that treatment plays a vital role in reducing the disease burden in a population.

### References

G. R. Phaijoo, & D. B. Gurung ```Mathematical Model of Dengue Fever with and without awareness in Host Population", International Journal of Advanced Engineering Research and Applications 1 (2015) 2454.

M. Andraud, N. Hens, C. Marais & P. Beutels ``Dynamic Epidemiological Models for Dengue Transmission: A systematic Review of Structural Approaches", PLOS ONE 7 (2012) 1.

S. A. Carvalho, S. O. Silva & C.I.Charret ``Mathematical Modeling of Dengue Epidemic: Control Methods and Vaccination Strategies", Theory Biosci. (2019). https://doi.org/10.1007/s12064-019-00273-7

B. Ibis, M.Bayram & G.Agargun ``Applications of Fractional Differential Transform Method to Fractional Differential-Algebraic Equations", European Journal of Pure and Applied Mathematics 4 (2011) 5543.

M. A. E. Osman, K.K.Adu & C.Yang ``A Simple SEIR Mathematical Model of Malaria Transmission", Asian Research Journal of Mathematics 7 (2017) 1.

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

G. Methi, ``Solution of Differential Equation Using Differential Transform Method", Asian Journal of Mathematics & Statistics 9 (2016) 13

F. Mirzaee ``Differential Transform Method for Solving Linear and Nonlinear Systems of Ordinary Differential Equations", Applied Mathematical Sciences 5 (2011) 70.

A. A. Idowu, I. M. Olanrewaju, P. O. James, S. Amadiegwu & F. A. Oguntolu, ``Differential Transform Method for Solving Mathematical Model of SEIR and SEI Spread of Malaria", International Journal of Sciences: Basic and Applied Research (IJSBAR) 40 (2018) 197.

J. Andrawus & F. Y. Eguda, ``Analysis of a Mathematical Model to Investigate the Dynamics of Dengue Fever", J. Appl. Sci. Environ. Manage 21 (2017) 626.

O. J. Peter & M. O. Ibrahim, ``Application of Differential Transform Method in Solving a Typhoid Fever Model", International Journal of Mathematical Analysis and Optimization: Theory and Applications (2017) 250.

S. A. Somma, N. I. Akinwande, R. A. Abah, F. A. Oguntolu & F.D.Ayegbusi ``Semi-analytical Solution for the Mathematical Modeling of yellow fever dynamics incorporating secondary host", Communication in Mathematical Modeling and Applications 4 (2019) 9.

D. Okuonghae & S. E. Omosigho ``Analysis of Mathematical Model for Tuberculosis", Journal of Theo. Biol. 269 (2011) 31.

S. M. Garba, A. B. Gumel & M.R.Abubakar, ``Backward Bifurcations in Dengue Transmission Dynamics", Mathematical Biosciences 215 (2008) 11.

M. Andraud, N. Hens, C. Marais & P. Beutels ``Dynamic Epidemiological Models for Dengue Transmission: A systematic Review of Structural Approaches", PLOS ONE 7 (2012) 1.

S. A. Carvalho, S. O. Silva & C.I.Charret ``Mathematical Modeling of Dengue Epidemic: Control Methods and Vaccination Strategies", Theory Biosci. (2019). https://doi.org/10.1007/s12064-019-00273-7

B. Ibis, M.Bayram & G.Agargun ``Applications of Fractional Differential Transform Method to Fractional Differential-Algebraic Equations", European Journal of Pure and Applied Mathematics 4 (2011) 5543.

M. A. E. Osman, K.K.Adu & C.Yang ``A Simple SEIR Mathematical Model of Malaria Transmission", Asian Research Journal of Mathematics 7 (2017) 1.

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

G. Methi, ``Solution of Differential Equation Using Differential Transform Method", Asian Journal of Mathematics & Statistics 9 (2016) 13

F. Mirzaee ``Differential Transform Method for Solving Linear and Nonlinear Systems of Ordinary Differential Equations", Applied Mathematical Sciences 5 (2011) 70.

A. A. Idowu, I. M. Olanrewaju, P. O. James, S. Amadiegwu & F. A. Oguntolu, ``Differential Transform Method for Solving Mathematical Model of SEIR and SEI Spread of Malaria", International Journal of Sciences: Basic and Applied Research (IJSBAR) 40 (2018) 197.

J. Andrawus & F. Y. Eguda, ``Analysis of a Mathematical Model to Investigate the Dynamics of Dengue Fever", J. Appl. Sci. Environ. Manage 21 (2017) 626.

O. J. Peter & M. O. Ibrahim, ``Application of Differential Transform Method in Solving a Typhoid Fever Model", International Journal of Mathematical Analysis and Optimization: Theory and Applications (2017) 250.

S. A. Somma, N. I. Akinwande, R. A. Abah, F. A. Oguntolu & F.D.Ayegbusi ``Semi-analytical Solution for the Mathematical Modeling of yellow fever dynamics incorporating secondary host", Communication in Mathematical Modeling and Applications 4 (2019) 9.

D. Okuonghae & S. E. Omosigho ``Analysis of Mathematical Model for Tuberculosis", Journal of Theo. Biol. 269 (2011) 31.

S. M. Garba, A. B. Gumel & M.R.Abubakar, ``Backward Bifurcations in Dengue Transmission Dynamics", Mathematical Biosciences 215 (2008) 11.

Published

2019-11-12

How to Cite

*Journal of the Nigerian Society of Physical Sciences*,

*1*(3), 82-87. Retrieved from https://journal.nsps.org.ng/index.php/jnsps/article/view/18

Section

Original Research

Copyright (c) 2019 Journal of the Nigerian Society of Physical Sciences

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