Comments on “The Solution of aMathematicalModel for Dengue Fever Transmission Using Differential Transformation Method: J. Nig. Soc. Phys. Sci. 1 (2019) 82-87”

The mathematical model for dengue fever transmission studied by [1], has been re-investigated. The differential transformation method (DTM) is used to compute the semi-analytical solutions of the non-linear differential equations of the compartment (SIR) model of dengue fever. This epidemiology problem is well-posed. The effect of treatment as a control measure is studied through the growth equations of exposed and infected humans. The inadvertent errors in the recurrence relations (DTM) of equations for dengue disease transmission including initial conditions have been removed. Furthermore, the semi-analytic solutions of the model are obtained and verified with the built-in function AsymptoticDSolveValue of Wolfram Mathematica. It has been found that results obtained from the DTM are valid only for small-time t (t < 1.5), as t becomes large, the human population (exposed and recovered) and infected vector population become negative.

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

Journal of the Nigerian Society of Physical Sciences ◽

10.46481/jnsps.2019.18 ◽

2019 ◽

pp. 82-87

Author(s):

Felix Yakubu Eguda ◽

Andrawus James ◽

Sunday Babuba

Keyword(s):

Mathematical Model ◽

Dengue Fever ◽

Transformation Method ◽

Vital Role ◽

Differential Transformation Method ◽

Linear Ordinary Differential Equations ◽

Differential Transformation ◽

Long Term Behavior ◽

The Mathematical Model

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.

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Generalized Differential Transformation Method for Solving system of Non linear Volterra integro-differential equations of fractional order

Journal of Education College Wasit University ◽

10.31185/eduj.vol1.iss25.139 ◽

2018 ◽

Vol 1 (25) ◽

pp. 523-550

Author(s):

Basim N.Abood ◽

Eman A.Hussain ◽

Mayada T. Wazi

Keyword(s):

Differential Equations ◽

Initial Conditions ◽

Approximate Solutions ◽

Convergent Series ◽

Transformation Method ◽

Differential Transformation Method ◽

Differential Transformation ◽

Modified Method ◽

Non Linear ◽

Generalized Differential

In this paper, the technique of modified Generalized Differential Transformation Method (GDTM) is used to solve a system of Non linear integro-differential equations with initial conditions. Moreover, a particular example has been discussed in three different cases to show reliability and the performance of the modified method. The fractional derivative is considered in the Caputo sense .The approximate solutions are calculated in the form of a convergent series, numerical results explain that this approach is trouble-free to put into practice and correct when applied to systems integro-differential equations.

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Study of Properties of Differential Transform Method for Solving the Linear Differential Equation

Asian Journal of Engineering and Applied Technology ◽

10.51983/ajeat-2019.8.2.1138 ◽

2019 ◽

Vol 8 (2) ◽

pp. 50-56

Author(s):

Nandita Das

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Linear Equations ◽

Transformation Method ◽

Differential Transformation Method ◽

Transform Method ◽

Differential Transformation ◽

Differential Transform ◽

Linear Differential ◽

Non Linear Equations

The differential transformation method (DTM) is an alternative procedure for obtaining an analytic Taylor series solution of differential linear and non-linear equations. However, the proofs of the properties of equation have been long ignored in the DTM literature. In this paper, we present an analytical solution for linear properties of differential equations by using the differential transformation method. This method has been discussed showing the proof of the equation which are presented to show the ability of the method for linear systems of differential equations. Most authors assume the knowledge of these properties, so they do not bother to prove the properties. The properties are therefore proved to serve as a reference for any work that would want to use the properties without proofs. This work argues that we can obtain the solution of differential equation through these proofs by using the DTM. The result also show that the technique introduced here is accurate and easy to apply.

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