Mathematics and Statistics Vol. 9(1), pp. 71 - 80
DOI: 10.13189/ms.2021.090112
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Applications of the Differential Transformation Method and Multi-Step Differential Transformation Method to Solve a Rotavirus Epidemic Model

Pakwan Riyapan ^1,*, Sherif Eneye Shuaib ¹, Arthit Intarasit ¹, Khanchit Chuarkham ^2
1 Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, 94000, Thailand
² Faculty of Commerce and Management, Prince of Songkla University, Trang Campus, Trang 92000, Thailand

ABSTRACT

Epidemic models are essential in understanding the transmission dynamics of diseases. These models are often formulated using differential equations. A variety of methods, which includes approximate, exact and purely numerical, are often used to find the solutions of the differential equations. However, most of these methods are computationally intensive or require symbolic computations. This article presents the Differential Transformation Method (DTM) and Multi-Step Differential Transformation Method (MSDTM) to find the approximate series solutions of an SVIR rotavirus epidemic model. The SVIR model is formulated using the nonlinear first-order ordinary differential equations, where S; V; I and R are the susceptible, vaccinated, infected and recovered compartments. We begin by discussing the theoretical background and the mathematical operations of the DTM and MSDTM. Next, the DTM and MSDTM are applied to compute the solutions of the SVIR rotavirus epidemic model. Lastly, to investigate the efficiency and reliability of both methods, solutions obtained from the DTM and MSDTM are compared with the solutions from the Runge-Kutta Order 4 (RK4) method. The solutions from the DTM and MSDTM are in good agreement with the solutions from the RK4 method. However, the comparison results show that the MSDTM is more efficient and converges to the RK4 method than the DTM. The advantage of the DTM and MSDTM over other methods is that it does not require a perturbation parameter to work and does not generate secular terms. Therefore the application of both methods

KEYWORDS
Differential Transformation Method, Multi-step Differential Transformation Method, Rotavirus

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Pakwan Riyapan , Sherif Eneye Shuaib , Arthit Intarasit , Khanchit Chuarkham , "Applications of the Differential Transformation Method and Multi-Step Differential Transformation Method to Solve a Rotavirus Epidemic Model," Mathematics and Statistics, Vol. 9, No. 1, pp. 71 - 80, 2021. DOI: 10.13189/ms.2021.090112.

(b). APA Format:
Pakwan Riyapan , Sherif Eneye Shuaib , Arthit Intarasit , Khanchit Chuarkham (2021). Applications of the Differential Transformation Method and Multi-Step Differential Transformation Method to Solve a Rotavirus Epidemic Model. Mathematics and Statistics, 9(1), 71 - 80. DOI: 10.13189/ms.2021.090112.