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
Highlights
Epidemic diseases remain an increasing threat worldwide challenging researchers, decision-makers, and public health officers to monitor, identify, and respond to near-real-time infection outbreaks [1]
To investigate the efficiency and reliability of both methods, solutions obtained from the Differential Transformation Method (DTM) and Multi-Step Differential Transformation Method (MSDTM) are compared with the solutions from the Runge-Kutta Order 4 (RK4) method
To examine the accuracy of the MSDTM, its solutions are compared with the solutions of the SVIR model using the RK4 method
Summary
Epidemic diseases remain an increasing threat worldwide challenging researchers, decision-makers, and public health officers to monitor, identify, and respond to near-real-time infection outbreaks [1]. Mathematical models are essential toolkits to understand epidemic diseases because they aid scientists in analyzing and predicting disease mechanisms and their future outbreaks. Compartmental models are described using a set of mathematical equations to understand how individuals in various “compartments” in a population interact with one another [2]. The SIR model is an example of a compartment model widely used to study epidemic diseases. This model describes the movement of human between the susceptible S, infective I and removed R compartments, respectively.
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