Differential transformation method (DTM) for solving SIS and SI epidemic models

Differential equations play an important role in modeling real world problem. One of the importance of differential equations is seen in the SIS and SIR epidemic models. Many researches have been proposed to solve SIS and SIR models numerically. However, there is no study about the application of Differential Transformation Method (DTM) for solving SIS and SI epidemic models. In this study, DTM is proposed to solve the SIS and SI epidemic models for constant population. Firstly, the theoretical background of DTM is studied and followed by constructing the solutions of SIS and SI epidemic models. Furthermore, the convergence analysis of DTM is proven by proposing two theorems. Finally, numerical computations are made and compare with the exact solution. From the numerical result, the solution produced by DTM approaches the exact solution which agreed with the proposed theorems. In summary, DTM is an alternative technique to be considered in solving many practical problems involving differential equations.