In this paper, the differential transformation method (DTM) is employed to find the semi-analytical solutions of 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 compared with the exact solutions. From the numerical results,
the solutions produced by DTM approach the exact solutions which agreed with the proposed theorems. It can be seen that
the DTM is an alternative technique to be considered in solving many practical problems involving differential equations.