A Comparison Between Adomian Decomposition Method and Differential Transformation Method in Solving SIR Epidemic Model with Constant Vaccination

Abstract

The trend of susceptible, infected and recovered of an epidemic can be mathematically
analyzed if the solution of its SIR model is obtained. Various analytical and numerical methods were
used by previous researchers in order to solve the model. Adomian Decomposition is one of the
methods. However, several studies discovered that ADM is tedious and time consuming in solving
certain kinds of problems. In this project, another method was used and compared to ADM in
solving SIR model with the coverage of vaccination. The method was Differential Transformation
Method (DTM). The main objective of this project is to analyse the difference between these two
methods in the process of getting the final solution. It was identified that to get only one term of the
polynomial solution model of SIR, ADM requires many iterations unlike DTM which only requires
one iteration for each term of the polynomial solution model. However, in terms of overall
polynomial model, ADM gives a higher degree of polynomial model compared to DTM for the
same number of iteration.