Study on SIR Epidemic Model with Constant Vaccination: A Differential Transformation Approach

Over the years, diligent vaccination campaigns have resulted in high levels of permanent immunity against the childhood disease among the population. Childhood diseases are the most common form of infectious diseases. In this article SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is developed. The qualitative analysis reveals the vaccination reproductive number . for disease control and eradication. The aim of this paper is to apply the differential transformation method (DTM) which is used to compute an approximation to the solution of the non-linear system of differential equations governing the problem. Graphical results are presented and discussed quantitatively to illustrate the solutions.