Application of Variational Iteration Method in Solving Typhoid Fever Model

This paper presents and studies a deterministic mathematical model of typhoid fever dynamics. We verified the uniqueness and the existence of the model's equations using the Lipchitz condition to check the validity of the model. The basic concept of disease transmission is discussed. We applied the Variational Iteration Method (VIM) to solve the model equations. The model equations are described by a nonlinear differential equation of order one. The model is solved using VIM. The validity of the method was verified by the Runge-Kutta method of order four (RK4) implemented in Maple 16 software. In order to confirm the efficiency of VIM, the solutions obtained by the two methods were compared. The profiles of the solutions of each variable in the model were presented and we confirmed that VIM and RK4 were in good agreement. The results reveal that VIM is accurate and efficient in finding the solution to the Typhoid fever model.