APPROXIMATE SOLUTION OF VACCINATION, SUSCEPTIBLE, EXPOSED, INFECTED, RECOVERED (VSEIR) MODEL OF TUBERCULOSIS IN NORTH SUMATERA INDONESIA - Rangkuti, Yulita Molliq; Setia Sinaga, Marlina (Malaysian Journal of Science, 2015)
In this paper, a vaccination susceptible exposed infected recovered (VSEIR) model f o r tuberculosis in North Sumatera is discussed. The VSEIR model is formed by a system of nonlinear differential equations. The approximate solution of this model is obtained by using the step variational iteration method (SVIM) and variational iteration method (VIM). VIM used the general Lagrange multiplier in the correction functional and runs iteratively. SVIM also used the general Lagrange multipliers for construction of the correction functional for the problems, and runs by step approach, where the computation is done b y d i v i d i n g the interval into subintervals with time steps. The two methods are alternative methods to obtain the approximate solutions of the VSEIR model. Comparison is made with the conventional numerical method, t h e fourth-order Runge–Kutta method (RK4). From the results, the SVIM solution is more accurate than the VIM solution for long time interval when compared to RK4. Keywords: VSEIR model, General Lagrange Multiplier, Variational Iteration Method, Step Variational Iteration Method, Fourth Order Runge Kutta