DEVELOPING VSEIR MODEL WITH THE VACCINATION TO REDUCE THE SPREAD OF TUBERCULOSIS DISEASE IN NORTH SUMATERA

This study aims to build a new model of the spread of pulmonary tuberculosis (TB) in order to reduce the level of distribution, with the added effect of vaccination models susceptible exposed to infection and recovery (VSIR) who had previously built up to be a model VSEIR. To test the validity of this model will be proven stability analysis. Analysis of both models is conducted using linearization method by studying the nature of equilibrium points. Simulation for models using derive parameter values in an attempt to study the spread of dengue viruses in North Sumatera. The research also aims to find out the value of Reproductive number over the total of the Tuberculosis cases reporting in North Sumatera. Furthermore, a comparison between the real data and the numerical solution using the fourth order Runge-Kutta method (RK4). To overcome the spread will be tested in the analysis of optimal singular control over this VSIR and Susceptible Exposed Infected and Recovery (SEIR) models of Tuberculosis, finally, we also proof the optimal singular control for Vaccination Susceptible Exposed Infected and Recovery (VSEIR) model.