DYNAMIC SYSTEM OF TUBERCULOSIS MODEL USING OPTIMAL CONTROL IN SEMARANG CITY INDONESIA

Abstract

Tuberculosis is a disease that is very contagious among humans. To prevent this from happening, the Semarang city government has enacted vaccination for exposed individuals and treatment for the infected individuals. Vaccination and treatment are forms of control that will be applied to dynamic model systems of Tuberculosis. The present paper will describe an epidemic model of Tuberculosis with control using the Pontryagin Minimum Principle to find the optimal solution of the control with a fixed time and free endpoint. The optimal control will aim to reduce or minimize the number of infected populations. Numerical calculation is carried out with MATLAB software programming to illustrate and compare the graph of the dynamic model with and without optimal control. The results of dynamic modeling of Tuberculosis with control state that vaccination and treatment have succeeded in reducing the population of infected individuals.