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

Mahardika, Dhimas
Kartika, Sopia

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application

Tuberculosis is a disease which is very contagious among human. To prevent this from happening, 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 epidemic model of Tuberculosis with control using Pontryagin Minimum Principle to find optimal solution of the control with fixed time and free end point. 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.