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

• Dhimas Mahardika Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University, Indonesia
• Sopia Kartika Department of Mathematics, Faculty of Science and Technology, Karangturi National University, Indonesia
Keywords: Tuberculosis, Dynamical System, Optimal Control

### Abstract

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.

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Published
2024-03-01
How to Cite
[1]
D. Mahardika and S. Kartika, “DYNAMIC SYSTEM OF TUBERCULOSIS MODEL USING OPTIMAL CONTROL IN SEMARANG CITY INDONESIA”, BAREKENG: J. Math. & App., vol. 18, no. 1, pp. 0043-0052, Mar. 2024.
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Articles