Control Analysis on Dynamic System Model of Tuberculosis Disease with Educational Campaign, Vaccination, and Treatment

Nur Ilmayasinta; Prismahardi Aji Riyantoko; Annisa Rahmita Soemarsono; Ulifatur Rochmatin

doi:10.37905/jjom.v7i1.30663

Control Analysis on Dynamic System Model of Tuberculosis Disease with Educational Campaign, Vaccination, and Treatment

Nur Ilmayasinta, Prismahardi Aji Riyantoko, Annisa Rahmita Soemarsono, Ulifatur Rochmatin

Abstract

Tuberculosis (TB) is caused by bacteria (Mycobacterium tuberculosis) that most commonly attacks the lungs. TB is spread from person to person through the air. When people with pulmonary TB cough, sneeze, or spit, they propel TB germs into the air. By inhaling only a small number of these germs, a person can become infected. Tuberculosis is curable and preventable. Prevention that can be done is by providing education about TB and vaccines. While treatment can be done by treating infected individuals. This study examines the TB epidemic model with the application of control, by finding optimal control solutions using the Pontryagin Minimum Principle method. In this study, three control variables were applied, namely education, vaccination and treatment. Numerical calculations were carried out using the Forward Backward Sweep 4th order Runge Kutta method and and then simulated. The results of the numerical simulation of the TB epidemic model show that by implementing control in the form of education, vaccination, and treatment, the population of infected individuals can be reduced.

Keywords

Dynamic system; Tuberculosis; Optimal Control; PMP Method

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DOI: https://doi.org/10.37905/jjom.v7i1.30663