Kontrol Optimal Model Dinamik Penyebaran Penyakit Tuberkulosis dengan Kekambuhan di Kota Semarang
DOI:
https://doi.org/10.12962/limits.v22i3.4349Keywords:
Tuberkulosis, Kekambuhan, Kontrol OptimalAbstract
In this study, we modified the SVIR (Susceptible, Vaccinated, Infectious, Recovered) dynamic model by considering relapse in the spread of Tuberculosis (TB). To reduce the spread of TB, we applied optimal control theory using Pontryagin's Minimum Principle. Two control variables were used: TB prevention education and treatment for actively infected individuals. This optimal control system was solved through numerical simulations using the Forward-Backward Sweep and fourth-order Runge-Kutta methods. The results of the numerical simulations were used to illustrate the difference between implementing a control strategy and no control. The results showed that the education intervention was able to reduce the actively infected subpopulation by 99.74%, while if the treatment intervention alone was given, the number of infected individuals showed a decrease of 99.69%. However, when both interventions were implemented simultaneously, the actively infected subpopulation was able to be reduced by up to 99.90%. In this case, implementing education and treatment controls simultaneously was more effective than implementing the controls separately and was able to significantly increase the recovered subpopulation, indicating more optimal disease control
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