Kontrol Optimal untuk Model SIR Campak dengan Imunisasi Menggunakan Prinsip Minimum Pontryagin
DOI:
https://doi.org/10.24843/JMAT.2026.v16.i01.p197Keywords:
Measles, SIR model, Optimal control, Pontryagin’s Minimum PrincipleAbstract
Measles is a contagious disease that continues to affect a significant portion of the population, particularly infants and children. The disease can be prevented through immunization programs, including both basic and booster immunizations, which are part of government public health initiatives. This study aims to reduce the spread of measles while minimizing immunization costs by incorporating a control variable into the SIR (Susceptible–Infected–Recovered) model of disease transmission. The method employed is Pontryagin’s Minimum Principle to determine the optimal immunization strategy that is both effective and cost-efficient. The results indicate that the inclusion of an immunization control in the model significantly decreases the susceptible population and reduces the growth rate of the infected compartment. Furthermore, the recovered population increases more rapidly compared to the model without control. The proportion of the immunized population demonstrates that a more optimal control strategy leads to greater effectiveness in suppressing disease transmission. Therefore, the application of optimal control in the SIR model provides a valuable mathematical framework to support immunization policies for measles prevention and control.
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Copyright (c) 2026 Dhea Wasila Rahmi, Elyin Fitrawati, Amilia Ulul Azmi, Bulqis Nebulla Syechah, Tri Maryono Rusadi
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