An Seir Model for Measles Transmission in North Sumatra Using the Fourth-Order Runge–Kutta Method for an Optimal Control Strategy
DOI:
https://doi.org/10.30605/proximal.v9i2.9552Keywords:
Measles, SEIR model, Fourth-Order Runge–Kutta method, Control variable, Numerical simulationAbstract
Measles remains one of the major public health concerns in North Sumatra Province. This study aims to analyze the dynamics of measles transmission using the Susceptible–Exposed–Infected–Recovered (SEIR) model, which is solved numerically using the Fourth-Order Runge–Kutta (RK4) method and incorporates a control variable to evaluate the effect of reducing social contact on disease transmission. The study employs secondary data on measles cases obtained from the North Sumatra Provincial Health Office. Numerical simulations were performed using MATLAB with a step size of h = 1 day over a simulation period of 100 days. The results show that the SEIR model is capable of describing the dynamics of measles transmission through changes in the number of individuals in each compartment. The RK4 method provides stable numerical solutions, while the implementation of the control variable effectively reduces the number of individuals in the Exposed (E) and Infected (I) compartments. Among the four control scenarios examined, namely u = 0, u = 0.3, u = 0.6, and u = 0.9, the control level of u = 0.9 was found to be the most effective in suppressing the spread of measles.References
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Beni, O., Anisa, K., Cahyanti, N., Nisa, R., & Agushybana, F. (2021). Dampak Revolusi Mobilisasi Penduduk terhadap Persebaran Penyakit Menular di Indonesia. Jurnal Kesehatan Masyarakat, 7(1).
Chebotaeva, V., Srinivasan, A., & Vasquez, P. A. (2025). Differentiating Contact with Symptomatic and Asymptomatic Infectious Individuals in a SEIR Epidemic Model. Mathematical Biology, 87(38), 1–25.
Costa, A. L. P. da, Pires, M. A., Resque, R. L., & Almeida, and S. S. M. da S. de. (2021). Mathematical Modeling of the Infectious Diseases: Key Concepts and Applications. Infectious Diseases and Epidemiology, 7(5), 1–9.
Lim, D., Ko, K. T., Hong, H., Lee, H., & Choi, B. (2025). A history-dependent approach for accurate initial condition estimation in epidemic models. 1–21. https://doi.org/10.1371/journal.pcbi.1013438
Nisa, S. F., Yulida, Y., Keahlian, K., & Lingkungan, M. (2022). MODIFIKASI MODEL SEIR PADA PENYAKIT CAMPAK. Jurnal Matematika Murni Dan Terapan, 16(1), 13–27.
Pasaribu, S. M., & Husein, I. (2024). Modeling The Proportion of Measles Cases in North Sumatra by The Jack-Knife Partial Least Squares Method. Journal of Computer Science, Information Technology and Telecommunication Engineering (JCoSITTE), 5(2), 669–678. https://doi.org/10.30596/jcositte.v5i2.20928
Vitanov, N. K. (2023). Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics. Computation, 11(129), 1–10.
Xerri, T., Darmanin, N., Zammit, M. A., & Fsadni, C. (2020). Complications of measles : a case series. BMJ Publishing Group Limited, 13(3), 3–6. https://doi.org/10.1136/bcr-2019-232408
Zahrah, N. D., Nurani, F. S., Amanda, A. P., Muthia, F., & Herbawan, C. K. (2023). STUDI LITERATUR: ANALISIS FAKTOR RISIKO CAMPAK PADA ANAK DI INDONESIA. Medika Malahayati, 7(3), 748–758.
Asy-syifaa, Kurniasih, A., Lubis, S. A. L., & Damanik, R. Z. (2024). KARAKTERISTIK KEJADIAN CAMPAK PADA ANAK DI RSUD DR. FAUZIAH KABUPATEN BIREUEN TAHUN 2022. Jurnal Kedokteran STM (Sains Dan Teknologi Medik), VII(I), 24–32.
Beni, O., Anisa, K., Cahyanti, N., Nisa, R., & Agushybana, F. (2021). Dampak Revolusi Mobilisasi Penduduk terhadap Persebaran Penyakit Menular di Indonesia. Jurnal Kesehatan Masyarakat, 7(1).
Chebotaeva, V., Srinivasan, A., & Vasquez, P. A. (2025). Differentiating Contact with Symptomatic and Asymptomatic Infectious Individuals in a SEIR Epidemic Model. Mathematical Biology, 87(38), 1–25.
Costa, A. L. P. da, Pires, M. A., Resque, R. L., & Almeida, and S. S. M. da S. de. (2021). Mathematical Modeling of the Infectious Diseases: Key Concepts and Applications. Infectious Diseases and Epidemiology, 7(5), 1–9.
Lim, D., Ko, K. T., Hong, H., Lee, H., & Choi, B. (2025). A history-dependent approach for accurate initial condition estimation in epidemic models. 1–21. https://doi.org/10.1371/journal.pcbi.1013438
Nisa, S. F., Yulida, Y., Keahlian, K., & Lingkungan, M. (2022). MODIFIKASI MODEL SEIR PADA PENYAKIT CAMPAK. Jurnal Matematika Murni Dan Terapan, 16(1), 13–27.
Pasaribu, S. M., & Husein, I. (2024). Modeling The Proportion of Measles Cases in North Sumatra by The Jack-Knife Partial Least Squares Method. Journal of Computer Science, Information Technology and Telecommunication Engineering (JCoSITTE), 5(2), 669–678. https://doi.org/10.30596/jcositte.v5i2.20928
Vitanov, N. K. (2023). Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics. Computation, 11(129), 1–10.
Xerri, T., Darmanin, N., Zammit, M. A., & Fsadni, C. (2020). Complications of measles : a case series. BMJ Publishing Group Limited, 13(3), 3–6. https://doi.org/10.1136/bcr-2019-232408
Zahrah, N. D., Nurani, F. S., Amanda, A. P., Muthia, F., & Herbawan, C. K. (2023). STUDI LITERATUR: ANALISIS FAKTOR RISIKO CAMPAK PADA ANAK DI INDONESIA. Medika Malahayati, 7(3), 748–758.
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