Transcendent Journal of Mathematics and Applications

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Home > Vol 3, No 2 (2024) > Samosir

Kontrol Optimal pada Penyebaran Penyakit Campak Model SIR

Restika Samosir, Yosina Arni Sihombing, Sitti Rosnafi’an Sumardi, Muhammad Hisyam

Abstract

The SIR model is a model used to group populations into 3 parts, namely susceptible or a subpopulation of individuals who are susceptible to disease, infected or a subpopulation of individuals who are infected and can transmit the disease and recovered or a subpopulation of individuals who have recovered from the disease. Measles is usually treated without a vaccine, so the disease is often found in the community. Giving the right and balanced vaccine will get results that are balanced with what is given. In this research, we develop a SIR model with additional controls. Where the control in this model is vaccination given to subpopulations S and I, so that the recovered subpopulation experiences an increase, because the number of subpopulation I decreases. The method used in this research consists of several steps, namely forming a SIR model which is formed in optimal control and determining the objective function. Next, solve the optimal control problem, which consists of several stages, namely forming the Hamiltonian function and finding states and co-states. Based on the research results, it is concluded that optimal control of the SIR model is obtained by state and co-state equations. Where this model is the result of reducing the Hamiltonian to obtain optimal control in the SIR model.

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References

Rohmah, A. M., Rohmaniah, S. A., & Kisno, R. A. (2022). Model Kontrol Optimal SIR Pada Penyakit Campak. Unisda Journal of Mathematics and Computer Science, 8, 67–73.

Widowati, & Sutimin. (2007). Buku Ajar Pemodelan Matematika. In Buku Ajar Pemodelan Matematika (p. 74).

Widoyono. (2005). Penyakit Tropis Epidemiologi, Penularan, Pencegahan & Pem-berantasannya. Erlangga.

DOI: https://doi.org/10.24815/tjoma.v3i2.42161

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Transcendent Journal of Mathematics and Applications (eISSN 2964-1845) is a scientific journal owned and managed by Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Syiah Kuala licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.