Kontrol Optimal Penyebaran Penyakit Mulut dan Kuku pada Sapi Ternak Menggunakan Prinsip Minimum Pontryagin

Sari, Dwi Ambar (2025) Kontrol Optimal Penyebaran Penyakit Mulut dan Kuku pada Sapi Ternak Menggunakan Prinsip Minimum Pontryagin. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Penyakit Mulut dan Kuku (PMK) adalah infeksi virus yang disebabkan oleh Foot and Mouth Disease Virus (FMDV) yang menyerang hewan berkuku belah atau genap, seperti sapi. Gejala awal penyakit ini adalah demam tinggi, penurunan nafsu makan, peningkatan produksi air liur, dan pelepuhan di sekitar mulut dan kuku. Penyakit ini menyebabkan kematian sapi dan kerugian besar bagi sektor ekonomi dan pangan. Sehingga untuk menurunkan penyebaran wabah, dilakukan analisis dan modifikasi model matematika SEIR (Susceptible, Exposed, Infected, Recovered) untuk memahami pola penyebaran PMK. Hasil analisis kestabilan menunjukkan bahwa model bersifat tidak stabil di sekitar titik kesetimbangan bebas penyakit dan bersifat stabil di sekitar titik kesetimbangan penyebaran penyakit. Hal ini mengindikasikan bahwa penyebaran penyakit akan terus menyebar di dalam populasi, sehingga diperlukan penambahan kontrol berupa vaksinasi, pengobatan, dan disinfeksi pada model SEIR untuk meminimalkan penyebaran. Ketiga kontrol tersebut dioptimalkan menggunakaan Prinsip Minimum Pontryagin dan disimulasikan secara numerik menggunakan metode Runge Kutta Orde Empat untuk mengetahui tingkat keefektifan pemberian kontrol. Hasil penelitian menunjukkan bahwa model matematika yang telah diberi kontrol dapat menurunkan proporsi populasi rentan sebesar 33%, proporsi populasi terpapar sebesar 34%, dan proporsi populasi terinfeksi sebesar 8.7%, serta meningkatkan proporsi populasi sembuh hingga 38.5%, secara signifikan lebih efektif dibandingkan model tanpa kontrol. Oleh karena itu, penambahan ketiga kontrol pada model SEIR terbukti efektif dan efisien dalam meminimalimalkan penyebaran penyakit.
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Foot and Mouth Disease (FMD) is a viral infection caused by Foot and Mouth Disease Virus (FMDV) that affects cloven-hoofed or even-hoofed animals, such as cattle. Early symptoms of the disease are high fever, decreased appetite, increased saliva production, and blistering around the mouth and hooves. The disease causes cattle deaths and huge losses to the economy and food sector. So to reduce the spread of the outbreak, the SEIR (Susceptible, Exposed, Infected, Recovered) mathematical model was analyzed and modified to understand the pattern of FMD spread. The stability analysis results show that the model is unstable around the disease-free equilibrium point and stable around the equilibrium point of disease spread. This indicates that the spread of the disease will continue to spread in the population, so it is necessary to add controls in the form of vaccination, treatment, and disinfection to the SEIR model to minimize the spread. The three controls are optimized using the Pontryagin Minimum Principle and numerically simulated using the Fourth Order Runge Kutta method to determine the effectiveness of the control. The results showed that the mathematical model with controls can reduce the proportion of susceptible population by 33%, the proportion of exposed population by 34%, and the proportion of infected population by 8.7%, and increase the proportion of recovered population by 38.5%, which is significantly more effective than the model without controls. Therefore, the addition of the three controls to the SEIR model proved to be effective and efficient in minimizing the spread of the disease.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Penyakit Mulut dan Kuku, model SEIR, kontrol optimal, Prinsip Minimum Pontryagin. Foot and Mouth Disease, SEIR model, optimal control, Pontryagin Minimum Principle
Subjects:	Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Dwi Ambar Sari
Date Deposited:	01 Aug 2025 01:56
Last Modified:	01 Aug 2025 01:56
URI:	http://repository.its.ac.id/id/eprint/124296

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