Kontrol Optimal pada Model Predator–Prey dengan Respons Fungsional Holling Tipe II untuk Pengendalian Hama Berbasis Predator Alami

Dewi Suhika; Nurul Indah Safitri; Nela Rizka

doi:10.35472/indojam.v6i2.2993

Dewi Suhika
Nurul Indah Safitri Institut Teknologi Sumatera
Nela Rizka Institut Teknologi Sumatera

DOI: https://doi.org/10.35472/indojam.v6i2.2993

Abstract

Hama tanaman merupakan salah satu faktor utama yang dapat menurunkan produktivitas pertanian, sehingga diperlukan strategi pengendalian yang efektif, terukur, dan tetap mempertimbangkan keberlanjutan ekosistem. Penggunaan pengendalian kimia secara berlebihan dapat memberikan dampak negatif terhadap lingkungan dan organisme bukan sasaran, termasuk predator alami. Oleh karena itu, diperlukan pendekatan pengendalian yang mampu menekan populasi hama sekaligus menjaga keberadaan predator alami dalam sistem. Penelitian ini membahas model kontrol optimal pada dinamika interaksi hama dan predator alami dengan dua strategi pengendalian, yaitu pengendalian hama dan pelepasan predator alami. Model yang digunakan berbentuk sistem predator-prey dengan respons fungsional Holling tipe II. Fungsi tujuan dirancang untuk meminimumkan kepadatan hama, biaya pengendalian hama, biaya pelepasan predator alami, serta penalti terminal terhadap populasi hama pada akhir waktu simulasi. Prinsip Maksimum Pontryagin digunakan untuk memperoleh sistem optimalitas yang terdiri atas sistem state, sistem adjoint, syarat transversal, dan karakterisasi kontrol optimal. Selanjutnya, solusi numerik diperoleh menggunakan metode forward-backward sweep. Hasil simulasi menunjukkan bahwa penerapan dua kontrol optimal mampu menekan kepadatan hama secara signifikan. Pada akhir simulasi, kepadatan hama tanpa kontrol sebesar , sedangkan dengan dua kontrol optimal turun menjadi , atau mengalami penurunan sekitar . Selain itu, kepadatan predator alami dengan kontrol tetap bernilai positif sebesar , sehingga predator alami masih dapat dipertahankan dalam sistem. Nilai fungsi objektif juga menurun dari tanpa kontrol menjadi dengan kontrol. Dengan demikian, kombinasi pengendalian hama dan pelepasan predator alami efektif dalam menekan populasi hama dengan tetap mempertimbangkan biaya kontrol dan keberlanjutan predator alami.

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