Predator-Prey Model in the Growth Phase of Rice Plants with Pest Control Using Pesticides

Afaf Himmatul Ulum; Muh. Fajar Safaatullah

doi:10.15294/ujm.v13i1.15133

Jurnal

Predator-Prey Model in the Growth Phase of Rice Plants with Pest Control Using Pesticides

Unnes Journal of Mathematics · Vol. 13 No. 1 (2025) · hlm. 1–10

DOI: 10.15294/ujm.v13i1.15133
ISSN: 2460-5859, 2252-6943
Terbit: 2025-06-11
Penerbit: Universitas Negeri Semarang
Bahasa: eng

Abstrak

In Indonesia, Rice is the primary food crop in Indonesia, with rice being the staple food for more than half of the population. However, pest infestations at each stage of rice growth pose a serious threat that can reduce crop yields. This study developed a predator-prey mathematical model to describe the interactions between rice plants at different growth stages, such as the vegetative, reproductive, and maturation phases, and three major pests: rice stem borers, brown planthoppers, and rats. The model also incorporates Pontryagin's maximum principle for optimal control through pesticide application. The method yields state and costate equations, which are solved using the fourth-order Runge-Kutta forward-backward sweep method with the assistance of Scilab 2024 software. The objective of this research is to examine the model, analyze its stability and controllability, and conduct numerical simulations. The results indicate that the model has a stable equilibrium point, suggesting that the system is controllable. The simulation shows that pesticide application is effective in controlling pests during all stages of rice growth. The populations of rice stem borers, brown planthoppers, and rats decrease significantly, with each pest population reduced to fewer than 10 individuals. These results demonstrate that pesticide use helps maintain ecological balance, and reduces pest damage to rice plants.

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State University of Semarang
Universitas Airlangga
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Rekan penulis	Organisasi	Artikel bersama
Mela Widyaningrum	Afiliasi tidak diketahui	1
Yunita Eka Sari	Afiliasi tidak diketahui	1
Amidi Amidi	Afiliasi tidak diketahui	1
Abdil Munir Pangestu	Afiliasi tidak diketahui	1
Walid Walid	State University of Semarang	1
Widya Rizky Fadhilla	Afiliasi tidak diketahui	1
Kartono Kartono	Universitas Airlangga	1
Scolastika Mariani	State University of Semarang	1
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Sumber metadata: OAI-PMH (metadata jurnal) https://journal.unnes.ac.id/journals/ujm/oai, pertama di-harvest 6 Nov 2026, terakhir terlihat 8 Nov 2026.

Metadata asli (oai_dc)

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	<dc:title xml:lang="en">Predator-Prey Model in the Growth Phase of Rice Plants with Pest Control Using Pesticides</dc:title>
	<dc:creator xml:lang="en">Afaf Himmatul Ulum</dc:creator>
	<dc:creator xml:lang="en">Muh. Fajar Safaatullah</dc:creator>
	<dc:subject xml:lang="en">Predator-prey model</dc:subject>
	<dc:subject xml:lang="en">pesticide control</dc:subject>
	<dc:subject xml:lang="en"> Pontryagin's maximum principle</dc:subject>
	<dc:subject xml:lang="en"> 4th-order Runge-Kutta forward-backward  Sweep</dc:subject>
	<dc:description xml:lang="en">In Indonesia, Rice is the primary food crop in Indonesia, with rice being the staple food for more than half of the population. However, pest infestations at each stage of rice growth pose a serious threat that can reduce crop yields. This study developed a predator-prey mathematical model to describe the interactions between rice plants at different growth stages, such as the vegetative, reproductive, and maturation phases, and three major pests: rice stem borers, brown planthoppers, and rats. The model also incorporates Pontryagin's maximum principle for optimal control through pesticide application. The method yields state and costate equations, which are solved using the fourth-order Runge-Kutta forward-backward sweep method with the assistance of Scilab 2024 software. The objective of this research is to examine the model, analyze its stability and controllability, and conduct numerical simulations. The results indicate that the model has a stable equilibrium point, suggesting that the system is controllable. The simulation shows that pesticide application is effective in controlling pests during all stages of rice growth. The populations of rice stem borers, brown planthoppers, and rats decrease significantly, with each pest population reduced to fewer than 10 individuals. These results demonstrate that pesticide use helps maintain ecological balance, and reduces pest damage to rice plants.</dc:description>
	<dc:publisher xml:lang="en">Universitas Negeri Semarang</dc:publisher>
	<dc:date>2025-06-11</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
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	<dc:type xml:lang="en">Peer-reviewed Article</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unnes.ac.id/journals/ujm/article/view/15133</dc:identifier>
	<dc:identifier>10.15294/ujm.v13i1.15133</dc:identifier>
	<dc:source xml:lang="en">Unnes Journal of Mathematics; Vol. 13 No. 1 (2024): Unnes Journal of Mathematics Volume 1, 2024; 1-10</dc:source>
	<dc:source>2460-5859</dc:source>
	<dc:source>2252-6943</dc:source>
	<dc:source>10.15294/ujm.v1i1</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://journal.unnes.ac.id/journals/ujm/article/view/15133/4357</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2024 Unnes Journal of Mathematics</dc:rights>
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