Analisis Numerik Model Predator-Mangsa dengan Transmisi Penyakit yang Bergantung pada Suhu

Arrival Rince Putri (Universitas Andalas)
Muhammad Farhan Bunayya (Universitas Andalas)
Muhafzan Muhafzan (Universitas Andalas)

Mandalika Mathematics and Educations Journal
Vol 8 No 3 (2026): Edisi September

This research aims to formulate and analyze a four-dimensional non-linear mathematical predator-prey model that integrates the impacts of environmental temperature variation on prey growth, horizontal disease transmission of mass-action type, and quarantine actions on infected prey. The research method used is pure analytical research to determine equilibrium points, supported by numerical simulations using the fourth-order Runge-Kutta method. The results identify four biological equilibrium points: disease-free without predator, disease-free with predator, endemic without predator, and endemic with predator. Numerical simulations show that a linear temperature rise up to an extreme of 35℃ drastically reduces prey growth rate, lowering prey density below the transmission threshold and naturally eliminating the pathogen, but triggering predator extinction due to the loss of food supply. In conclusion, quarantine actions act as an effective functional refuge in maintaining predator survival, indicating that conservation policies must integrate population health management and global warming mitigation.