Analisis Model Mangsa Pemangsa dengan Adanya Penyakit dan Pemanenan pada Pemangsa - fardinah, Fardinah (Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika, 2023)
The interaction between two populations that are prey and predator can be described in a prey-predator model. In fact, in the interaction of prey and predators it can occur that when the density of prey is low, the effect of predation is also low, but if the size of the prey population increases, predation will be more intense which is stated in the Holling III Type response function model. In addition, it can also be found in an environment where there are populations of sick predator that result in death from the disease. This study aims to analyze the stability of the prey-predator model with the Holling III Type response function which consists of three subpopulations namely prey, healthy predator and sick predator. The analysis was carried out using the linearization method and then the type of stability was determined based on the characteristic eigenvalues obtained using the Routh-Hurwitz criteria. From this research it was found that population extinction is not possible while prey exists, extinction of diseased predator and populations exist is still possible if the required conditions are satisfy. Numerical simulations show that an increased harvesting rate in healthy predator populations results in a decrease in healthy predator populations, an increase in prey populations and a decrease in diseased predator populations. Meanwhile, a reduced harvesting rate for sick predator populations does not have a significant effect on the number of diseased predator populations, but results in an increase in the number of healthy predator populations and a decrease in prey populations