Analisis Model Mangsa-Pemangsa dengan Fungsi Respon Holling Tipe II dan Adanya Infeksi Penyakit pada Mangsa

fardinah fardinah, Hikmah Hikmah, Nadia Salsabila

Abstract


This research discusses the predator-prey model with the Holling Type II response function and the presence of disease in the prey population. It is assumed that the disease infection only spreads within the prey population and cannot be cured so there are three subpopulations in the model, namely susceptible prey, infected prey and predators. This research aims to construct a prey-prey model with a Holling Type II response function and the presence of disease infection in the prey population, analyze the stability of the model equilibrium point and interpret the model. Analysis of the stability of the equilibrium point begins with the linearization method, and then the type of stability is determined based on the characteristics of the eigenvalues using the Routh-Hurwitz criterion. The results of this research obtained 5 (five) equilibrium points, namely population extinction, vulnerable prey existing, extinction of infected prey, extinction of predators and existing population. The results of the equilibrium point analysis show that all equilibrium points are stable if they fulfill the specified conditions. Based on the numerical simulations carried out, the interpretation was obtained that if the parameter values of the interaction rate of susceptible prey and infected prey as well as the rate of death due to disease were changed, this could cause a change in the stability of the equilibrium point.


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DOI: http://dx.doi.org/10.24014/jsms.v10i2.30041

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Jurnal JSMS

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