DYNAMIC ANALYSIS OF PREDATOR-PREY MODEL WITH CANNIBALISM INTERVENTION AND DISEASE INFECTION IN PREY USING HOLLING TYPE II RESPONSE FUNCTION

  • Fardinah Fardinah Department of Mathematics, Faculty of Mathematics and Sciences, Universitas Sulawesi Barat, Indonesia https://orcid.org/0009-0003-9672-5400
  • Hikmah Hikmah Department of Statistics, Faculty of Mathematics and Sciences, Universitas Sulawesi Barat, Indonesia https://orcid.org/0009-0005-0081-3356
  • Rahmah Abubakar Department of Actuarial Sciences, Faculty of Mathematics and Sciences, Universitas Sulawesi Barat, Indonesia https://orcid.org/0009-0006-0288-805X
  • Laila Qadrini Department of Statistics, Faculty of Mathematics and Sciences, Universitas Sulawesi Barat, Indonesia https://orcid.org/0009-0004-8063-662X
  • Haris Haris Department of Mathematics, Faculty of Mathematics and Sciences, Universitas Sulawesi Barat, Indonesia https://orcid.org/0009-0003-1179-1215
  • Nadia Salsabilah Department of Statistics, Faculty of Mathematics and Sciences, Universitas Sulawesi Barat, Indonesia https://orcid.org/0009-0002-7396-2895
DOI: https://doi.org/10.30598/barekengvol19iss3pp1945-1956
Keywords: Cannibalism, Desease Infection, Holling type II, Predator-Prey Model

Abstract

This study discusses the intervention of cannibalism and disease spread with Holling Type II response function in the predator-prey model. It is assumed that disease infection is limited to the prey population and cannot be cured so that in this model there are three subpopulations namely susceptible prey, infected prey and predators. In addition, there is cannibalism in the predator population. The objectives of this study include constructing a predator-prey model with cannibalism intervention and disease infection in prey using Holling Type II response function, identifying the stability of the equilibrium point of the model and interpreting the model based on simulation results. Analysis of the stability of the equilibrium point is carried out with a linearization approach and the Routh-Hurwitz criterion was used to determine equilibrium stability. Based on the stability analysis, 5 (five) equilibrium points are obtained, namely population extinction, susceptible prey exists, predator extinction, infected prey extinction and population exists where the population extinction equilibrium point is unstable and the other equilibrium points are stable with the certain conditions. From the simulation, it is obtained that the numerical results are in accordance with the analytical results of the stability analysis of the equilibrium point of the model and for infinite time, there will be no population extinction while the state of susceptible prey exists, predator extinction, infected prey extinction and population exists can occur if the stability conditions are met. Based on the numerical simulations, it was found that changes in the parameter values of the rate of change of susceptible prey to infected prey and the coefficient of predator cannibalism in day-1 can cause changes in the type of stability of the equilibrium point. Thus, rate of change susceptible prey to infected prey and the coefficient of predator cannibalism affects the population of prey and predator.

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Published
2025-07-01
How to Cite
[1]
F. Fardinah, H. Hikmah, R. Abubakar, L. Qadrini, H. Haris, and N. Salsabilah, “DYNAMIC ANALYSIS OF PREDATOR-PREY MODEL WITH CANNIBALISM INTERVENTION AND DISEASE INFECTION IN PREY USING HOLLING TYPE II RESPONSE FUNCTION”, BAREKENG: J. Math. & App., vol. 19, no. 3, pp. 1945-1956, Jul. 2025.
Issue
Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
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Articles

Copyright (c) 2025 Fardinah Fardinah, Hikmah Hikmah, Rahmah Abubakar, Laila Qadrini, Haris Haris, Nadia Salsabilah

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