Analyzing effect of harvesting on prey population when prey growth depend on fear-factor and Allee-effect

Egi Safitri, Dipo Aldila

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A mathematical model of predator-prey considering Allee effect, fear factor and harvesting in prey population constructed in this topic. Meanwhile, anti-predation involved in predator population such that prey can counterattack their predators. The second type of Holling type functional response chosen to describe a predator who active searching for prey. We non-dimensionalize our model to reduce the number of parameters, then we analyzed the existence and local stability criteria of all equilibrium points analytically. There are maximum four equilibrium are found, where the extinction of predator population equilibrium might not unique. Our results suggest to consider the rate of harvesting in prey population wisely to guarantee the coexistence of prey and predator in the environment. Our results also show that the level of fear of prey might effect the final size of coexistence equilibrium. Our numerical results show that although the time scale do not effect the size of the coexistence equilibrium, it does change the speed of the system to reach the equilibrium point.

Original languageEnglish
Title of host publicationProceedings of the 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019
Subtitle of host publicationDeepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations
EditorsHerni Utami, Fajar Adi Kusumo, Nanang Susyanto, Yeni Susanti
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735419438
DOIs
Publication statusPublished - 19 Dec 2019
Event8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations - Yogyakarta, Indonesia
Duration: 29 Jul 20191 Aug 2019

Publication series

NameAIP Conference Proceedings
Volume2192
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations
CountryIndonesia
CityYogyakarta
Period29/07/191/08/19

Keywords

  • Allee-effect
  • Anti-predator behavior
  • Fear factor
  • harvesting
  • Predator-prey

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    Safitri, E., & Aldila, D. (2019). Analyzing effect of harvesting on prey population when prey growth depend on fear-factor and Allee-effect. In H. Utami, F. A. Kusumo, N. Susyanto, & Y. Susanti (Eds.), Proceedings of the 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations [060017] (AIP Conference Proceedings; Vol. 2192). American Institute of Physics Inc.. https://doi.org/10.1063/1.5139163