### 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 language | English |
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Title of host publication | Proceedings of the 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019 |

Subtitle of host publication | Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations |

Editors | Herni Utami, Fajar Adi Kusumo, Nanang Susyanto, Yeni Susanti |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735419438 |

DOIs | |

Publication status | Published - 19 Dec 2019 |

Event | 8th 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 2019 → 1 Aug 2019 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2192 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations |
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Country | Indonesia |

City | Yogyakarta |

Period | 29/07/19 → 1/08/19 |

### Keywords

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

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## Cite this

*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