Analysis of a Discrete Predator-Prey Model for Controlling The Extinction of The Pesut Mahakam (Orcaella brevirostris) with Toxic Effect at The Mahakam River

Baso Indar; Moh. Nurul  Huda; Syaripuddin Syaripuddin

doi:10.20956/j.v20i1.26460

Authors

Baso Indar Mulawarman University
Moh. Nurul Huda University, Samarinda, Indonesia
Syaripuddin Syaripuddin University, Samarinda, Indonesia

DOI:

https://doi.org/10.20956/j.v20i1.26460

Keywords:

Pesut Mahakam, numerical simulation, predator-prey model, stability analysis, toxic effect

Abstract

The Pesut Mahakam (Orcaella brevirostris) is an East Kalimantan animal in critical condition and on the verge of extinction. One of the causes of the extinction of the Mahakam dolphins is the toxic effects of environmental pollution. In this study, an analysis of the discrete predator-prey model using Euler's forward difference between the Pesut Mahakam (Orcaella brevirostris) and its prey was investigated. Dynamic analysis includes determining the equilibrium point, stability analysis of the equilibrium point, and numerical simulation. The value of the Mahakam dolphin growth rate parameter (predator) is obtained by adjusting the curve based on data in the field. Numerical simulations were carried out to describe the results of the analysis. Changes in the value of the toxic effect rate parameter affects the number of Mahakam dolphins and their prey.

References

Aisyah, Dharmadi, Nasution, S.H., Oktaviani, D., Hartoto, D.I., 2007. Kondisi Kualitas Air Habitat Pesut Mahakam (Orcaella brevirostris) Di Wilayah Daerah Aliran Sungai Mahakam, Kalimantan Timur. Jurnal Penelitian Perikanan Indonesia. Vol 14. No 1. 47-53.

Budi, T., Krisnamurti, G.C., To’bungan, N. ,2023. Analisis Bioinformatika NADH2 sebagai Penanda Seleksi Adaptif Pesut Perairan Tawar dan Pesisir. Biota: Jurnal Ilmiah Ilmu-Ilmu Hayati. Vol 8. No 8. 30-39.

Haque, M., and Sarwardi, S., 2016. Effect of toxicity on a harvested fishery model. Modeling Earth Systems and Environment, Vol. 2, No.3, 1–10. doi: 10.1007/s40808-016-0175-x.

Huda, M. N., Amijaya, F. D. T. and Purnamasari, I., 2020. The Effect of Harvesting Activities on Prey-Predator Fishery Model With Holling Type Ii in Toxicant Aquatic Ecosystem, Australian Journal of Mathematical Analysis and Applications, Vol. 17, No.2, 1–11.

Jefferson, T. A. et al., 2016. Orcaella brevirostris (Mahakam River subpopulation), Irrawaddy Dolphin, The IUCN Red List of Threatened Species 2008 (Errata version 2016), e.T39428A9, 2–11.

Kreb, D. et al., 2010. Final Workshop Report : Establishing protected areas for Asian freshwater cetaceans, October.

Kreb, D. dan Budiono.,2019. Laporan Teknis Akhir Survei Monitoring Pesut Mahakam dan Kualitas Air Periode Agustus 2018 – Mei 2019. [Laporan]. Samarinda, Yayasan Konservasi RASI.

Kreb, D., 2023. Abundance of freshwater Irrawaddy dolphins in the Mahakam River in East Kalimantan, Indonesia, based on mark-recapture analysis of photo-identified individuals. Journal of Cetacean Research and Management. Vol 6. No 3. 269-277.

Liu, W., Cai, D. and Shi, J., 2018. Dynamic behaviors of a discrete-time predator–prey bioeconomic system, Advances in Difference Equations. Vol. 2018, No. 1, 1–22. doi: 10.1186/s13662-018-1592-0.

Lv, Y. et al., 2010. Harvesting of a phytoplankton-zooplankton model, Nonlinear Analysis: Real World Applications. Vol. 11, No.5, 3608–3619. doi: 10.1016/j.nonrwa.2010.01.007.

Ndii, M. Z., 2018. ‘Pemodelan matematika Dinamika Populasi dan Penyebaran Penyakit’, Deepublish.

Noor, I. Y., 2016. Pesut Mahakam, Profil, Peluang Kepunahan dan Upaya Konservasinya, Bidang Inventarisasi Daya Dukung Daya Tampung Sumber Daya Alam dan Lingkungan Hidup , P3E Kalimantan.

Nur, M.M., Azmi, M., Abidin, S., 2020. Sejarah Konservasi Pesut Mahakam Di Desa Pela Kabupaten Kutai Kartanegara 1970-2020. LANGGONG: Jurnal Ilmu Sosial dan Humaniora.Vol 1. No 2. 74-90.

Saha, T. and Bandyopadhyay, M., 2009. Dynamical analysis of toxin producing Phytoplankton-Zooplankton interactions, Nonlinear Analysis: Real World Applications, Vol. 10, No. 1, 314–332. doi: 10.1016/j.nonrwa.2007.09.001.

Rosmini, R., Zainuddin,Z., Aini, S.N., 2022. Legal Protection of Mahakam Dolphins Through Water Conservation Areas in Kutai Kartanegara Regency. Substantive Justice International Journal of Law. Vol 5. No 1, 1-10.

Suzyanna, 2013. Interaksi Antara Predator-Prey dengan Faktor Pemanen Prey, Journal of Scientific Modeling & Computation, Vol 1. No. 1, 58–66.

Zhuang, K. and Wen, Z., 2011. Dynamical behaviors in a discrete predator-prey model with a prey refuge, World Academy of Science, Engineering and Technology, Vol. 80, No. 8, 679–681.