A predator-prey model for the optimal control of fish harvesting through the imposition of a tax

Anal Chatterjee; Samares  Pal

doi:10.11121/ijocta.2023.1218

Authors

Anal Chatterjee Department of Mathematics, Barrackpore Rastraguru Surendranath College, Barrackpore, Kolkata, India https://orcid.org/0000-0001-5780-9511
Samares Pal Department of Mathematics, University of Kalyani, Kalyani, India https://orcid.org/0000-0002-8792-0031

DOI:

https://doi.org/10.11121/ijocta.2023.1218

Abstract

This paper is devoted to the study of ecosystem based fisheries management. The model represents the interaction between prey and predator population with Holling II functional response consisting of different carrying capacities and constant intrinsic growth rates. We have considered the continuous harvesting of predator only. It is observed that if the intrinsic growth rate of predator population crosses a certain critical value, the system enters into Hopf bifurcation. Our observations indicate that tax, the management object in fisheries system play huge impacts on this system. The optimal harvesting policy is disposed by imposing a tax per unit of predator biomass. The optimal harvest strategy is determined using Pontryagin's maximum principle, which is subject to state equations and control limitations. The implications of tax are also examined. We have derived different bifurcations and global stability of the system. Finally, numerical simulations are used to back up the analytical results.

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Author Biographies

Anal Chatterjee, Department of Mathematics, Barrackpore Rastraguru Surendranath College, Barrackpore, Kolkata, India

received his M.Sc degree in Applied Mathematics from University of Kalyani. He has qualified NET (2007) and GATE (2008). He became a Lecturer in Sheikhpara A.R.M. Polytechnic, Sheikhpara, and Murshidabad in 2012 and later joined Barrackpore Rastraguru Surendranath College, 85, Middle Road, 6, River Side Rd, Kolkata as an Assistant Professor in 2017. He obtained his PhD in Mathematical Biology from Kalyani University in 2014. His field of research interests is in mathematical ecology. The current research work is devoted to present several mathematical models on the dynamics of marine plankton ecology with planktivorous fish and eco-epidemiological models with prey refuge. He has already published more than 25 international research articles. He participated and delivered lectures in conferences, workshops in India.

Samares Pal, Department of Mathematics, University of Kalyani, Kalyani, India

received his MSc and MPhil degree in Applied Mathematics from University of Calcutta. He obtained his PhD in Mathematical Biology from Jadavpur University in 2004. He became a Lecturer in Ramakrishna Mission Vivekananda Centenary College, Rahara, Kolkata, in 1998 and later joined University of Kalyani as an Associate Professor in 2008 and promoted to professor in 2013. His field of research interests are in mathematical ecology and epidemiology. The current research work is devoted to present several mathematical models on the dynamics of marine plankton ecology, coral bleaching due to invasive predators, nonlinear transmission of a stage structured eco-epidemiological models with prey refuge, non-autonomous prey- predator model and ecosystem modeling including nitrogen stable isotopes in marine environments. He has already published more than 75 international research articles. He received INDO-US Research Fellowship for collaborative research work at Georgia Institute of Technology, Atlanta, Georgia, USA. Obtained fellowship under INSA International bilateral exchange programme for collaborative research work at National Centre for Theoretical Sciences (NCTS), Department of Mathematics, National Tsing Hua University, Taiwan. He participated and delivered invited lectures in conferences, workshops and visited Institutions in India and abroad.

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