Mathematical Modelling of Harmful Algal Blooms on West Coast of Sabah

Fatin Nadiah Yussof, Normah Maan (), Mohd Nadzri Md Reba and Faisal Ahmed Khan
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Fatin Nadiah Yussof: Department of Mathematics, Faculty of Science and Technology, Universiti Teknologi Malaysia, Skudai 81310, Malaysia
Normah Maan: Department of Mathematics, Faculty of Science and Technology, Universiti Teknologi Malaysia, Skudai 81310, Malaysia
Mohd Nadzri Md Reba: Faculty of Geoinformation and Real Estate, Universiti Teknologi Malaysia, Skudai 81310, Malaysia
Faisal Ahmed Khan: Institute of Environmental Studies, University of Karachi, Karachi 75270, Pakistan

Mathematics, 2022, vol. 10, issue 16, 1-29

Abstract: Algal bloom is a condition in which there is a massive growth of algae in a certain region and it is said to be harmful when the bloom causes damage effects. Due to the tremendous impact of harmful algal bloom (HAB) on some aspects, this research proposes the mathematical modelling of an HAB model to describe the process of HAB together with population dynamics. This research considers the delay terms in the modelling since the liberation of toxic chemicals by toxin-producing phytoplankton (TPP) is not an instantaneous process in which the species need to achieve their maturity. A model of fish interaction is also being studied to show the effect of HAB on fish species. Time delay is incorporated for the mortality of fish due to the consumption of toxic zooplankton. Stability analysis is conducted and numerical simulations are applied to obtain the analytical results which highlight the critical values for the delay parameters. The existence of Hopf bifurcation is established when the delay passes the threshold value. The results of both models show that the inclusion of the delay term affects the model by stabilizing and destabilizing the model. Therefore, this research shows the effect of an inclusion delay term on the model and also gives knowledge and an understanding of the process of HAB occurrence as well as the effect of HAB on fish populations.

Keywords: harmful algal bloom; Hopf bifurcation; population dynamics; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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