Mathematical Modelling of Harmful Algal Blooms on West Coast of Sabah

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.

Automated summary

This research proposes a mathematical model to study the population dynamics and fish interaction effects of harmful algal bloom (HAB). The inclusion of delay terms in the model is considered, and stability analysis is conducted to determine critical values for the delay parameters.