Mathematical analysis of plankton population dynamics

Abstract

Harmful algal blooms (HABs) event that causes enormous economic loss and health effect raises concerns among environmentalists. In this paper, a mathematical model of interaction between nutrient, toxin-producing phytoplankton (TPP), non-toxic phytoplankton (NTP), zooplankton, and toxic chemicals is proposed to study on how the process of these HABs occurred. The model of interaction is represented by Ordinary Differential Equations (ODEs) and stability analysis of the model is conducted. Several conditions for the system to be stable around trivial and interior equilibrium point are obtained. From the analysis, it is observed that under nutrient limitation, the amounts of toxic chemicals secreted out by the TPP are increased. As a result, NTP population and zooplankton population are affected by the situation. If this situation is prolonged, this will result in the extinction of both populations. Overall, this study shows that TPP release more toxic chemicals when the nutrient is limited and gives a better understanding on the occurrence of HABs event.