The role of zooplankton in the growth of algal bloom: a mathematical study

Abstract

. Here a nonlinear mathematical model for an aquatic ecosystem containing both non-toxic and toxin-producing algal blooms is formulated and analyzed. The presence of harmful algae impacts the aquatic population, subsequently affecting the human population that relies on zooplankton (fish, crabs, etc.). It also deteriorates the water quality, and it is advisable not to use water from lakes containing harmful algae. Here, our focus is to understand the dynamics of aquatic ecosystems when we have both types of algae, one that is non-toxic and acts as food to zooplankton, and another that is toxin-producing algae that causes death to zooplankton. The predation of zooplankton on algae influences the growth of the algae population. First, we consider a deterministic model, and later, this model is extended to stochastic model to check whether it has any impact on the dynamics of the populations under consideration. Various equilibria of the proposed model are derived, and the local stability of these equilibria is thoroughly examined. The existence of Hopf-bifurcation is also demonstrated for a suitable set of parameters. The results of deterministic and stochastic models are compared using numerical simulation. Upon examining our results and simulation data, it is evident that modifying specific key parameters, such as the growth rate of non-toxic algae due to nutrient intake and the parameter associated with the predation of non-toxic algae by zooplankton, has a substantial impact on algal bloom dynamics. Minor adjustments to these parameters can result in an augmented presence of non-toxic algae and a simultaneous decrease in toxin-producing algae, aligning with the primary objectives set by policymakers.