Optimal control of harvesting effort in a phytoplankton–zooplankton model with infected zooplankton under the influence of toxicity

Abstract

In the present investigation, a prey–predator model consisting of phytoplankton, susceptible zooplankton, and infected zooplankton, incorporating the response function of Holling type II, has been explored. Logistic growth is assumed to be followed by the phytoplankton species. A combined effort (E) is applied to harvest all of the three populations. Environmental toxicity is considered to affect the phytoplankton species directly and the predating zooplankton indirectly. The dynamical behaviour of the model is examined for each of the possible steady states. Hopf-bifurcation analysis has been carried out with the combined harvesting effort E as the bifurcation parameter. The optimal control is characterized by using Pontryagin’s maximum principle. In the end, the analytical discoveries found so far have been established employing numerical simulations.