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 $\left(E\right)$ 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.

在目前的调查中，已经探索了一种由浮游植物、易感浮游动物和受感染的浮游动物组成的猎物 - 捕食者模型，结合了 Holling II 型的反应功能。假设浮游植物物种跟随物流增长。共同努力$\left(乙\right)$用于收获所有三个种群。环境毒性被认为直接影响浮游植物物种，间接影响捕食浮游动物。针对每个可能的稳态检查模型的动态行为。Hopf 分岔分析已与联合收获努力进行$乙$作为分岔参数。最优控制的特点是使用庞特里亚金的最大值原理。最后，迄今为止发现的分析发现已通过数值模拟得到证实。