The presence of populations potentially harmful dinoflagellate phytoplankton like Oxyrrhis marina requires vigilance and control, because these species, in high density or under certain conditions, can have serious economic consequences and a negative impact on public health. In this investigation, we formulate bioeconomic model of a prey and predator planktonic species. The positivity and boundedness of the solution are studied. The possible equilibriums and their local stability are analyzed; also the global stability of the system around the interior equilibrium is established. We examine the optimal harvesting policy to discuss the dynamical profit of the interacting planktonic species. To show the impact of the toxicity coefficient, we have made analytical estimates that are validated using simulations.

存在对象洋蛇滨这样的潜在有害的鞭毛藻浮游植物的种群需要警惕和控制，因为这些物种在高密度或一定条件下会产生严重的经济后果并对公共卫生产生不利影响。在这项调查中，我们制定了一个猎物和捕食者浮游生物物种的生物经济模型。研究了溶液的正性和有界性。分析了可能的平衡及其局部稳定性；还建立了围绕内部平衡的系统的整体稳定性。我们研究了最佳收获政策，以讨论相互作用的浮游物种的动态利润。为了显示毒性系数的影响，我们进行了分析估计，并通过模拟进行了验证。