This paper presents a mathematical model that explores the intricate dynamics between nutrients, phytoplankton, and zooplankton populations, incorporating viral infection phenomena in the frame of the Caputo fractional derivative. The conceptual properties such as the existence, uniqueness, and stability of multiple equilibria are analyzed under specific conditions. We have defined some threshold parameters whose biological meaning helps in strengthening the stability conditions. Furthermore, an optimal control strategy is proposed for the suggested model and the impacts of the optimal control strategy on both commensurate and non-commensurate systems are investigated. A dynamic framework is developed to investigate the optimal use of resources, stock sustainability, and resource benefits. The control variables considered are concerned with the infection of the susceptible phytoplankton and the nutrient consumption of infected phytoplankton. Pontryagin’s maximum principle is employed to determine the best control strategy. Using the Adam-Bashforth-Moulton predictor–corrector method we have performed the numerical simulation that provides the justification of the theoretical findings.

中文翻译：

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浮游生物病毒感染营养物-浮游植物-浮游动物模型的新型最优控制策略


本文提出了一个数学模型，探索营养物质、浮游植物和浮游动物种群之间复杂的动态，并将病毒感染现象纳入卡普托分数导数的框架中。分析特定条件下多重均衡的存在性、唯一性、稳定性等概念性质。我们定义了一些阈值参数，其生物学意义有助于加强稳定性条件。此外，针对所建议的模型提出了最优控制策略，并研究了最优控制策略对相称和非相称系统的影响。开发了一个动态框架来研究资源的最佳利用、库存可持续性和资源效益。所考虑的控制变量涉及易感浮游植物的感染和受感染浮游植物的营养消耗。采用庞特里亚金极大值原理来确定最佳控制策略。使用 Adam-Bashforth-Moulton 预测校正器方法，我们进行了数值模拟，证明了理论结果的合理性。