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چکیده
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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.
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