Fish survival subject to algal bloom: Resource-based growth models with algal digestion delay and detritus-nutrient recycling delay

In this paper, we propose a class of resource-based growth models with delays in algal digestion and detritus-nutrient recycling, and investigate the model based on two different survival scenarios of algae during nutrient transformation. One scenario considers the survival rates of algae during nutrient uptake, while the other overlooks this factor. We find a significant difference in the estimated time window required for clearing the lake of detritus between the two models, and both are longer compared to the model without algal digestion delay. Moreover, the internal equilibria of both scenarios undergo an infinite number of stability switches, however, the key parameters leading to these stability switches differ. Notably, in the model accounting for algal death during nutrient uptake, there exists a safe zone where the stability of the internal equilibrium remains unaffected by the detritus-nutrient recycling delay, provided that the algal digestion delay falls within a suitable range. The findings derived from this study can provide valuable insights for the development of efficacious approaches in safeguarding the ecological integrity, managing algal blooms, facilitating sustainable fishery practices, and fostering favorable economic outcomes within the realm of water resources advancement.