A Model for Self-Sustaining Litopenaeus Vannamei Farm Alternatives

We investigate a semi-contained, two-tank model for a Litopenaeus vannamei (White Pacific Shrimp) aquaculture farm. Our model simulates the possibility of a self-sustaining aquaculture system, with an interdependent triad of shrimp, algae, and bacteria. The two tanks are symmetric: the first containing developing shrimp through the hatchery and nursery phase and the second containing full grown shrimp through the grow-out phase. This system is modelled by six, first order differential equations. Using analytic and numeric techniques, we examine the dynamics and equilibria of this system as well as each of its individual components. This paper examines the effects of varying harvesting frequencies and magnitudes, and searches for an optimal harvesting strategy. Our analysis concluded that in the confines of our model, a technique of harvesting 81.5% of harvestable shrimp every 2 days provides a hypothetical optimal strategy. However, upon consideration of practical constraints, a harvesting strategy of 98% of harvestable shrimp every 10 days represents a real-world optimal harvesting strategy.