Stability Analysis and Optimal Control of a Limnothrissa Miodon Model with Harvesting

We construct a theoretical, deterministic mathematical model of the dynamics of Limnothrissa miodon with nutrients, phytoplankton, and zooplankton and investigate the effect of harvesting on the population density of Limnothrissa miodon in a lake. For the autonomous model, results from local stability analysis are in agreement with numerical simulations in that the coexistence equilibrium is locally stable, provided certain conditions are satisfied. The coexistence equilibrium is globally unstable if it is feasible. Numerical results show that a stable limit cycle exists for the nonautonomous model. Optimal control results show an optimal harvesting monthly effort of 15394 boat nights which corresponds to 505 fishing units, showing that there is overcapacity in Lake Kariba. A maximum sustainable annual catch of 34669 tonnes is obtained and simulation results show that Limnothrissa miodon abundance is more closely related to nutrient inflow than to harvesting.