No abstract

In this paper, we construct and analyze a theoretical, deterministic 5 D mathematical model of Limnothrissa miodon with nutrients, phytoplankton, zooplankton, and Hydrocynus vittatus predation. Local stability analysis results agree with the numerical simulations in that the coexistence equilibrium is locally stable provided that certain conditions are satisfied. The coexistence equilibrium is globally stable if certain conditions are met. Existence, stability, and direction of Hopf bifurcations are derived for some parameters. Bifurcation analysis shows that the model undergoes Hopf bifurcation at the coexistence point for the zooplankton growth rate with periodic doubling leading to chaos.

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.

Global warming is a serious world problem where earth’s temperature has been reported to increase over the years; the aquatic ecosystems are also not the exceptions. But, the effects of this phenomenon on the aquatic ecosystems are not well understood. This study aims to understand the influence of surface temperature on the population density of Limnothrissa miodon in Lake Kariba. We constructed a mathematical model on the population dynamics of Limnothrissa miodon with nutrients, phytoplankton, zooplankton, and Hydrocynus vittatus. Lake surface water temperature was modelled by a cosine function, and the parameters were estimated from data fitting. Numerical simulations were used to determine the stability of the nonautonomous model. Numerical simulation results of the nonautonomous model showed a stable periodic orbit for varying initial conditions, and therefore, instability. Numerical techniques were used to investigate the influence of surface water temperature on Limnothrissa miodon. Results from the model with fitted lake surface water temperature data showed that a shift in the optimal temperature for phytoplankton growth from 25 ° C to 34 ° C, corresponding to dominance of Cyanophyceae over Chlorophyceae, resulted in a decline in the population density of Limnothrissa miodon. Numerical results showed that the population density of Limnothrissa miodon declines after an optimum temperature of 30 ° C for phytoplankton growth. Numerical simulation results suggested that warming of the lake may lead to a decline in Limnothrissa miodon population density in Lake Kariba.