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

Farikayi K. Mutasa, Brian Jones, Senelani D. Hove-Musekwa, Itai H. Tendaupenyu, Tamuka Nhiwatiwa, Mzime R. Ndebele-Murisa and Leonid Shaikhet

Discrete Dynamics in Nature and Society, 2022, vol. 2022, 1-27

Abstract: 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.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ddns/2022/8504993.pdf (application/pdf)
http://downloads.hindawi.com/journals/ddns/2022/8504993.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:8504993

DOI: 10.1155/2022/8504993

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().