Research Article
Using the Logistic Growth Model to Assess Fishing Techniques for Sustainable Tilapia Catch and Management at Omega Farm
Issue:
Volume 14, Issue 1, February 2025
Pages:
1-7
Received:
29 August 2024
Accepted:
23 December 2024
Published:
9 January 2025
DOI:
10.11648/j.pamj.20251401.11
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Abstract: Mathematical modeling utilizes a differential equation, either a partial differential equation or ordinary differential equation to depict physical scenarios, such as Tilapia harvesting strategies and other population dynamics models. Fish farming constitutes the cornerstone of the Kenyan economy, notably in Baringo, where it serves as the primary economic activity. Additionally, it holds significance in the health sector due to the nutritious protein provision derived from the harvested fish. Despite the commercialization of Tilapia fish farming, the utilization of mathematical models to determine harvesting strategies remains largely unexplored in Omega Farm. Consequently, this oversight has resulted in a decline in harvest quantity over recent years. The primary objective of this study was to leverage the Logistic Growth Model to implement harvesting and management strategies for Tilapia at Omega Farm, Baringo County. The specific aims were determining the maximum sustainable yield (MSY) of the Tilapia population in the Farm after a six-month duration, employing an adapted logistic growth model to delineate harvesting rates (both constant and periodic), and identifying an efficient harvesting strategy for managing the Tilapia population by comparing the two approaches. The study investigated the existence of equilibrium solutions and their stabilities of the modified Logistic Growth Model under both constant and periodic harvest scenarios. A maximum sustainable yield of 13,000, with a growth rate of 80%, was achieved for optimal harvest, maintaining a carrying capacity of 65,000 without compromising ecological integrity. The obtained results were discussed and presented graphically. By analysing different harvesting strategies constant and periodic using Python simulations, the impact of these approaches was determined on the sustainability and productivity of fish populations. The findings underscore the importance of adaptive management and strategic harvesting to maintain a balance between maximizing yields and ensuring population stability. The study findings suggest that periodic harvesting emerges as the most effective strategy, fostering sustainable fish farm management. Future research endeavors should delve deeper into refining these strategies and exploring additional avenues for enhancing Tilapia farming sustainability.
Abstract: Mathematical modeling utilizes a differential equation, either a partial differential equation or ordinary differential equation to depict physical scenarios, such as Tilapia harvesting strategies and other population dynamics models. Fish farming constitutes the cornerstone of the Kenyan economy, notably in Baringo, where it serves as the primary ...
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Research Article
Consequences of Generalized Ratio Tests That Lead to More Efficient Convergence and Divergence Tests
Joseph Granville Gaskin*
Issue:
Volume 14, Issue 1, February 2025
Pages:
8-12
Received:
13 December 2024
Accepted:
6 January 2025
Published:
17 February 2025
DOI:
10.11648/j.pamj.20251401.12
Downloads:
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Abstract: The Ratio Test, developed by Jean Le Rond d'Alembert, is a fundamental method for determining the convergence or divergence of an infinite series and is commonly used as a primary test for many series. However, due to its restricted range of applicability, several generalized forms of the Ratio Test have been introduced to extend its usefulness. In this paper, we combine two of the most effective and reliable generalized Ratio Tests to create more efficient convergence tests. To this end, we show that if a positive valued function, f, is defined for all numbers greater than or equal to one, and if the improper integral of the reciprocal of f, over the interval from one to infinity, diverges, then f has a close relationship with a sister function φ. We then show that these paired functions satisfy a remarkable relationship that completely characterizes all monotonically decreasing sequence of terms whose sum diverge. We demonstrate through several examples the ease with which φ can be found if f is known and vice-versa. Next, we combine the generalized Ratio Tests of Dini and Ermakoff by focusing on a ‘thin’ subsequence of the terms of a large category of infinite series to develop other convergence and divergence tests. Furthermore, we refine these tests to produce practical and easier to apply convergence and divergence tests. Lastly, we demonstrate that for many infinite series, one can factor their terms into the product of the reciprocal of f and L. We then show that the limit superior and limit inferior of an expression based on L determines the convergence or divergence of the original series.
Abstract: The Ratio Test, developed by Jean Le Rond d'Alembert, is a fundamental method for determining the convergence or divergence of an infinite series and is commonly used as a primary test for many series. However, due to its restricted range of applicability, several generalized forms of the Ratio Test have been introduced to extend its usefulness. In...
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