Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria

Abstract

In this research, we propose the use of mathematical models in determining harvesting strategies for fish farming.The work considered three logistic growth models, namely constant harvesting, periodic harvesting, and proportional harvesting model. For each of the scheme, it is estimated the optimal amount of fish harvested to protect the population from extinction. The data for this work are obtained from fish owners of selected pond in Bade (Gashua). Although, fish farming has been commercialized in Bade but there is little or no literature available in studying fish harvesting strategies. The Logistic model is appropriate for population growth of fishes when overcrowding and competition for the resource are taken into consideration. The objectives of the study where to estimate the highest continuing yield from fish harvesting strategies implemented. We compare the results obtained between the three strategies and observed the best harvesting strategy for the selected fish farm is periodic (seasonal) harvesting. The periodic harvesting strategy optimizes the harvest while maintaining stable the population of fish if the harvesting is lower or equal with the bifurcation point. Our findings can assist fish farmers in Bade, Yobe State, North East Nigeria, to increase fish supply to meet its demand and positively affect the economic growth of the area.

Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level

“…Figures 6 and 7 show that the results for parameter = 0.3 are opposite to the results for parameter = 300. Figures 6 and 7 show that the steady state of model ( 2) is faster than the steady state of model ( 3) at = [10,1] with initial values = 11 and = 2.…”

“…Based on Equation (10), when c > puqx, the profit obtained will be negative (loss). Therefore, profit (existence of bionomic equilibrium) is obtained when puqx > c [22].…”

“…Suppose P ∞ (x ∞ , E ∞ , u ∞ ) represents the bionomic equilibrium point. Based on Equation (10), the bioeconomic equilibrium point is given by…”

“…The parameter K represents the tuna population's carrying capacity. Besides the harvesting function in Schaefer [2], there are also other harvesting functions, including the constant harvesting function [4,5], the rational harvesting function [6][7][8], the periodic harvesting function [9][10][11], and the piecewise harvesting function [11,12].…”