Abstract
In this paper, we develop and study a mathematical model for the dynamics of Scomber colias and Thunnus thynnus prey-predator with parasitic helminths. We search to analyze a bioeconomic model in which both susceptible and infected prey populations Scomber colias are exposed to the predator Thunnus thynnus, with varying degrees of exposure. However, the predator feeds preferentially on the most numerous prey types. This implies a kind of switching from the susceptible class to the infected class, and vice versa, as these two types of prey change in numerical superiority. So, the positivity, boundedness, equilibria, stability, and bioeconomic equilibrium are studied. Some numerical simulation of stability is cited. For giving a high yield and keeping the Scomber colias and Thunnus thynnus populations away from extension, we use the Maximum Principle of Pontryagin.
Highlights
Morocco is one of the largest fish producers in the world, according to the 2018 report from the Food and Agriculture Organization of the United Nations (FAO)
We present the biological model of susceptible and infected Scomber colias with the presence of the predators Thunnus thynnus; in other words, we resolve a system of three ordinary differential equations, the first equation describes the natural growth of the susceptible Scomber colias fish population a prey of the Thunnus thynnus fish population, the second equation describes the natural growth of infected Scomber colias fish population a prey of the Thunnus thynnus fish population, and the third equation describes the natural growth of the Thunnus thynnus fish population as a predator of the susceptible and infected Scomber colias
The basic idea of this section is to define a bioeconomic model of the susceptible Scomber colias, the infected Scomber colias, and the Thunnus thynnus population exploited by three fishing fleets, and we seek to maximize the profit of each fishing fleets
Summary
Morocco is one of the largest fish producers in the world, according to the 2018 report from the Food and Agriculture Organization of the United Nations (FAO). If fish eat these organisms, they in turn can carry parasites These reasons encouraged us to study this phenomenon and to see all the interactions that occur between populations of fish. Authors have defined a bioeconomic equilibrium model for Parapeaneus longirostris and small pelagic fish populations in two different areas; the first one is protected against fishing and the second is a free access zone. They studied the influence of the predator mortality rate variation on the evolution of prey biomass and the profit of coastal trawlers.
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