Bioeconomic-Epidemiological Model of Scomber colias Population in the Moroccan Coasts

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.