A mathematical analysis and numerical simulation of fish and zooplankton model with age-structured in the prey population taking account the fishing effect

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The work presented in this paper is part of the general framework of mathematical ecology regarding the complex dynamics in predatory prey model. The main objective is the formulation and study of a prey-predator model to describe the dynamics of fish and zooplankton population taking into account two phenomenons: the catching effect in the fish population and the age-structure in the zooplankton dynamics. We present some mathematical results concerning the positive solution existence, the stability and persistence of the model equilibria using a positive initial condition. The total population of zooplankton and the total population of fish are uniformly weakly persistent if R_0>1 and R_* 1. Some numerical simulations according to the mathematical conditions are performed using the finite volume method, are done to illustrate those results in the different fish exploited and inexploited areas.

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