Development of a mathematical model for better management of fisheries resources

Abstract

This article describes the size and space-time structured model of fish population dynamics. It is expressed as a hyperbolic system of partial differential equations continuous in size and time with non-local boundary data. The space is represented using discrete regions (patches) interconnected by exchange rates. The model is nonlinear because all the parameters such as birth rate, growth function, mortality rate, and movements are chosen to be size-dependent and age independent. This article provides the mathematical model and proves existence and uniqueness of the solution. By using the finite volume method the continuous problem is discretised and then upwind explicit scheme is developed. Consequently, this model approaches the problem by the upwind explicit scheme where the consistence and stability are established. A computer code in programming language FORTRAN® compatible with the formulation is used to compute the numerical solutions and the results are shown graphically.