MSc Math Defence: Mathematical Analysis of a Delay System as an Equivalent Model for a Size-Structured Fish Population

CANDIDATE:  MONA GHWILA

This thesis is centered on a study of a delay system as an equivalent model of a size-structured fish population model. The delay system consists of a renewal equation for the consumer population birth rate and a delay differential equation for the resource concentration. We generalize the delay system by including realistic functional responses that contain the attack rate and the handling time. We analyze the stability of the equilibrium solution and present the linearization of the delay system, based on Diekmann et al. (2010b), to derive the characteristic equation for a general class of fish population models. The model is investigated numerically to illustrate the stability of the steady-state and to analyze various harvesting strategies and their effect on the fish population. We show how a single-stage harvesting for either juveniles or adults is less harmful than harvesting both juveniles and adults.