Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2010.Non-negative matrices arise naturally in population models. In this thesis, we look at the theory
of such matrices and we study the Perron-Frobenius type theorems regarding their spectral
properties. We use these theorems to investigate the asymptotic behaviour of solutions to
continuous time problems arising in population biology. In particular, we provide a description
of long-time behaviour of populations depending on the nature of the associated matrix. Finally,
we describe a few applications to population biology
