Banasiak, Jacek.Willie, Robert.Namayanja, Proscovia.2013-01-162013-01-1620102010http://hdl.handle.net/10413/8308Thesis (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.en-ZAMatrices.Population biology.Theses--Mathematics.Thesis