A contribution of sparse matrices tools to matrix population model analysis

When one wants to study the dynamics of structured populations, matrix type models are widely used. The complexity of such models increases with the number of classes of individuals considered, and a mathematical analysis becomes difficult to perform when a further heterogeneous spatial structure is introduced. The use of efficient computational tools is also required for numerical simulations. In this note we deal with the contribution of sparse matrices tools which allow to numerically simulate and to numerically perform stability analysis of large sized structured population models including density dependence and spatial heterogeneities. Our main motivation through this work is to show that such numerical tools can be useful when mathematical methods become difficult to employ.