Large scale dynamical systems in mathematical population dynamics

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Large scale dynamical systems (or large systems, for short) lie at the interface between theory and applications. Theoretically, there is no limitation to the size of a system. When an application is considered to a particular system, the problem of size becomes relevant.    A standard example of such limitations is the n-body problem, which describes the movement of stellar bodies submitted to the gravitational interactions of the other stellar bodies present. Standard results of ordinary differential equations theory show the existence and uniqueness of solutions, as well as many other simple properties. However, when one considers the evolution of the system, the problem becomes intractable.    In the field of mathematical population dynamics, that is, the mathematical aspects of the evolution of populations, large systems are also frequent. One context in which they are arise is the description of the spatial spread of infectious diseases between distinct geographical units. In this case, what are considered are networks of regions (or cities), where in each region the evolution of epidemiological parameters is modeled by a set of differential equations. The regions are then coupled together to describe the movement of individuals between them.    My project has two components: an applied one, and a more theoretical one. I will study spatially discrete models of infectious disease spread, as well as some other large models in mathematical population dynamics. I will try to detect regularities, patterns, in the methods used. These patterns will allow me to generalise and consider more theoretical aspects of large systems.