Epidemic spreading in random rectangular networks.

The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGGs) is one of such network models that allows for the consideration of spatial properties on disease propagation. In certain real-world scenarios-like in the analysis of a disease propagating through plants-the shape of the plots and fields where the host of the disease is located may play a fundamental role in the propagation dynamics.

Random rectangular graphs.

A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1](2). The topological properties of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides lengths a and b=1/a, and the radius r used to connect the nodes. When a=1 we recover the RGG, and when a→∞ the very elongated rectangle generated resembles a one-dimensional RGG.