Hyperuniformity on spherical surfaces.

We study and characterize local density fluctuations of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to date few works have dealt with the problem of hyperuniformity in curved spaces. Indeed, some systems that display disordered hyperuniformity, like the spatial distribution of photoreceptors in avian retina, actually occur on curved surfaces.

SIR model with local and global infective contacts: A deterministic approach and applications.

An epidemic model with births and deaths is considered on a two-dimensional L×L lattice. Each individual can have global infective contacts according to the standard susceptible-infected-recovered (SIR) model rules or local infective contacts with their nearest neighbors. We propose a deterministic approach to this model and, for the parameters corresponding to pertussis and rubella in the prevaccine era, verify that there is a close agreement with the stochastic simulations when epidemic spread or endemic stationarity is considered.