In this work we study rotation curves of spiral galaxies using a model of dark matter based on a scalar-tensor theory of gravity. We show how to estimate the scalar field dark matter parameters using a sample of observed rotation curves.
Recently the A/H1N1-2009 virus pandemic appeared in Mexico and in other nations. We present a study of this pandemic in the Mexican case using the SIR model to describe epidemics. This model is one of the simplest models but it has been a successful
description of some epidemics of closed populations. We consider the data for the Mexican case and use the SIR model to make some predictions. Then, we generalize the SIR model in order to describe the spatial dynamics of the disease. We make a study of the spatial and temporal spread of the infected population with model parameters that are consistent with temporal SIR model parameters obtained by fitting to the Mexican case.
We build a spherical halo model for galaxies using a general scalar-tensor theory of gravity in its Newtonian limit. The scalar field is described by a time-independent Klein-Gordon equation with a source that is coupled to the standard Poisson equat
ion of Newtonian gravity. Our model, by construction, fits both the observed rotation velocities of stars in spirals and a typical luminosity profile. As a result, the form of the new Newtonian potential, the scalar field, and dark matter distribution in a galaxy are determined. Taking into account the constraints for the fundamental parameters of the theory (lambda,alpha), we analyze the influence of the scalar field in the dark matter distribution, resulting in shallow density profiles in galactic centers.
