  In this paper we analyze a system of PDEs recently introduced in [P. Amorim,
{\it Modeling ant foraging: a {chemotaxis} approach with pheromones and trail
formation}], in order to describe the dynamics of ant foraging. The system is
made of convection-diffusion-reaction equations, and the coupling is driven by
chemotaxis mechanisms. We establish the well-posedness for the model, and
investigate the regularity issue for a large class of integrable data. Our main
focus is on the (physically relevant) two-dimensional case with boundary
conditions, where we prove that the solutions remain bounded for all times. The
proof involves a series of fine \emph{a priori} estimates in Lebesgue spaces.
