  In this paper we present continuous age- and space-structured models and
numerical computations of Proteus mirabilis swarm-colony development. We base
the mathematical representation of the cell-cycle dynamics of Proteus mirabilis
on those developed by Esipov and Shapiro, which are the best understood aspects
of the system, and we make minimum assumptions about less-understood
mechanisms, such as precise forms of the spatial diffusion. The models in this
paper have explicit age-structure and, when solved numerically, display both
the temporal and spatial regularity seen in experiments, whereas the Esipov and
Shapiro model, when solved accurately, shows only the temporal regularity.
  The composite hyperbolic-parabolic partial differential equations used to
model Proteus mirabilis swarm-colony development are relevant to other
biological systems where the spatial dynamics depend on local physiological
structure. We use computational methods designed for such systems, with known
convergence properties, to obtain the numerical results presented in this
paper.
