  Myxobacteria are social bacteria, that can glide in 2D and form
counter-propagating, interacting waves. Here we present a novel age-structured,
continuous macroscopic model for the movement of myxobacteria. The derivation
is based on microscopic interaction rules that can be formulated as a
particle-based model and set within the SOH (Self-Organized Hydrodynamics)
framework. The strength of this combined approach is that microscopic knowledge
or data can be incorporated easily into the particle model, whilst the
continuous model allows for easy numerical analysis of the different effects.
However we found that the derived macroscopic model lacks a diffusion term in
the density equations, which is necessary to control the number of waves,
indicating that a higher order approximation during the derivation is crucial.
Upon ad-hoc addition of the diffusion term, we found very good agreement
between the age-structured model and the biology. In particular we analyzed the
influence of a refractory (insensitivity) period following a reversal of
movement. Our analysis reveals that the refractory period is not necessary for
wave formation, but essential to wave synchronization, indicating separate
molecular mechanisms.
