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 equa-
tions, 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.