A one-dimensional model of trail propagation by army ants

We develop and analyze a model for the swarming behaviour observed in army ants. The model assumes that the ants coordinate their movements by using chemical pheromones as trail markers. The markers continuously evaporate, and are reinforced by new markers laid down by the ants as they move. The motion of the swarm is modelled by a system of partial differential equations (PDEs). The equations are derived from the motions of the individuals, but represent the collective motion of the group, and the formation and decay of the trail network. The PDEs have travelling wave solutions which correspond to the propagation of the leading edge of the swarm. We describe these solutions qualitatively, and use them to determine how both the shape and the speed of the swarm depend on the parameters describing the motion of the individual ants.