  Natural phenomena frequently involve a very large number of interacting
molecules moving in confined regions of space. Cellular transport by motor
proteins is an example of such collective behavior. We derive a deterministic
compartmental model for the unidirectional flow of particles along a
one-dimensional lattice of sites with nearest-neighbor interactions between the
particles. The flow between consecutive sites is governed by a soft simple
exclusion principle and by attracting or repelling forces between neighboring
particles. Using tools from contraction theory, we prove that the model admits
a unique steady-state and that every trajectory converges to this steady-state.
Analysis and simulations of the effect of the attracting and repelling forces
on this steady-state highlight the crucial role that these forces may play in
increasing the steady-state flow, and reveal that this increase stems from the
alleviation of traffic jams along the lattice. Our theoretical analysis
clarifies microscopic aspects of complex multi-particle dynamic processes.
