  In this paper we consider a biased velocity jump process with excluded-volume
interactions for chemotaxis, where we account for the size of each particle.
Starting with a system of N individual hard rod particles in one dimension, we
derive a nonlinear kinetic model using two different approaches. The first
approach is a systematic derivation for small occupied fraction of particles
based the method of matched asymptotic expansions. The second approach, based
on a compression method that exploits the single-file motion of hard core
particles, does not have the limitation of a small occupied fraction but
requires constant tumbling rates. We validate our nonlinear model with
numerical simulations, comparing its solutions with the corresponding
noninteracting linear model as well as stochastic simulations of the underlying
particle system.
