  Complex biological and physical transport processes are often described
through systems of interacting particles. Excluded-volume effects on these
transport processes are well studied, however the interplay between volume
exclusion and reactions between heterogenous particles is less well known. In
this paper we develop a novel framework for modeling reaction-diffusion
processes which directly incorporates volume exclusion. From an off-lattice
microscopic individual based model we use the Fokker--Planck equation and the
method of matched asymptotic expansions to derive a low-dimensional macroscopic
system of nonlinear partial differential equations describing the evolution of
the particles. A biologically motivated, hybrid model of chemotaxis with volume
exclusion is explored, where reactions occur at rates dependent upon the
chemotactic environment. Further, we show that for reactions due to contact
interactions the appropriate reaction term in the macroscopic model is of lower
order in the asymptotic expansion than the nonlinear diffusion term. However,
we find that the next reaction term in the expansion is needed to ensure good
agreement with simulations of the microscopic model. Our macroscopic model
allows for more direct parameterization to experimental data than the models
available to date.
