  Transportation processes, which play a prominent role in the life and social
sciences, are typically described by discrete models on lattices. For studying
their dynamics a continuous formulation of the problem via partial differential
equations (PDE) is employed. In this paper we propose a symbolic computation
approach to derive mean-field PDEs from a lattice-based model. We start with
the microscopic equations, which state the probability to find a particle at a
given lattice site. Then the PDEs are formally derived by Taylor expansions of
the probability densities and by passing to an appropriate limit as the time
steps and the distances between lattice sites tend to zero. We present an
implementation in a computer algebra system that performs this transition for a
general class of models. In order to rewrite the mean-field PDEs in a
conservative formulation, we adapt and implement symbolic integration methods
that can handle unspecified functions in several variables. To illustrate our
approach, we consider an application in crowd motion analysis where the
dynamics of bidirectional flows are studied. However, the presented approach
can be applied to various transportation processes of multiple species with
variable size in any dimension, for example, to confirm several proposed
mean-field models for cell motility.
