  The paper gives the bounds on the solutions to a Stein equation for the
negative binomial distribution that are needed for approximation in terms of
the Wasserstein metric. The proofs are probabilistic, and follow the approach
introduced in Barbour and Xia (Bernoulli 12 (2006) 943-954). The bounds are
used to quantify the accuracy of negative binomial approximation to parasite
counts in hosts. Since the infectivity of a population can be expected to be
proportional to its total parasite burden, the Wasserstein metric is the
appropriate choice.
