Motivated by structured parasite populations in aquaculture we consider a
class of size-structured population models, where individuals may be recruited
into the population with distributed states at birth. The mathematical model
which describes the evolution of such a population is a first-order nonlinear
partial integro-differential equation of hyperbolic type. First, we use
positive perturbation arguments and utilise results from the spectral theory of
semigroups to establish conditions for the existence of a positive equilibrium
solution of our model.