The interactions between macroparasites and their hosts, in terms of parasite-induced acquired immunity and additional mortality of the host, are of considerable interest and importance. In this paper, a simple nonlinear stochastic model for the parasite load within a single host over the lifetime of the host is investigated. By concentrating on a model incorporating only parasite-induced excess host mortality, exact algebraic results are possible, which provide insight into the effects of this interaction mechanism. A method of approximating the moments of parasite load is explored under a range of parametric assumptions. Extensions of the model to allow for heterogeneity between hosts and to incorporate various types of acquired immunity within the host are discussed briefly.