Applying an aggregative dispersive dichotomy (ADD) model to parasitic infections in host populations

An aggregative dispersive dichotomy (ADD) model is presented to describe the distribution of parasites in host populations. The ADD model is a mathematical construct which provides two complementary measures extracted from a reformulated negative binomial (NBD) and an inequality model, which combine to capture observed patterns of a parasitic infection. The dispersion element is modelled using the NBD with the threshold set at a parasite level above zero. By applying binomial dichotomy, the host community is divided into two sub-populations, one including hosts harbouring parasites up to the threshold and the other with parasites above the threshold level. The k parameter, derived from the NBD, provides a cumulative probability. However, k is relatively insensitive to variations in the degree of aggregation, a known feature of the NBD model. The aggregation of parasites above the threshold in the host sub-population is evaluated by using an inequality model which is indexed by a scale-free parameter delta(delta >/= 1) and provides an accurate measure of parasite aggregation. Applications of this model are made from field and simulated data in wood mouse populations infected with the trichostrongylid nematode Heligmosomoides polygyrus from a woodland site in Surrey.