ANALYSIS OF A MODEL FOR MACROPARASITIC INFECTION WITH VARIABLE AGGREGATION AND CLUMPED INFECTIONS

A model for macroparasitic infection with variable aggregation is cons idered. The starting point is an immigration-and-death process for par asites within a host, as in [3]; it is assumed however that infections will normally occur with several larvae at the same time. Starting fr om here, a four-dimensional, where free-living larvae are explicitly c onsidered, and a three-dimensional model are obtained with same method s used in [26]. The equilibria of these models are found, their stabil ity is discussed, as well as some qualitative features. It has been fo und that the assumption of ''clumped'' infections may have dramatic ef fects on the aggregation exhibited by these models. Infections with se veral larvae at the same time also increases the stability of the ende mic equilibria of these models, and makes the occurrence of subcritica l bifurcations (and consequently multiple equilibria) slightly more li kely. The results of the low-dimensional model have also been compared to numerical simulations of the infinite system that describes the im migration-and-death process. It appears that the results of the system s are, by and large, in close correspondence, except for a parameter r egion where the four-dimensional model exhibits unusual properties, su ch as the occurrence of multiple disease-free equilibria, that do not appear to be shared by the infinite system.