Aggregation, stability and oscillations in different models for host–macroparasite interactions

Aggregation is generally recognized as an important factor in the dynamics of host–macroparasite interactions and it has been found relevant in stabilizing the dynamics toward an equilibrium coexistence. In this paper we review the models of Anderson and May (1978, J. Anim. Ecol. 47, 219–247, 249–267) and compare them with some more recently developed models, which incorporate explicit mechanisms (multiple infections or host heterogeneity) for generating aggregation and different degrees of mathematical accuracy. We found that the stabilization yielded by aggregation depends strongly on the mechanism producing the aggregation: multiple infections are much less stabilizing than when aggregation is assumed to be fixed from the outside, while the opposite holds for host heterogeneity. We also give analytical estimates of the period of oscillations occurring when the equilibrium is unstable. Finally, we explore in these models the role of aggregation in host regulation and in determining a threshold value for parasite establishment