On the variance-to-mean ratio in models of parasite distributions

We study the variance-to-mean ratio of the distributions of parasites among hosts for some models of parasite infection, using the cohort approach. We consider a model with density dependence in parasite mortality, and two di fferent formulations of disease induced host mortality. We show that the di stributions of parasites, conditional on host survival, converge to quasi-s tationary distributions as host age increases. When there is density depend ence in parasite mortality, the limiting variance-to-mean ratio is less tha n 1 (an 'under-dispersed' distribution). In contrast, the two modes of dise ase induced host mortality show that either over- or underdispersed distrib utions may result.