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

Barbour, A D; Pugliese, A (2000). On the variance-to-mean ratio in models of parasite distributions. Advances in Applied Probability, 32(3):701-719.

## Abstract

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 different formulations of disease induced host mortality. We show that the distributions of parasites, conditional on host survival, converge to quasi-stationary distributions as host age increases. When there is density dependence in parasite mortality, the limiting variance-to-mean ratio is less than 1 (an under-dispersed' distribution). In contrast, the two modes of disease induced host mortality show that either over- or underdispersed distributions may result.

## Abstract

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 different formulations of disease induced host mortality. We show that the distributions of parasites, conditional on host survival, converge to quasi-stationary distributions as host age increases. When there is density dependence in parasite mortality, the limiting variance-to-mean ratio is less than 1 (an under-dispersed' distribution). In contrast, the two modes of disease induced host mortality show that either over- or underdispersed distributions may result.

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