Macdonald's model and the transmission of bilharzia

Abstract
The paper considers a model for the transmission of bilharzia based on Macdonald's assumptions, in the light of data observed in the field. It is shown, in particular, that the threshold parameter governing whether or not an endemic cycle can be established is closely related to the proportion of infected snails in a community, and that this proportion is normally observed to be rather smaller than is compatible with the model. By considering more sophisticated models, allowing for the latent period of infection in the snails, and also for spatial and seasonal heterogeneity, the effective proportion of infected snails, from the point of view of Macdonald's model, is shown to be rather larger, and expressions are given whereby it can be evaluated from observable quantities. However, for the data from Malirong which are taken as illustration, it is also demonstrated that an even more plausible threshold value is obtained from a simple model incorporating human immunity in addition to the assumptions of Macdonald's model, and that, if this model were reasonable, human immunity would appear to be the most important factor in controlling the level of the disease in Malirong.

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