On the application of mathematical models of schistosome transmission dynamics. I. Natural transmission.

The many mathematical models of the transmission dynamics of schistosomes that have been published since 1965 have had little impact on field studies or on the design of schistosome control programmes. At least in part, this is due to limited interaction between theoretician and field worker, resulting in unrealistic models that are not easily applied to field data. This review aims to make explicit the assumptions and limitations of existing models and their relationships with field data. A basic model is described which considers the mean number of schistosomes per person and the prevalence of patent infections of snails. Various modifications to this model are introduced. These include: prepatent infections of snails; loss of infection of snails; the effects of snail population dynamics; the effects of miracidia and cercariae population dynamics; miracidia searching efficiency; reservoir hosts; heterogeneous patterns of transmission; seasonality; and predisposition to infection. Variation in levels of infection with age and the effects of acquired immunity to infection are also considered. Published models of schistosome transmission dynamics are reviewed within this framework. Approaches to the modelling of schistosome control measures are considered in a companion paper. It is suggested that future theoretical studies give greater attention to the details of snail population dynamics, heterogeneous patterns of transmission and the effects of acquired immunity. There is a need for field studies explicitly designed to provide estimates of transmission parameters and for studies of the epidemiological effects of acquired immunity.