  In low-resource settings, prevalence mapping relies on empirical prevalence
data from a finite, often spatially sparse, set of surveys of communities
within the region of interest, possibly supplemented by remotely sensed images
that can act as proxies for environmental risk factors. A standard
geostatistical model for data of this kind is a generalized linear mixed model
with binomial error distribution, logistic link and a combination of
explanatory variables and a Gaussian spatial stochastic process in the linear
predictor. In this paper, we first review statistical methods and software
associated with this standard model, then consider several methodological
extensions whose development has been motivated by the requirements of specific
applications. These include: methods for combining randomised survey data with
data from non-randomised, and therefore potentially biased, surveys;
spatio-temporal extensions; spatially structured zero-inflation. Throughout, we
illustrate the methods with disease mapping applications that have arisen
through our involvement with a range of African public health programmes.
