Biology Reference
In-Depth Information
The increase in mass drug administration (MDA, the preventive
chemotherapy approach advocated by the World Health Organization)
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poses a dilemma for geo-statistical modeling approaches as infection
levels may become progressively more linked to the impact of past and
ongoing local control interventions and less tied to environmental,
climatic and socio-economic variables and indeed to local historical data.
Consequently, it will become increasingly important to include temporal
components in spatial models,
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potentially informed by mathematical
transmission models. Spatially explicit transmission models have been
developed for directly-transmitted microparasitic infections, such as
measles,
foot-and-mouth disease and influenza,
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and also on
a community scale for schistosomiasis.
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Fitting Transmission Models to Data
It is quite common for some parameters of human transmission models
(see “Dynamic models of infection and transmission,” below) to be
directly unobservable. For example, plausible density-dependent effects
on the establishment of adult A. lumbricoides within the gut cannot be
directly observed. In such cases, estimation relies on fitting transmission
models to baseline, reinfection or longitudinal data with respect to the
“free” unobservable parameters. How this is achieved, and to what
degree of statistical rigor, depends on the transmission model and data in
question.
The first important point to note is that fitting transmission models
generally falls outside of the realms of traditional (linear) regression anal-
ysis, which rests on the assumption that parameters are multiplicative
coefficients of covariates. The covariatewhen fitting a transmissionmodel is
typically time and/or host age, and it is common for population parameters
of interest to be non-linearly related to these variables. This means that the
highly efficient algorithms used for fitting regression models, such as least
squares, weighted least squares or iteratively reweighted least squares, are
inappropriate, and more general-purpose and computationally more
intensive numerical methods, including Markov chain Monte Carlo, are
required. Computational demand is also stepped up since models often
require solving by numerical integration for each iterated value of the
parameter(s) of interest during the fitting procedure.
Deterministic transmission models typically consider only the mean of
the distribution, which is modeled with respect to time and/or age. This is
sufficient to fit the model to mean-based data (such as the mean intensity
of infection within an age category) estimated from a reasonably large
sample size using a non-linear weighted least squares methodology.
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This technique is called trajectory matching or shooting. For example, to
fit a simple immigration
death transmission model (see “Dynamic
models of infection and transmission,” below) of A.
e
lumbricoides to
