Biology Reference
In-Depth Information
progress has been made in parameterizing mathematical models using
baseline (endemic equilibrium) parasitological data, and modifying basic
model structures to facilitate understanding of observed epidemiological
patterns which are driven by directly unobservable population processes
(for a brief history of human helminth models see Bas´ ˜ ez et al.).
11
Models of directly-transmitted helminths, such as the STHs, generally
have an immigration
death structure at their core. The rate of immi-
gration (establishment) of adult worms depends on the distribution of
infective stages within the environment, density-dependent processes
operating upon parasite establishment (including immunity), and on
numerous potential host-related factors which drive heterogeneity. The
rate of death (or loss) is determined by the per capita mortality rate of the
parasite, which again may depend on density- and host-dependent
factors.
e
Deterministic, Stochastic and Hybrid Approaches
The structure of helminth transmission models ranges from a simple
deterministic description of changes in the mean number of worms per
host,
118
to stochastic considerations of changes in the number of worms
within individual hosts.
63
Deterministic models which ignore all
stochastic elements, such as the distribution of worms among hosts, can
be used to model the population mean of an underlying stochastic model
under assumptions of a modestly large population size and an absence of
non-linear population processes. The latter assumption is extremely
restrictive given the range of non-linearities (essentially density-
dependent
processes) which
characterize
helminth
population
dynamics.
16,20
Stochastic models (see, for example,
64,184
,
189
e
191
) provide a mechanistic
framework with which to model the dynamic and fundamentally random
processes which define transmission of infection among individuals
within a community. Such models can be used to explore and predict how
the dynamics of the mean and higher moments of the parasite frequency
distribution are driven by underlying population processes. For example,
a common application of stochastic models of A. lumbricoides and other
STHs has been to understand how heterogeneities in host susceptibility,
61
the number of infectious eggs or larvae acquired per infection event
(clumped infections) and parasite-induced host mortality can drive
overdispersion
61,62,192
in the distribution of worms among hosts. Such
models have also been used to predict how overdispersion will change
with time (host age) under different generative mechanisms, with the aim
of formulating hypotheses for testing against observed epidemiological
data.
193,194
A general conclusion arising from stochastic formulations of STH
population dynamics is that a quite bewildering array of heterogeneous
