Biology Reference
In-Depth Information
Parameter Estimation
Mathematical models play an important role in parameter specification
and estimation. The specification of a model structure involves the defi-
nition and inclusion of a number of key biological (e.g. parasite life
expectancy in the host) and epidemiological (e.g. the force or rate of
infection) parameters. Ideally, the typical values for these should be
estimated independently from any data which a model is fitted to, such as
temporal changes in mean intensity and the prevalence of infection, in
order to test its accuracy in describing observed pattern.
A good example of such data is given in
Figure 9.1
,where,using
worm expulsion techniques, the frequency distribution of Ascaris in
a set of villages in India provided estimates of the aggregation
parameter k.
30
A similar example is given in
Figure 9.4
where fecal egg
counts prior to worm expulsion provide estimates of the strength
of density dependence in fecundity, z (seeChapter7forfurther
examples).
It is often the case, however, that some parameters cannot be estimated
without recourse to model fitting to observed changes in the key outcome
variables of intensity and prevalence. Obvious examples are the rate of
infection,
b
,andR
0
, both of which may be dependent on host age and
gender. To fill this need it is possible to draw on a range of statistical
methods used in other areas of epidemiology and science in general.
These statistical tools are being used to fit dynamic models in many areas
of infectious disease epidemiology,
31,32
and are currently being devel-
oped in this field. This will allow models to be fitted to transmission
dynamics from multiple settings, aiding their future development and
applicability.
THE STRUCTURE OF MATHEMATICAL MODELS FOR
THE T
RANSMISSION DYNAMICS OF
ASCARIS
We now outline the detail of some common model structures for the
transmission dynamics of Ascaris. This section is useful, but not essential,
for the understanding of the final section on insights from modeling of
mass treatment interventions.
Basic Model
The simplest model structure represents the population biology of the
mature adult worms (M) in the human host and the free-living infective
egg stage (E), taking into account maturation delays in eggs (
s
2
) and
adult worms (
s
1
) in progression to, respectively,
infectivity and the
