Biology Reference
In-Depth Information
The functions f
1
, f
2
, and f
3
represent, respectively: the collapsed details
of parasite survival, reproduction, and transmission via segments of the
life-cycle not involving the mature worms in humans; density-dependent
constraints on parasite fecundity; and survival of adult parasites in the
human host. The term l(a) denotes the age-dependent survival function
for the human host. In some countries in sub-Saharan Africa this is
roughly an exponential decay term. In this formulation mating proba-
bilities have been ignored based on the assumption of high degrees of
worm aggregation. Analytical insights from this model are difficult to
obtain, but details of equilibrium properties under various assumptions
on human survival and age dependence in infection rates are given by
Anderson and May.
14
For most applications numerical work is required to solve Eq.
(9.10)
and this can form the basis for parameter estimation of the age-specific
infection rates (
L
(a,t)). Parameterization of this model, however, is not
straightforward, given that age dependence in parasite establishment in
the human host may involve a degree of acquired immunity where
parasite survival and fecundity depend on an integral of past exposure for
each individual in the host population. A simpler approach to the
inclusion of age structure in the human population is described in
a subsequent section dealing with heterogeneities, where a crude three
age class model is presented to mimic infection in pre-school children
(0
4 years of age, school-aged children (5
14 years of age), and the rest
e
e
(
14 years of age) (see later section). Some formal elaborations of the
model to include the slow buildup of immunity in a manner dependent
on accumulated past exposure are given in Anderson and May.
18
However, the relevance of these models remains in question at present in
the absence of a consensus on the role of immunity in Ascaris infection in
humans.
34
The basic structure of the age-structured model has been used to
construct a user friendly software interface (EpiWorm) to help policy
makers in the design of control programs for intestinal worm infections
and other helminths (
http://www.schoolsandhealth.org
)
. As is often the
case with user friendly software used by those who are not specialists in
mathematical model use in epidemiology, the assumptions underpinning
the software and the uncertainties surrounding parameter estimation are
not always clearly specified.
Stochastic Individual-based Simulation Models
There are many situations where a fully stochastic individual-based
model is better able to capture the fine details of transmission and
control impact at individual and community-based levels. An individual-
based model is one in which each individual is included explicitly in the
model, rather than a model of the average behavior of the population, as
>
