Biology Reference
In-Depth Information
FIGURE 9.2
The relationship between prevalence and mean egg output, from a study
in Myanmar.
60
The dots are the observed relationships and the solid line is the fitted curve,
given in Eq.
(9.1)
, with a k value of 0.194. For large changes in infection intensity there may
be almost no change in prevalence.
The Biological and Ecological Determinants of Parasite
Abundance
One of the benefits of using models are that, for simpler model struc-
tures in particular, larger scale behavior can be summarized by relatively
simple expressions which can give powerful insights on the underlying
processes. This type of analysis generates a template for understanding
how each individual parameter influences the reproductive or trans-
mission success of the parasite. This is encapsulated in the definition of R
0
by derivation from the basic model (which is described in the next
section).
16
This model is illustrated by means of a flow chart of the life-
cycle of Ascaris, definition of the key parameters determining flow
through the life-cycle (
Figure 9.3
), a simple equation or equations to
capture this flow by reference to changes in the mean worm burden per
person M, and the derivation of an expression for the basic reproductive
number R
0
.
For the flow chart represented in this figure, and by ignoring for the
time being mating probabilities, density dependence in fecundity and
host age, the equation for R
0
is given by:
R
0
¼ð
slbNd
d
2
Þ
=
½ðm þ m
1
Þðm
2
þ bN
Þ
(9.2)
1
The parameters (which are presented in the flow chart) are defined as
follows. The parameter s represents the sex ratio of worms,
l
denotes
average egg production per female worm,
is the infection rate of hosts
defined as the rate of contact between humans and infective stages times
b
