Biology Reference
In-Depth Information
Moving beyond transmission success, simple theory can provide
insights into the dynamics of how a population of Ascaris is likely to
respond to perturbation induced either by seasonal environmental or host
behavioral factors, and
the impact of control
measures such as chemotherapy. This is illustrated by a very simple
example, where we ignore age structure and mating probabilities on the
assumption that aggregation of worms is high (k small) such that the
breakpoint is just above a mean of zero worms per host, but include worm
aggregation and density dependence in fecundity. In this case we can
obtain a closed form solution for the equilibrium worm burden M*:
most importantly
e
e
k R 1=ðkþ1Þ
0
.
M ¼
1
ð1
z
Þ
(9.3)
Here R 0 and k are as defined above for Eqs (9.1) and (9.2) , and z is
a measure of the strength of density dependence in fecundity (the rapidity
with which per capita fecundity declines as worm burden rises
see
Figure 9.4 ). 16 Note how density dependence, transmission success, and
the degree of worm aggregation are the sole determinants of average
e
0
5
10
15
20
25
30
Worm burden
FIGURE 9.4 Density dependence in fecundity. The number of eggs output by indi-
viduals with different worm burdens in Pulicat, India. 30 Individual data are shown as
crosses, and the black line is the fitted model (Eq. (9.8) ), with light gray dotted lines giving
the 95% confidence intervals.
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