Biology Reference
In-Depth Information
while those arising from adults are less likely to come into contact with
children. Therefore the model should include heterogeneous mixing.
58
A simple way to mimic non-random contact is to stratify the population
into two age groups, namely: school-aged children (5
14) and the rest (0
4
e
e
and 15
combined for simplicity, although patterns may also be different
between these two groups), and assume different contact patterns with the
infective stages within and between these larger age groupings. Such
a stratification of hosts groups has the further advantage of facilitating the
modeling of school-based treatment programs. We assume that the child
and adult age groups have negative-binomially distributed worm distri-
butions with the same shape parameter, k,butdifferentmeans,M
c
and M
a
,
respectively. The means evolve independently according to the degree of
contact of each group with a common infectious “reservoir.” The model
equations are
55
(extending the approach by Chan et al.)
58
:
dM
c
dt
þ
¼ b
c
l
sM
c
;
(9.15)
dM
a
dt
¼ b
a
l
sM
a
The quantity l is the per capita infectiousness of the shared reservoir.
The parameters
b
c
and
b
a
determine the strength of contact with the
reservoir for children and adults, respectively. The dynamics of the
infectious reservoir are described by the following equation:
f
n
a
p
m
2
d
dt
l
R
m
2
s
0
¼
2
ð
M
c
;
k
Þ
n
c
p
þ
f
2
ð
M
a
;
k
Þ
l
(9.16)
lðb
c
n
c
p
þ b
a
n
a
q
Þ
The parameters in Eqs.
(9.15) and (9.16)
are as defined earlier. The
parameters n
c
and n
a
represent the proportion of the population in the two
age classes and p and q the fraction of egg output that enters the reservoir
from children aged 5
14 years and other age groups, respectively.
We investigate the effect of regular school-based treatment on the
evolution of worm burdens in the community for three scenarios:
e
A. Homogeneous model. As defined in Eq.
(9.6)
. Treatment is applied to
a fraction g
0
of the population with efficacy h and at intervals of
years.
B. Heterogeneous model. As described in Eqs.
(9.15) and (9.16)
assuming
children and adults are identical epidemiologically. Treatment is
applied to a fraction g of school-aged children with efficacy h and at
intervals of
s
years
C. Heterogeneous model with heterogeneous exposure. As described in
Eqs.
(9.15) and (9.16)
assuming that children are both twice as potent
a source of eggs and have twice the infectious contact rate. Treatment
is applied to a fraction g of school-aged children with efficacy h and at
intervals of
s
years.
s
