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individuals they come into contact with are already immune to chicken pox. For the
four older age cohorts, the weights are decreased, taking on values of 0.5 for the
10- to 19-year cohort, 0.25 for the 20- to 29-year cohort, 0.1 for the 30- to 39-year
cohort and 0.05 for the 50-year cohort.
We assume that the virus is present at the beginning of the model run. Specif-
ically, we postulate that 20 percent of the population have contracted chicken pox
by the age of 4; 65 percent by the age of 9; 88 percent by the age of 19; 95 percent
by the age of 29; 97 percent by the age of 39; 98 percent by the age of 49; and 99
percent by age 50 or older 3 . The initial susceptible population in each age cohort,
measured in thousands of individuals, is shown in Table 8.1. Initially, no individual
in either age cohort is assumed to be within the incubation period, and the incubation
time for all age cohorts is 7 days.
Initial infective stocks (measured in thousands of individuals) are given in
Table 8.1. Since chicken pox is mainly a childhood disease, the assumption is made
that the largest infective stock would be Infective 1, for the age cohort of 0 to 9
years. The infective stock was then decreased for each subsequent age cohort.
The total number of infective individuals includes those who are infected with
shingles. By assumption, only individuals in the last age cohort may be afflicted
with shingles, and at the beginning of the model no one suffers from shingles. To
model the contraction with shingles, we invoke a “shingle rate” of 0, which allows
us to study its effects when increased. For subsequent runs, we assume 0.15 cases
of shingles per thousand individuals, and a recovery time of 10 days. In contrast, the
number of days it takes individual to recover from chicken pox is 14.
The model is shown in Figure 8.1. It contains a flow to reflect immunization, cal-
culated as the product of the number of individuals who are susceptible to chicken
pox and an immunization rate. For the model runs discussed below, we varied immu-
nization rates, starting at zero and increasing it for subsequent runs to reflect more
prevalent childhood immunization. The total stock of infective individuals is shown
as the sum of all individuals with chicken pox and with shingles. The total force of
infection is simply defined as the (unweighted) transmission coefficient multiplied
by the total number of infective individuals. From this, we can calculate the average
age of first infection as the inverse of the force of infection, divided by 365 days.
Table 8.1 Initial Valu es of Stocks (Thousands of Individuals)
Cohort
Susceptibles
Infective
Immune
0-9
20,710
40
15,252
10-19
93,961
8
29,035
20-29
1927
1
36,604
30-39
1254
1
40,541
40-49
654
0
32,044
50 Plus
637
0
63,033
3 Finger, Reginald, Jeffrey Hughes, Barry J. Meade, Andrew R. Pelletier, and Clarkson T. Palmer.
“Age-Specific Incidence of Chickenpox.” Public Health Reports. Nov/Dec 1994: 750-755.
 
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