Biomedical Engineering Reference
In-Depth Information
Table 1. Some AIDS Incidence Data from the SWISS Population of
Homosexual and Bisexual Men
Year
J
F
M
A
M
J
J
A
S
O
N
D
80
.
.
.
.
.
.
.
.
.
.
1
.
81
.
.
.
.
.
.
.
.
.
1
.
1
82
.
.
.
.
.
.
.
.
.
.
.
.
83
.
.
.
2
.
.
1
1
2
.
1
.
84
2
2
1
2
2
.
4
.
.
3
4
1
85
6
.
5
4
4
2
13
1
6
6
4
3
86
4
6
5
5
9
6
27
4
6
9
4
15
87
13
4
4
12
7
11
15
9
7
14
15
14
88
17
18
15
14
18
15
30
18
16
5
6
19
89
18
18
15
14
20
14
18
15
21
20
23
15
90
15
21
22
13
20
20
37
21
12
20
17
9
91
17
16
22
18
14
15
23
27
14
21
15
14
92
15
22
20
18
27
22
35
22
26
16
27
23
93
24
24
15
20
17
25
44
16
11
10
13
22
94
22
17
19
24
17
24
23
21
15
15
24
21
95
17
14
15
18
14
23
13
11
13
15
26
13
5.1. The Initial Size
Since the average AIDS incubation period is around 10 years and since the
rst AIDS case was reported in 1981, to derive the estimates from the state
space model we thus assume January 1, 1970 as t
0
= 0. Tan and Xiang
13;14
have shown that the estimates were very insensitive to the choice of the
time origin t
0
.) It is also assumed that at time 0 there are no AIDS cases
and no HIV infected people with infection duration u > 0 but to start the
HIV epidemic, some HIV were introduced into the population at time 0 so
that I(0; 0) > 0.
To specify the initial numbers of S people and I(0; 0) people at time 0,
we proceed as follows: (1) We take I(0; 0) as I(0; 0) = 3 for the homosexual
since this is the observed number of AIDS incidence in this population in
1981 and since the average incubation period is about 10 years. (2) We
assume S(0) as S(0) = 25; 000 for the Swiss homosexual population by
comparing the observed AIDS incidence with that of the San Francisco
homosexual population and by noting that the estimate of S(0) in the
latter population is roughly 40,000 in January 1970. We have also tried
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