The National Medical Journal of India; Vol.16: 126-31, No.3, 2003
The Natural History of Adult patients infected with Human
Immunodeficiency Virus in Mumbai
Hira Subhash K, MD, MPH1/2/5
Shroff HJ,MD3
Lanjewar DN, MD4
Dholkia YN, MD1
Bhatia, Vandana P, MD1
Dupont HL, MD5
1
: AIDS Research and Control Centre (ARCON), Sir J. J. Hospital, Mumbai
2
: Department of Infectious diseases, M. G. M. Medical College, Navi Mumbai
3
: Formerly at Department of Skin & VD, Grant Medical College & Sir J.J.Hospital,
Mumbai
4
: Department of Pathology, Grant Medical College & Sir J. J. Hospital, Mumbai
5
: The University of Texas-Houston, USA
Word count: 1862 (text only)
Corresponding author:
Dr. Subhash K. Hira
AIDS Research and Control Centre (ARCON)
STD Building, Sir J. J. Hospital, Mumbai 400 008.
e-mail: subhash_hira@hotmail.com
ABSTRACT
Background: The natural history studies of untreated HIV infection are useful for clinicians, public
health experts and policy makers to improve and monitor care, to plan services and control, and for
modelling the epidemic. Several natural history studies have been published in developed countries for
gay men and IV drug users. Few studies have emerged for heterosexual populations from Africa.
However, India with an emerging epidemic required a similar study. Hence, a study was designed to
determine the HIV-disease progression in a prevalent cohort of adult HIV-seropositive patients.
Patients and Methods: A prevalent cohort of 1009 patients comprising of 488 asymptomatic HIV seropositive persons, 259 with AIDS-Related Complex (ARC), and 262 with Acquired Immunodeficiency
Syndrome (AIDS) were recruited for the study at Sir J. J. hospital in Mumbai. Case control study was
conducted to determine the correlation of clinical features and other factors on disease progression. The
disease progression from the stage of asymptomatic to that of ARC and AIDS was determined using time
series analysis. Also, the incubation period from HIV to AIDS was determined using Weibull curves.
Results: The median incubation periods for progression were: HIV to AIDS - 7.9 years and ARC to
AIDS - 1.9 years. The median survival after attaining AIDS was 19.2 months. Comparison of progressors
and nonprogressors revealed that disease progression was correlated with the clinical features like chronic
fever (OR 5.6), persistent generalised lymphadenopathy (OR 4.7), persistent cough of > one month (OR
3.5), chronic diarrhoea (OR 3.3), oral candidiasis (OR 3.2), weight loss of > 10% of the body weight
within one month (OR 2.9), incident tuberculosis (OR 2.8), and herpes zoster (OR 2.5). The annual
incidence of active clinical tuberculosis was 86/1503 p-y (5.7/100p-y). The median time to occurrence of
active tuberculosis was 21.6 months. The annual incidence of mortality was 96/2009 p-y (4.8/100p-y,
CI0.95 3.4,6.2).
Conclusions: Progression to AIDS and death was faster among heterosexual cohort in Mumbai than that
reported for gay men and hemophiliacs in the US and Europe. Strategies need to be developed to prevent
the occurrence of tuberculosis among HIV-infected patients because that will help reduce the risk of
morbidity and mortality. This is the first large-scale study in the Indian sub-continent where longitudinal
followup of HIV-infected persons was performed. The findings will be useful for advocacy and for assessing
impact of anti-retroviral therapy in India.
Key word(s): HIV/AIDS natural history, incubation period, correlates of disease
progression, India.
2
INTRODUCTION:
The natural history studies of untreated HIV infection are relevant because these allow a
comparison of the disease in different regions of the world. Such studies will continue to be
useful for epidemiologists, clinicians and policy makers in developing countries to improve care,
planning of services and control, to project the number of AIDS cases, and to assess the impact
of anti-retroviral therapy (ART) as most governments of developing countries are still evaluating
priority options for phased introduction of ART. Extensive studies of the natural history of HIV
infection were conducted among gay men and intravenous drug users in the United States and
Europe in mid-80s1-4. There were several other studies, which had established biologic and
clinical predictors of HIV-disease progression. The disease progression depends upon the
intensity of host immune responses5,6, ability of virus to induce syncytia formation7, prophylaxis
for some opportunistic infections such as Pneumocystis carinii and Mycobacterium tuberculosis
among others8, and the occurrence of acute HIV stage9. Furthermore, disease progression also
depends on a ‘set-point or balance’ that is reached between the degree of viral replication and
immune control as determined by the level of circulating virus (viral load)10, the ongoing viral
mutations that allow the virus to escape partially effective immune control at future time
points11, the high levels of certain cytokines (IL-4,IL-10) released by the activated cells pressure
the immune response towards a less effective antibody response12, and the recent introduction of
ART13. The natural history studies in the United States and Europe were conducted
predominantly among blood transfusion recipients or gay men; hence, have limited application to
developing countries where primary mode of transmission is heterosexual. Recent studies on
natural history come from Uganda and Haiti, where the population under study was
heterosexual14-17. This study of natural history among heterosexual population is first of its kind
in India and in the Asian region.
Patients and Methods:
Between April 1994 and December 2000, 3510 patients referred with clinical features
3
suggestive of immune suppression or those with clinical evidence of sexually transmitted infections
(STI) referred to AIDS Research and Control Centre (ARCON) at Sir J. J. Hospital in Mumbai were
screened for the natural history study. Detailed demographic and sexual histories were obtained.
Thorough clinical and genital examinations were performed. Prior to investigation, all patients were
offered pre-test counselling by trained clinical psychologists. The laboratory investigations included
full blood count, ESR, liver and renal function tests, ELISA for HIV-1/2 (Sanofi Pasteur, France)
and those found positive were re-tested with Genodia (Serodia, Japan). Western blot (Genelab,
Singapore) was performed on 1009 patients who were followed for more than 6 months and formed
the final cohort for this study. Routine RPR test for syphilis and confirmation of positives with
TPHA (Glaxo-Wellcome) and testing for CD4/CD8 cell enumeration (Sanofi Pasteur, France) was
done. Montoux skin test was performed for all patients18. Using globally standardised definitions of
clinical markers described in WHO reference manual
19
, the presence or absence of the clinical
markers like weight loss > 10 per cent of the body weight within a month, chronic fever > one
month, persistent cough > one month, recurrent diarrhoea > one month, tuberculosis18, oral
candidiasis, persistent generalised lymphadenopathy, STI, including genital ulcer diseases (GUD) 20
were recorded at the base line for all
patients. Overall, patients were classified either as
Asymptomatic HIV sero-positive; AIDS Related Complex (ARC); or AIDS based on clinical
definition and CD4 counts21. WHO guidelines for case definition now refer to ARC stage as
“intermediate HIV-related illness”. Similarly, laboratory tests and staging were conducted on
several follow-up sessions. The final cohort comprised of 488 asymptomatic HIV seropositive
persons, 259 with ARC, and 262 with AIDS.
The follow-up procedure included several sessions of post-test counselling based on the
patients' requirements and as determined by the counsellor(s). Asymptomatic HIV seropositive
patients and those with minor non-opportunistic infections were encouraged to return for follow-up
visits at 3-month intervals. Those with moderate and serious opportunistic infections (OI) 1,2,5 were
provided co-trimoxazole prophylaxis and further treated as outpatients or admitted on the wards
based on clinical judgement. Option of prescription of anti-retroviral therapy (ART) costing
>Rs.20,000/month was offered to symptomatic and cases of AIDS; however, few were able to
4
afford and were transferred to a different cohort that was being followed on ART. Disease
progression was studied in four outcome categories as follows: (1) Asymptomatic to ARC (2)
Asymptomatic to AIDS (3) ARC to AIDS (4) AIDS to death. Rate of disease progression to any
stage from the proceeding stage was defined as the ratio of number of new entries in that stage and
person-years followed. However, this caused some overlap in person-years of followup between
outcome categories 1 and 2 because most individuals progress to AIDS through stage of ARC. To
evaluate the impact of age, gender, social variables like occupation, education, marital status,
sexual orientation, and the clinical features on the risk of HIV progression to higher stages
including death, case-control analysis was performed using the time series method. The entire
analysis was done using the software packages such as Mathematica22 and Epi-Info 23. The data
was analysed with cut-off point of June 2001. Also, to determine the incubation periods for disease
progression, the Weibull curve was considered a good fit due to the flexibility of its shapes24.
Additionally, truncated Weibull distribution was applied to estimate mean incubation period from
HIV to AIDS because exact time of acquisition of HIV infection was not known. In such a
situation, truncated Weibull was recommended technique to compensate for missed durations on
both sides of the data25.
Patient’s anonymity was protected and informed, written and signed consent forms were
obtained. The study was approved by the IRB of the Government of Maharashtra (Office of
Medical Education and Research), the Dean of Sir J. J. Hospital and an internal ARCON review
committee.
Results:
The prevalent cohort of 1009 patients comprised of 775 (76.8%) males and 234 (23.2 %)
females. The cohort comprised predominantly of heterosexual individuals among whom 20%
had never attended formal education, one-third were single, two-third gave current history of
substance use, and significantly greater number of males had clinical diseases as compared with
females. Their demographic, social variables, and the spectrum of clinical features at the time of
5
recruitment in to the study are presented in table 1. Montaux test was negative (0-5mm) in 896
(88.8%), 6-15mm in 71 (7%), and >15mm in 42 (4.2 %).
Of the 1009 patients followed for 2009 person-years (p-y); mean 2.0 years (range
>0.6<7.0). Three hundred sixty one (17.9/100p-y) of the prevalent cohort progressed to higher
stage or death. This progression was not significantly different for all four-outcome categories
(table 2). The entire case-control analysis for disease progression was categorised in the
following categories:
Progression by gender and age
Over all, the disease progression among males and females was not significantly different
(OR1.1, CI 0.9,1.5;p=0.40) (table 3). Among the cohort, 20% were in 15-24 years age group,
58% were in 25-34 years age group, 18% were in 35-44 age group and remaining 4% were in
44+ age group. The average age of males and females that progressed to AIDS was above 31
years. Evidently, these persons were at the peak of productivity. The multivariate analysis of
progressors revealed that the risk of disease progression was not significantly related to their age
(Table 4).
Progression by Social variables
Individuals employed on clerical jobs showed relatively higher rate of disease
progression (table 5). Skilled workers, housewives and married men were all at identical risk of
disease progression. Also, the literacy level and recent history of substance use was not a
significant factor contributing towards the disease progression (OR literates vs illiterates
OR1.17; CI 0.95 0.77, 1.91).
Progression by clinical and immunologic features
Of 1009 persons recruited in the study, 714 did not have evidence of clinical active
tuberculosis. The latter were followed for 1503 p-y and 86 incident cases of active tuberculosis
were diagnosed (incidence 5.6/100 p-y). Case-control analysis revealed that patients with chronic
6
fever were at highest risk of progression (OR 5.6). Also, the progression was high among
patients with the following clinical features in decreasing order of risk: persistent generalised
lymphadenopathy (OR 4.7), persistent cough of > one month (OR 3.5), chronic diarrhoea (OR
3.3), oral candidiasis (OR 3.2), weight loss of > 10 per cent of the body weight within one month
(OR 2.9), incident tuberculosis (OR 2.8), and herpes zoster (OR 2.5)(table 6). The loss of CD4+
cells in asymptomatic males and females was 55/p-y and 49/p-y, respectively (OR1.2; CI0.95
0.8,1.7).
Incidence of mortality:
The rate of mortality in the prevalent cohort was 4.8/100p-y (96/2009 p-y). The incidence
of AIDS to death was lower possibly due to some deaths being missed because terminally ill
patients tend to return to their villages. Incidence of death in the cohort was also studied by
controlling for tuberculosis. It was found that 49/96 (51.0%) deaths were directly attributable to
incident tuberculosis.
Weibull Curve Analysis
Figure 1 presents the median time for occurrence of AIDS at 7.6 years using simple
Weibull and 7.9 years using truncated Weibull curves. The latter median incubation period did
not alter by adding some artificial length of 3, 6, 9, 12,15…. n months to the date of recruitment
visit to adjust for the actual dates of HIV infection. This was the advantage of application of
truncated Weibull distribution and detailed discussion can be found elsewhere19. The estimated
median duration of 1.9 years (22.8 months) from ARC to AIDS and 1.6 years (19.2 months)
from AIDS to death are presented in Figures 2 and 3, respectively. The median duration for the
occurrence of clinical tuberculosis was 1.8 years i.e. 21.6 months (figure 4).
Discussion:
This is the first study describing the natural history of HIV infection among
heterosexual persons in South-Asia. The cohort comprised of skilled and unskilled workers and
housewives. More than 80 per cent of the patients were educated; hence, literacy did not seem to
7
be a deterrent for acquiring the HIV infection. The rate of disease progression was not directly
proportional to the age, education, occupation or substance (predominantly tobacco or alcohol)
use by the patients. This finding was identical to that of tricontinental seroconverter study26.
Also, gender of patients was not an important correlate of disease progression. Identically, the
European27 study revealed that after adjusting for age, gender was not a correlate of disease
progression. Since the cohort of this study was not exposed to any anti-retroviral therapy,
findings of this study will be relevant to the Asian region for some time to come because
widespread use of anti-retroviral drugs (ART) is likely to happen in developing countries in a
phased manner. Subsequently, these findings will provide historical baseline for determining the
impact of ART.
The median incubation period for AIDS among gay and bisexual men was reported to be
11.0 years (mean, 11.8 years, 95% confidence interval, 10.6 to 13.0 years)
studies on natural history of HIV come from the US and Europe
29-31
28
. Although the best
, those results may not be
comparable with the Mumbai cohort due to differences in populations among whom studies were
done, their nutritional status, the level of tropical endemic infections, their sexual orientations,
racial differences in immunity, virus variations, and varied environments. However, median
disease progression from HIV infection to AIDS in Mumbai was 7.9 years, which is similar to
9.4 years from HIV to death in the Ugandan natural history study of heterosexual population14-16.
Apparently, incubation period for AIDS is shorter in Mumbai. Yet, the median survival of 19
months in Mumbai cohort after attaining AIDS was similar to heterosexual patients in the New
York City cohort32. However, the incidence of AIDS to death in our study may be an
underestimation due to some deaths being missed because terminally ill patients tend to return to
their villages. These findings will be useful for demographers, epidemiologists and policy
makers to forecast the impact of the epidemic in Asia.
Chronic fever, diarrhoea, oral candidiasis, weight loss, incident tuberculosis, and herpes zoster
were seen as significant clinical markers associated with disease progression among the
heterosexual cohort in Mumbai. Similar findings for gay men and intravenous drug users were
8
also observed in the Italian and Chilean cohorts27,33. There was temporal association between the
occurrence of clinical tuberculosis and death34. The degree of association of these clinical
markers with disease progression observed in this study will be useful for clinicians providing
care and support to patients with HIV/AIDS. Clinicians will be able to anticipate stages and
prepare their patients and families accordingly.
The increased availability of anti-retroviral therapy (ART) has significantly altered the natural
history and the occurrence of opportunistic infections (OI) in several developing countries. The
most striking benefit of ART in South Africa is the 80% reduction in the incidence of HIV-1
associated tuberculosis (95% CI 62,91)13. Studies in Brazil 35 and Chile 36 have shown the declining
annual trends for the occurrence of OI after widespread introduction of ART and safe
discontinuation of OI prophylaxis. Italian ART studies reported significantly fewer infections and
consequent shorter hospital stay 37 and modification of the natural history of cryptosporidiosis and
microsporidiosis
38
. With scaling-up of access to ART in India, the findings of this study will
provide historical baseline for assessing the impact of ART on the natural history of HIV.
Acknowledgement:
Authors wish to thank Drs. Arni Srinivas Rao, Clements Fernandes, Malavika Kohli, ARCON
and JJ Hospital staff for their inputs in the conduct of this study. The resources for this study
were provided by the University of Texas-Houston and the Government of Maharashtra.
9
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Table 1: Demographic, Social Factors, and Clinical Features of Natural History Cohort
(n=1009)
Male
Female
14
Total
Mean Age (yrs)
n=775(%)
30.71
Occupation
Trading
Unemployed
Unskilled Labour
Skilled Labour
Clerical
Professional
Student
Housewife
CSW
Not known
47 (6.0)
86 (11.0)
308 (39.7)
229 (29.5)
34 (4.3)
23 (2.9)
4 (0.5)
0
0
44 (5.6)
n=234 (%)
26.81
0
n=1009 (%)
29.96
29 (12.4)
2 (0.8)
6 (2.6)
5 (2.1)
1 (0.4)
160 (68.4)
10 (4.3)
7 (0.9)
47 (4.7)
100 (9.9)
337 (33.4)
231 (22.9)
40 (4.0)
28 (2.8)
5 (0.5)
160 (15.9)
10 (0.9)
51 (5.1)
Educational Level
Nil
114 (14.7)
School
388 (50.0)
SSC
161 (20.7)
HSC
62 (8.0)
Graduate
38 (4.9)
Post Graduate
8 (1.0)
Not known
4 (0.5)
71 (30.3)
106 (45.3)
43 (18.4)
9 (3.8)
4 (1.7)
0
1 (0.4)
185 (18.3)
494 (49.0)
204 (20.2)
71 (7.0)
42 (4.2)
8 (0.8)
5 (0.5)
Marital Status
Unmarried
Married
Divorced
Widowed
Remarriage
Not known
273 (35.2)
480 (61.9)
9 (1.1)
11 (1.4)
0
2 (0.2)
16 (6.8)
177 (75.6)
5 ((2.1)
33 (14.1)
1 (0.4)
2 (0.8)
289 (28.7)
657 (65.1)
14 (1.4)
Addiction
Alcohol
Tobacco
Smoking
Non-IV Drugs
IV Drugs
Nil
Not known
419 (54.0)
108 (13.9)
71 (9.1)
1 (0.1)
2 (0.2)
161 (20.7)
13 (1.7)
10 (4.3)
20 (8.5)
2 (0.8)
2 (0.8)
1 (0.4)
190 (81.2)
9 (3.8)
429 (42.5)
128 (12.7)
73 (7.2)
3 (0.3)
3 (0.3)
351 (34.8)
22 (2.2)
Sexuality
Heterosexual
Homosexual
Bisexual
Not known
677 (87.4)
9 (1.2)
19 (2.5)
70 (9.0)
213(91.0)
0
1(0.4)
20(8.5)
895 (88.7)
9 (0.9)
20 (2.0)
90 (9.0)
14 (6.0)
Presenting Clinical Features
44 (4.4)
1 (0.1)
4 (0.4)
OR(CI0.95)
15
Weight loss more
than 10 % of the
body weight
200 (25.8)
37 (15.8)
237 (23.5)
1.6 (1.1,2.4;p=0.01)
113 (11.1)
1.8 (1.0,3.3;p=0.03)
Diarrhoea more
than one month
97 (12.5)
Fever more
than one month
197 (25.4)
43 (18.4)
240 (23.8)
1.4 (0.9,2.0;p=0.07)
Cough more
than one month
139 (17.9)
28 (12.0)
167 (16.6)
1.5 (0.9,2.4;p=0.06)
PGL
73 (9.4)
8 (3.4)
82 (8.0)
2.8 (1.3,6.3;p=0.008)
Herpes zoster
121 (15.6)
17 (7.3)
138(13.7)
2.2 (1.3,3.8;p=0.003)
Oral candidiasis 83 (10.7)
16 (6.8)
9 (3.8)
Tuberculosis
223 (28.8)
33 (14.1)
Incident TB
70 (9.0)
16 (6.8)
16
92 (9.1)
2.8 (1.4,6.1;p=0.004)
256(25.4)
2.0 (1.4,3.4;p=0.000)
86 (8.5)
1.3 (0.7,2.4;p=0.33)
Table 2: Incidence of progression from recruitment stage to ARC, AIDS, or Death in
the prevalent cohort (n=361)
Progression category
No. Patients
Progressed
P-Y
followed
Incidence Rate%
(CI 0.95)
1. Asymptomatic to ARC
105
789.94
13.29 (9.89, 16.69)
2. Asymptomatic to AIDS
106
822.56*
12.89 (9.54, 16.23)
3. ARC to AIDS
96
462.61
20.75 (14.53, 26.98)
4. AIDS to Death
54
519.18
10.40 (6.25, 14.55)
___________________
* Person-years overlapping with category 1.
Table 3: Incidence of Progression from recruitment stage to ARC, AIDS and Death by
Gender (n=361)
17
Progression category
Male (/100 p-y)
Female (/100 p-y)
1. Asymptomatic to ARC
69/535.1 p-y(12.9)
36/254.9 p-y(14.1)
2. Asymptomatic to AIDS
79/577.9* p-y (13.7)
27/244.7* p-y (11.0)
3. ARC to AIDS
84/393.9 p-y (21.3)
12/68.7 p-y (17.5)
4. AIDS to Death
47/446.2 p-y(10.5)
7/73.0 p-y (9.6)
Total progression
279/1953.1p-y(14.3)
82/641.3p-y (12.8)
____________________________________
* Person-years overlapping with category 1
Table 4: Comparison of Incidence of Progression among Age Groups (n=361)
Progression
Category
15-24
n/p-y(/100p-y)
Asymptomatic to ARC
27/69.8(38.7)
25-34
n/p-y(/100p-y)
35-44
n/p-y(/100p-y)
58/134.5(43.1) 18/41.9(43.0)
18
45+
n/p-y(/100p-y)
2/8.3(24.0)
Asymptomatic to AIDS
25/63.1(39.6)
ARC to AIDS
13/35.5(36.6)
3/8.7(34.7)
15/34.6(43.4)
58/118.3(49.0) 19/36.3(52.3)
4/7.1(56.3)
AIDS to Death
5/9.3(53.8)
28/42.9(65.3)
Total progression
72/176.7(40.7) 209/475.4(44.0)
OR
1.0
65/179.8(36.2)
16/22.0(72.9)
5/12.0(41.7)
66/135.6(48.7)
14/36.1(38.8)
1.1(0.8,1.5)
1.2(0.8,1.8)
0.9(0.5,1.9)
Table 5: Incidence of Progression from recruitment stage to ARC, AIDS and Death by
social variables (n=361).
Progressors
Non-progressors
OR(CI0.95)
N=361
n=626*
Trading
16
30
1.0 (0.5,2.0)
Unemployed
38
60
1.2 (0.7,2.0)
Unskilled labour
121
209
1.1 (0.8,1.60)
Skilled labour
78
146
1.00
Occupation
19
Clerical
19
20
1.8 (0.9,3.7)
Professional
7
20
0.7 (0.2,1.7)
Student
1
4
0.5 (0.0,4.5)
Housewife
58
99
1.1 (0.7,1.7)
Sex Worker
3
7
0.8 (0.2,3.6)
Others/Not known
20
31
Nil
64
117
0.8 (0.5,1.3)
School
167
314
0.8 (0.6,1.2)
Secondary level
80
121
1.00
High school
29
40
1.1 (0.6,2.0)
Graduate
15
27
0.8 (0.4,1.2)
Postgraduate
3
5
0.9 (0.2,4.5)
Not known
3
2
Unmarried
100
179
1.0 (0.7,1.3)
Married
239
407
1.00
Divorced
5
9
1.0 (0.3,3.1)
Widowed
15
29
0.9 (0.4,1.8)
Others/Not known
2
2
Alcohol
156
266
1.1 (0.8,1.5)
Tobacco
48
75
1.2 (0.8,1.9)
Smoking
25
45
1.0 (0.6,1.8)
Nil
120
225
1.00
Not known
12
15
Educational Level
Marital Status
Addiction

22 missing values
20
Table 6: Incidence of clinical features among progressors and non-progressors(n=361)
Diseases Among Progressors/100p-y
Asympt-
Asympt-
to-ARC
to-AIDS
ARC-
Diseases Among OR(CI0.95)
Non-p rogressors (Prog vs
to-Death
/100p-y
Nonprog)
AIDS-
to-AIDS
Clinical Feature
Weight loss >
10per cent of
body weight
4.7
5.8
6.0
150.2
3.6
2.9(1.9,4.6)
Diarrhoea >
One month
2.4
2.9
3.6
43.1
1.6
3.3(1.8,6.1)
Fever >
One month
9.2
6.7
4.1
126.0
1.8
5.6(3.1,10.1)
Cough >
One month
4.4
5.9
7.8
56.8
2.6
3.5(2.1,5.7)
PGL
4.9
0.7
3.0
13.1
0.8
4.7(2.0,11.2)
Herpes Zoster
2.0
1.1
0.7
14.7
1.0
2.5(1.1,5.8)
Oral Candidiasis
4.0
2.5
9.2
24.6
2.0
3.2(1.8,5.6)
Incident
0.4 17.9
16.1
122.6
Tuberculosis
21
5.7
2.8(2.0,4.1)
Figure Captions:
Figure 1. Estimated incubation period of adult HIV to AIDS in Mumbai.
Truncated distribution is plotted with estimated parameters = 0.0340 and =1.4674:
Simple distribution is plotted with estimated parameters 1= 0.1200 and 1=0.8680.
Figure 2. Estimated duration from ARC to AIDS
= 0.2280 and =1.7662
Figure 3. Estimated duration from AIDS to death
= 0.2641 and =2.2289
Figure 4. Weibull estimates for the incidence of tuberculosis.
= 0.2748 and =1.6603
22
23
Figure 1. Estimated incubation period of adult HIV to AIDS in Mumbai
1
0.9
Cumulative probability
0.8
0.7
Truncated Weibull
0.6
Simple Weibull
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
20
Years
2
25
30
Figure 2. Estimated duration from ARC to AIDS
1
0.9
Cumulative probability
0.8
0.7
0.6
(Median 1.9 years)
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
Years
3
Figure 3. Estimated duration from AIDS to death
1
Cumulative probability
0.9
0.8
0.7
0.6
(Median 1.6 years)
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
Years
4
Figure 4. Weibull estimates for the incidence of tuberculosis
1
Cumulative probability
0.9
0.8
0.7
0.6
Median is 1.8 years
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
Years
5