Projecting the Minimum Size of HIV Infection and AIDS Epidemic in China

At present, intravenous drug users (IVDUs) comprise the largest risk group to develop acquired immunodefeciency syndrome (AIDS) in China, and their sex partners seem the second largest risk group. It is necessary to understand long-term trends in the spread of human immunodeficience virus (HIV) among IVDUs and their sex partners and the trends about AIDS cases development for disease prevention and control. The compartment model was used to project the number of HIV infectious individuals and the number of AIDS patients for the next 10 years. The model assumes that transmission is concentrated among IVDUs and their sex partners according to the current situation. The model estimes that by the year 2002, the number of HIV positives will reach 2, 891, AIDS cumulative cases to 1, 124, out of which 776 will have died of the disease ; if we include oral drug users who also have experienced intravenous drug use, HIV positives will be 3, 304, AIDS cases 1, 285, death 887; if unsurveyed IVDUs are included, HIV positives can be estimated to be 4, 129, AIDS cases 1, 606, death 1, 109; with increasing knowledge about AIDS, if persons at risk stop their risk behaviour are doubled, HIV positives will be 2, 496, AIDS cases 1, 024, death 714. these conclusions indicate that prevention efforts among male IVDUs and their female sex partners must be appropriately directed.


Projecting the Minimum Size of HIV Infection and AIDS Epidemic in China
Tao Jian1, Shinsuke Morio2, Kenji Soda3, and Hideaki Nakayama2 At present, intravenous drug users (IVDUs) comprise the largest risk group to develop acquired immunodefeciency syndrome (AIDS) in China , and their sex partners seem the second largest risk group.
It is necessary to understand long-term trends in the spread of human immunodeficience virus (HIV) among IVDUs and their sex partners and the trends about AIDS cases development for disease prevention and control.
The compartment model was used to project the number of HIV infectious individuals and the number of AIDS patients for the next 10 years.
The model assumes that transmission is concentrated among IVDUs and their sex partners according to the current situation.
The model estimes that by the year 2002, the number of HIV positives will reach 2,891, AIDS cumulative cases to 1,124, out of which 776 will have died of the disease ; if we include oral drug users who also have experienced intravenous drug use, HIV positives will be 3,304, AIDS cases 1,285, death 887; if unsurveyed IVDUs are included, HIV positives can be estimated to be 4,129, AIDS cases 1,606, death 1,109; with increasing knowledge about AIDS, if persons at risk stop their risk behaviour are doubled, HIV positives will be 2,496, AIDS cases 1,024, death 714. these conclusions indicate that prevention efforts among male IVDUs and their female sex partners must be appropriately directed. acquired immunodefeciency syndrome, HIV, mathematical mobel, substance abuse, intravenous The first AIDS case was recognized in the United States in 19811), and the etiolgical agent, the HIV was discovered in 19832). In China, serological screening of HIV antibody was begun in 19843), and AIDS surveillance was begun in 19854). The first indigenous HIV seropositive person was detected in 1986, who had had an experience of using foreign blood product5). The first AIDS case was diagnosed on January 19876). At present, 80% of HIV positive persons in China are concentrated in Yunnan Province, the border area between China and Myanmar7). According to the investigation conducted by Yunnan Provincial Health and Anti-epidemic Center of China, by the end of 1990, a total of 17,021 people had been surveyed and 429 HIV positives were detected (include 2 AIDS cases). 347 out of 1,292 HIV positives are IVDUs (27%), and 2 out of 68 are their sex partners(3%). 48 out of 4,088 HIV carriers are oral drug users who admitted to an intravenous drug use habit after further confirmation. 331 of 372 indigenous HIV positives belong to IVDUs and their sex partners7). Projecting the size of HIV infection and AIDS epidemic are of major importance for future health care prevention and disease control.
Based on the fact that IVDUs and their sex partners are the main high risk group for contraction of AIDS in China, a compartment model was designed to project HIV positives and AIDS cases in IVDUs and their sex partners for the next 10 year. In this study, we take no account of the type of HIV, because there has been almost no report of HIV-2 epidemics in Asian countries, and because serological data in China were those of HIV-13).

METHODS
Several authors have used compartment models for projecting the HIV/AIDS epidemics in different population and situations8-11). This compartment model is aimed at the assumption that intravenous drug abuse is the main source of HIV transmission in China ( Table  Table 1 Figure 1). The exact year that HIV was introduced into the IVDU population in China is unknown, but we will assume that it is 1988, for reasons presented in the discussion. This is an open compartment model because it allows for immigration and emigration. 1. The model 1.1. Estimation of susceptible and infected IVDUs Susceptible individuals at risk in year t are expressed as S1(t), which includes susceptible individuals from the year before [S,(t-1)] and people who became IVDUs this year (ns). In the year from t-1 to t, some susceptible males become HIV infected with the probability r1 because of sharing needles with HIV infected IVDUs and leave the population as a result of detoxification, death or other reasons with the proba-bility dr, so the expression will be : Infected individuals in year t [I1(t)] consist of infected individuals from the year before [I1(t-1)] and newly infected individuals in the year between t-1 and t who were susceptible the year before [S1(t-1)] and become infected with the probability r1. Furthermore, persons who developed AIDS symptoms 1 year before [ (t-1)] are excluded. The expression is Estimation of susceptible and infected persons among sex partners of IVDUs. We assumed that every IVDU has one sex partner, so newly susceptible females at risk in year t [S2(t)] are equal to male IVDUs who were HIV positives one year before [I1(t-1)], that is: Because of unprotected vaginal intercouse between year t-1 and year t, females get infected in year t from male IVDUs who were HIV positives in year t-1 with the probability r2. The expression is

Estimation of AIDS incidence in year t [ (t)]
Both male IVDUs and their female sex partners who get infected will develop AIDS gradually. Newly infected persons from year t-1 to year t will develop AIDS according to the Weibull distribution with the scale parameter (B0) and the shape parameter (B1). Between year I and year n, AIDS incidence in year t [ (t)] can be expressed as : where (t) is the Weibull incubation period distribution.
1.5. Estimation of the number of deaths due to AIDS AIDS patients will die in first year after disease at a rate of v1, in the second year v2..., in the fifth year v5. After the fifth year, the rates are neglected since they get smaller and more unstable. Death in year t (t= 1 to n) after onset d(t) can be expressed as: The exact probability is unknown. According to Zhao's report7), seroprevalence of anti-HIV was 26 .86% (347/1292) by the end of 1990. Furthermore, if we assume HIV entered the male IVDU population in 1988 and that 350 males become IVDUs every year, the probability 0.2 seems appropriate. With this probability, the projected number of HIV seropositives is approximately equal to that of Zhao's report. This group consists of IVDUs Who undergo detoxification (male), condom users (female), and individuals who die of non-AIDS causes (male, female), as well as those who migrate abroad. No study shows this proportion up to now, so we assume that 5% will exit before becoming infected for the time being.

Scale parameter of Weibull distribution of AIDS incubation period for AIDS (B0)
Many authors have estimated the mean incubation period and/or incubation time distribution for AIDS13-18) Some authors express it directly as mean incubation period, while others use scale and sharp parameters to express the incubation time period indirectly. Here, we choose Kuo JM's parameters18). They used data from a cohort study of 177 homosexual or bisexual men enrolled in Los Angeles between 1982 and 1983 to estimate the incubation period distribution of AIDS.     Table 3 presents the projected cumulative numbers of HIV positives in male IVDUs and their female sex partners, the incidence of AIDS cases, and deaths associated with AIDS up to the year 2002. We haveTable 6. Estimated number of HIV positives, AIDS cases and deaths due to AI assumed that HIV infection began in 1988, and that 350 males enter the IVDU population every year. By the year 2002, the number of male and female HIV positives will be 2,444 and 477 respectively, cumulative AIDS cases will be 1,124, and 776 of them will have died of AIDS ( Figure 2, line a).

Inclusion of oral drug users and their sex partners
As mentioned above, a survey of 39 indigenous oral drug users out of 48 HIV positives revealed that almost all of them had experienced intravenous drug use at least once. In the border area between China and Myanmar, indigenous oral drug use seems rather popular. Yunnan Provincial Anti-epidemic Center examined 4,088 oral drug users in 1989 and 1990, 48 of them were HIV positives (1.17%)7). Up to now, no evidence shows that HIV can be transmitted orally, so we think it is reasonable to include this group in the IVDUs group. Thereby, we can assume that 400 individuals enter the IVDUs population every year. The result of the same model is, by the year 2002, the number of male and female HIV positives will be 2,793 and 511 respectively, cumulative AIDS cases will be 1,285, and 887 of them will have died of AIDS (Table  4 ; Figure 2, line b).

Inclusion of IVDUs who were not surveyed
The real numbers of this population is impossible to know. If we assume, however that 20% were missed in the survey, the newly susceptible IVDUs will reach 500 per annum. In this case, by the year 2002, the number of male and female HIV positives will be 3,491 and 638 respectively, cumulative AIDS cases will be 1,606, and 1,109 of them will have died of AIDS (Table 5 ; Figure  2, line c).

Doubling susceptible individuals who give up risk behavior
At first, we assume that 5% of the population at risk will exit before becomimg infected for the time being. With the expanding general knowledge of AIDS, if we double the current number of people at risk who stop their risk behaviour (dr=0.1), by the year 2002, the number of male and female HIV positives will be 2,108 and 388 respectively, cumulative AIDS cases will be 1,024, and 714 of them will have died of AIDS (Table  6 ; Figure 2, Line d).
Because this estimation only considers HIV positives among IVDUs and their sex partners in Yunnan Province of China who represent about 80% of HIV positives throughout the country by the end of 1990, we consider our estimation to be the minimum size of HIV infection in China.

DISCUSSION
The exact year that HIV was transmitted to IVDUs in China is unknown.
1988 is assumed to be the first year that HIV entered IVDUs.
1989 is the first year that HIV positives were detected in male IVDUs7). Up to 1990, there were 347 known HIV positives but no AIDS case among IVDUs. With the knowledge of AIDS incubation period distribution, we believe that the phenomenon would occur only in the first 3 years, because the Weibull distribution indicates that after 3 years of HIV infection, the AIDS incidence rate will reach 3% (with an incubation period of 8 years). Although a few IVDUs may have been infected before the year 1988, it seems to have little effect on our projection result.
According to the survey in China7), there are 48 HIV positives among 4,086 oral drug users (1.17%). We did not include this population in our model independently. As further investigation of 39 out of these 48 HIV positives confirmed, most of them had experienced intravenous drug use. Thus, we considered them to be IVDUs in spite of their oral drag use habit which appears to have no relationship to HIV transmission.
The probability that a male IVDU is HIV positive (r1=0.2) is derived from the anti-HIV seropositive rate (26.86%) in 19907). With this probability, the seropositive rate will rise from 20% at the beginning to 70% in the year 2002. Jarlais  No consideration has been given to how many sex partners one IVDU has, because N is determined.
If one HIV positive person has 2 sex partners, the probability r2 will be reduced by half. In this case, the infectivity that one HIV positive person contributed is dependent on p and N, but not on the number of sex partners.
In an estimation of HIV transmission rate among female sex partners of male IVDUs in New York, USA, Fordyce et al. 12) assumed that only 18,615 sexually active womem in New York select a male IVDUs as a sex partner, nevertheless, the number of male IVDUs in same city is 169,400. This implied that most male IVDUs in New York are homosexual or abstinent, which is obviously different from the situation in China.
It is impossible to use paramaters such as scale and shape from China since these parameters require longterm observation.
The parameters we used are derived from studies conducted in the United States. Some parameters may not be suitable in China. For example, the death probability for patients with AIDS also appears to be too high. These factors do have an effect on our estimate.
The proportion of susceptible persons who leave the at risk population before getting infected (dr) may deflect the development of disease from its original trend. In a survey on knowledge and attitudes towards AIDS among administrative and medical staff and policemen in Yunnan Province of China 23), 208 persons were interviewed.
Out of these subjects, 88.9% showed concern about an indigenous AIDS epidemic, but 56.7% did not know the difference between an HIV infected person and an AIDS patient. This indicates that it is necessary to inform local residents about