The relationship between decreased infectiousness as a result of treatment and increases in unsafe sex on changes in HIV incidence are explored further in Fig. 7. This figure shows for each of the 1000 simulations the level of change in HIV incidence (split into six roughly equal strata) plotted by a decrease in infectiousness and increases in unsafe sex. Increases in HIV incidence are shown as black squares (> 20% increase) and black dots (0–20% increase), whereas decreases in HIV incidence are plotted in shades of grey. This figure illustrates how any reduction in HIV incidence through decreased infectiousness as a result of treatment could be counterbalanced by increasing levels of unsafe sex. Decreases in infectiousness of two-, five- and 10-fold would be counterbalanced by increases in unsafe sex of approximately 40, 60 and 70%, respectively. It also appears that if the effect of treatment on decreasing infectiousness is modest and less than a twofold reduction, then an increase in HIV incidence would be expected with any increases in levels of unsafe sex.
The results presented here are broadly consistent with those of a previously published model , which suggested that a 10-fold decrease in infectiousness as a result of treatment could be counterbalanced by only a 10% increase in the levels of unsafe sex. This increase in the levels of unsafe sex required to counterbalance an average 10-fold decrease in infectiousness is, however, rather lower than the increase of approximately 70% suggested by our model. This discrepancy may result from differences in the models used, with Blower et al.  modelling the transmission of drug-resistant strains, which was not allowed for in our model, but not splitting HIV disease natural history into separate states based on CD4 cell counts and AIDS, as was the case in our model. However, the most likely explanation for this discrepancy appears to result from the differing way in which the uptake of effective combination antiretroviral treatment was modelled. Our models essentially assume that treatment uptake, and increases in the levels in unsafe sex, were instantaneous and coincident, giving a clear picture of the trade-off between the two in terms of changes in HIV incidence. In the models of Blower et al. , increases in the levels of unsafe sex were assumed to be instantaneous, whereas the uptake of antiretroviral treatments was modelled to increase gradually over time to a maximum of between 50 and 90% of all HIV-infected men. The 10% increase in the levels in unsafe sex needed in the models of Blower et al.  to overcome a 10-fold decrease in infectiousness corresponds to the first year after the availability of treatments, in which only a relatively small proportion all HIV-infected men were modelled to be receiving treatment.
The likely effect of antiretroviral treatments in reducing infectiousness is uncertain. Probably the best data regarding the relationship between HIV viral load and risk of HIV transmission comes from the cohort study of Quinn et al. , and suggests that a 1 log lower viral load corresponded to a 2.45 reduction in the rate of HIV transmission. Effective combination antiretroviral treatment produces an average 2–3 log reduction in HIV viral load , at least over a 12 month period. This suggests that the effect of treatment is likely to be in the range of a two- to 10-fold decrease in infectiousness. In Australia there are some data to suggest that there have been some increases in the levels of unsafe sex since the advent of effective combination antiretroviral treatments. The prevalence of unprotected anal intercourse with casual partners reported by homosexual men in Sydney and Melbourne has increased by between 20 and 50% since 1996 [5–7,17], although data on other cities in Australia suggest very little or no increase over this time period [18–20]. These increases in the levels of unsafe sex are of the order of magnitude that our models indicate would counterbalance any decrease in HIV incidence if treatments had a fivefold reduction in infectiousness. There has also been an increase in the reported diagnoses of gonorrhoea in New South Wales since 1998, including an increase in rectal gonococcal isolates in men, from 72 in 1997 to 158 in 1998 . These gonorrhoea rates corroborate the increases in unsafe sex reported in behavioural surveys, but are also a further cause for concern. Concurrent infection with a sexually transmissible infection (STI) is known to increase the risk of HIV transmission . The role of increased rates of STI on new HIV transmissions is not included in our model, suggesting that the increases in unsafe sex required to counterbalance the effect of treatments may be lower than our models indicate. Taken together, these data suggest that new HIV infections in homosexual men may be on the verge of increasing in Australia, and in particular in Sydney, in the near future.
The available epidemiological data show that new HIV diagnoses among men who reported homosexual contact or no known exposure to HIV have declined slowly in Australia from 764 in 1995 to 466 in 1998 and 500 in 1999, whereas newly acquired HIV diagnoses (defined as new HIV diagnoses with a previous negative HIV test within 12 months or a concurrent seroconversion illness) have also decreased slightly from 200 in 1995 to 135 in 1998 and 134 in 1999. Although these epidemiological surveillance data should be interpreted cautiously, and in particular should not be cited as good evidence of declining HIV incidence in Australia since 1995, they are at least some evidence that any increases in unsafe sex in homosexual men in Australia have not yet resulted in substantial increases in HIV incidence.
The mathematical model developed in this paper is, by necessity, a simplified model of HIV transmissions among homosexual men, and in particular assumes that trends in new HIV infections can be modelled on the basis of average rates of HIV diagnosis, antiretroviral treatment, and unsafe sex in homosexual men. The model aimed to capture two essential features of HIV transmission that were thought to be particularly important regarding the impact of combination antiretroviral treatments and the levels of unsafe sex on HIV incidence. First, that an uninfected homosexual man would be less likely to have unsafe sex with a man diagnosed with HIV than with a man undiagnosed (regardless of true HIV status). Second, that for an HIV-infected homosexual man to become less infectious as a result of combination antiretroviral treatment he must be diagnosed with HIV infection, and also receive treatment. There are, however, two important limitations in the model. First, that increased rates of unsafe sex could lead to increased rates of STI, which carry an independent increased risk of HIV transmission. The models could therefore underestimate the negative impact of increased unsafe sex on HIV incidence. Second, the model assumes that men take up antiretroviral treatment independent of their HIV viral load. If men with higher viral loads are more likely to adopt treatment, the models may underestimate the effect of treatments on reducing HIV transmissions, particularly if there is some threshold level of HIV viral load below which HIV transmission is virtually impossible .
The models presented in this paper suggest that reduced HIV transmissions through apparently large decreases in infectiousness as a result of combination antiretroviral treatment could be counterbalanced by much more modest increases in the levels of unsafe sex. Although the available epidemiological data provide little evidence of increasing HIV incidence in Australia, increased rates of unprotected anal intercourse with casual partners among homosexual men, linked with increased rates of rectal gonorrhoea, suggest that an increase in HIV incidence among homosexual men in Australia, and particularly in Sydney, is a real possibility. The fact that there are data suggesting recent increases in HIV incidence among homosexual men in San Francisco, USA  and Ontario, Canada  lend support to this possibility. The need for the continued adoption of safe sexual practices among homosexual men in the era of effective combination antiretroviral treatments needs to be reinforced.
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Appendix 1. HIV transmission equations
X = number of uninfected homosexual men
Y1 = number of infected men with CD4 cell count > 500 cells/μl
Y2 = number of infected men with CD4 cell count between 200 and 500 cells/μl
Y3 = number of infected men with CD4 cell count < 200 cells/μl
Y4 = number of infected men living with AIDS
NX = number of new uninfected homosexual men each year
1/g = mean duration of sexual activity in homosexual men
pdi = proportion diagnosed with HIV in group Yi (i = 1,2,3,4)
pti = proportion of those diagnosed treated in group Yi
1/li = mean survival in group Yi (to group Yi + 1).
ftsi = effect of treatment on increasing average survival in group Yi
fdu = effect of diagnosis on reducing rate of unsafe sex between uninfected men and HIV-diagnosed men
ftu = increased levels of unsafe sex
ftinf = average decrease in infectiousness as a result of treatments, allowing for non-compliance with treatment in some men
c = average annual number of HIV-infected partners with whom uninfected men have unprotected anal intercourse (the level of unsafe sex). This includes inadvertent unsafe sex through incorrect condom use or condom failure.
b = average probability of HIV transmission occurring with that partner (infectiousness)
EQUATION where EQUATION where EQUATION where EQUATION where EQUATION where EQUATION
Values, and simulated uncertainties, of parameters are given in Table 1, or are described in the text. The value of the product b×c (= 0.8) was chosen to give approximately 400 infections per year in the absence of treatment or any increase in unsafe sex.