Mathematical models are useful tools for guiding public health policy in many diseases, including HIV. The parameters used to calibrate such models are usually not known with sufficient accuracy to allow the models to make definitive, quantitative predictions and their chief value lies in producing general predictions and rules of thumb that can be used to guide policy. Blower and colleagues  recently provided several such general predictions, one being the assertion that ART rollout in Africa will not drive an epidemic of drug-resistant HIV infection (transmission of resistance remaining below the 5% Who Health Organization surveillance threshold) and, consequently, that transmission of resistance will be a relatively minor source of resistance compared to that arising de novo in individual patients. We are not convinced by this assertion and argue that transmission of resistance does become highly important once the model is calibrated in a manner more appropriate to resource-poor African settings.
The model used to generate these predictions is apparently the one originally developed for a San Francisco cohort of homosexual men . We believe this model severely underestimates the transmission of HIV resistance in Africa through making three critical assumptions. Firstly, it assumes people infected with drug-resistant HIV will also transmit sensitive forms (apparently at a rate of 50% in their calculations). This may be appropriate if a person is superinfected with both sensitive and resistant forms (the model lacks an explicit class for such ‘mixed’ infections) and is not drug treated, but we consider it distinctly unlikely that a person infected by resistant HIV and currently being drug treated, would transmit a significant proportion of sensitive infections, especially because both nucleoside reverse transcriptase inhibitors (NRTI) and non-NRTI pass into the semen compartment and can also select resistance there . Secondly, they assume that drug-resistant HIV rapidly reverts to drug sensitivity once drug pressure is removed. This may be appropriate where resistance has arisen de novo, and sensitive forms are archived, but its seems unlikely that this will occur in new infections acquired as drug-resistant forms, certainly not at the rapid rate used in this model (an average time to reversion of 6 weeks); recent data suggest resistance remains stable on a timescale of years rather than weeks [4,5]. Thirdly, they assume that if a resistant infection reverts to sensitivity, it must undergo the full process of re-acquiring resistance if re-treated, despite the presence of archived resistant forms . Their first assumption slows the predicted spread of resistance because people infected with resistant infections transmit sensitive infections 50% of the time. The second assumption reduces its subsequent impact because a newly-acquired resistant infection will rapidly revert to sensitivity before that person has had the chance to be counselled, diagnosed and enter ART. The third assumption underestimates the rate at which these sensitive ‘revertants’ re-acquire resistance. These assumptions severely, and we think artificially, curtail the spread of resistant forms. We have recalibrated their model to reflect this, and the impact is shown on Fig. 1 where the Blower et al. approach (Scenario 2) is compared to ours (Scenarios 3 and 4). Our calculations suggest than an epidemic of drug resistance may result from ART mass deployment, the transmission of resistance approaching the World Health Organization surveillance threshold of 5% within a year, and becoming the major source of resistance within 5 years. Unsurprisingly, given the different underlying assumptions, the differences between the scenarios shown in Fig. 1 are consistent over a wide range of parameter values.
The model is simplified in several important respects. It lack an explicit class for mixed superinfections (i.e., people infected with independently-acquired resistant and sensitive strains), does not distinguish between patients who have developed resistance de novo (and hence have archived sensitive viruses) and those who were initially infected with resistant strain (and may have no archived sensitive forms), implicitly assumes that a single mutation can encode resistance to all drugs in the ART mixture, ignores heterogeneity in behaviour, notably the variation in the frequency of sexual contacts, and so on. More sophisticated models explicitly directed at primarily heterosexual transmission in an African context, are urgently needed to effectively inform policy. In the absence of these models, the one developed by Blower and colleagues is currently the best available, and simple models have the advantage of providing a relatively transparent method of guiding public health policy. We have shown that selecting parameter inputs more appropriate to an African setting can reverse two of their central conclusions. The assertion that an epidemic of drug resistant HIV will not accompany mass deployment of ART appears to be overly optimistic and it appears equally plausible that transmission of drug resistant HIV may well have a rapid and substantial impact on disease epidemiology. We strongly assert that this is a more realistic scenario and that measures to control the spread of resistance must be a priority in ART rollout. As ever, the best policy will be to hope for the best (Scenario 2), while planning for the worst (Scenario 3).
The original equations given in  contained misprints that are corrected here, i.e., (i) subscripts for β in the third and fourth terms of their equation 6 have been corrected, (ii) the terms in the numerator of their equation 7 now contain the factors (1–p); this is necessary because if a proportion p of transmissions from people with resistant infections are of drug-sensitive forms (as defined by Blower et al.), then the proportion transmitted as resistant must be 1–p. A prerequisite for using models to make policy recommendations is transparency, that the model be clearly defined and the underlying parameter values are clearly stated. The latter was not the case in  so we have tried to identify and use their previous values where possible, and used our own estimates, taken as representative of Sub-Saharan Africa, elsewhere. Here we explicitly state the values of the underlying parameters allowing readers to properly evaluate our approach. In addition we have made the model freely available at http://pcwww.liv.ac.uk/hastings/HIV_models for users to directly enter their own choice of parameters.
The parameter values used to calibrate the scenarios were as follows. The rate at which resistant infections revert to sensitive after cessation of drugs is taken as 6 weeks in Scenarios 1 and 2 ( page 7), never occurs in Scenario 3, and occurs at 10% per year in Scenario 4. The probability of a resistant infection undergoing treatment but transmitting a sensitive infection is 0.5 in Scenarios 1 and 2 ( page 654), and 0 in Scenarios 3 and 4. The probability of an untreated resistant infection transmitting a sensitive infection is 0.5 in Scenarios 1 and 2 ( page 654), 0 in Scenario 3 and 0.05 in Scenario 4. All other parameter values were identical in all Scenarios except where stated. The rate at which treated sensitive infections develop resistance is 45% per year ( page 348), but only 10% per year in Scenario 4. The rate at which HIV infected patients commence treatment is 20% per year ( page page 347). The rate at which patients terminate treatment is 12% per year ( page page 346). The rate of new sexual contacts is four per year. The probability that an HIV infected person will infect an uninfected partner during the course of their relationship is 5% except in a treated patient with sensitive virus infection whose chance is zero. A parameter describing the efficacy of ART appears redundant in this context because efficacy is also expressed in terms of altered death rate and infectivity, so is given a value of 1. The rate at which people enter the sexually active at-risk population is assumed to equal overall death rate, thus keeping the size of the at-risk population constant. The background non-HIV-related death rate is 5% per year, so people entering the at-risk population can expect to live on average a further 20 years. Note that ‘death’ is used in its broadest sense of people leaving the at-risk population; physical death is one possibility, two uninfected people entering an exclusive monogamous relationship is another, and so on. HIV-related death rate is 20% per year except for treated sensitive infections when it is zero.
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