Data for this review were identified by searches of Medline, Current Contents, and references from relevant articles; numerous articles were identified through searches of the extensive files of the authors. Search terms were “antiretroviral therapy”, “prediction models”, “mathematical model”, “HIV transmission dynamics”, “epidemic control strategies”. English language papers were reviewed.
ReviewCould widespread use of combination antiretroviral therapy eradicate HIV epidemics?
Introduction
Current combination antiretroviral therapies (ARV) increase survival time of HIV-infected individuals, but do not lead to viral eradication within individuals and hence do not cure. These therapies are based upon three or more anti-HIV medications that typically combine a protease inhibitor (PI), or a non-nucleoside reverse transcriptase inhibitor (nnRTI), with at least two nucleoside reverse transcriptase inhibitors (nRTI). However, to eradicate an epidemic it is not necessary to cure any individuals, but simply to reduce the transmission rate to below a certain threshold value that is specified by the basic reproduction number R0; where R0 is the average number of new infections that one infectious case generates during his/her infectious lifetime in a community of susceptible individuals.1 R0 can be reduced either through behavioural or medical interventions. If R0 is reduced to below one then epidemic eradication occurs, because each infected individual (on average) will generate less than one new infection. Here, we have quantified the effect of ARV on R0 (for both drug-sensitive and drug-resistant infections) and we have answered the question, “Could widespread usage of ARV eradicate HIV epidemics?”
We addressed this question by deriving an analytical expression for R0 for HIV in a community where ARV is available and where both drug-sensitive and drug-resistant strains are co-circulating (R0ARV). We used clinical, virological, and behavioural data from the gay community in San Francisco to estimate numerical values for R0ARV under three different assumptions: ARV plus decreases in risky sex, ARV with no change in risky sex, and ARV plus increases in risky sex. For each assumption, we then identified the key factors that substantially increase (or decrease) the value of R0ARV. Finally, we calculated the probability that a high usage of ARV could eradicate the current high prevalence (30%) HIV epidemic in San Francisco, and we also determined the time dynamics of eradication.
The concept of R0 was first proposed by Macdonald in the 1950s2 and applied to malaria. The numerical value of R0 indicates the severity of the epidemic; the greater the value of R0 (above one) the greater the severity of the epidemic. By deriving an expression for R0, and setting the value equal to one, the specific levels of treatment, vaccination, or reductions in risky behaviour that are necessary to achieve epidemic eradication can be determined for any infectious disease.3, 4, 5, 6 The expression for R0 based upon the transmission dynamics of sexually transmitted HIV in an untreated community is simple and is dependent upon only three parameters: β (the probability that sexual transmission of HIV occurs during a sexual partnership), c (the average number of new sexual partners per unit time), and D (the average duration of infectiousness).1 However, the situation is more complex if one needs to compute a reproduction number for HIV where ARV is available, since ARV leads: directly to the emergence of drug-resistant strains during treatment,7, 8, 9, 10 and indirectly to the transmission of drug-resistant strains.7, 9, 10, 11. Under these circumstances it is necessary to calculate a reproduction number based upon the transmission potential of treated and untreated individuals infected with either drug-sensitive and/or drug-resistant strains of HIV.
Blower et al12, 13 have previously defined a mathematical model of an HIV epidemic that includes the effects of ARV on the transmission dynamics of both drug-sensitive and ARV-resistant strains. The model is specified by five ordinary differential equations;12 a web version can be run at http://www.biomath.ucla.edu/faculty/sblower. Previously, this model has been used to assess the effect of ARV (over a 10 year period) on the incidence of HIV,12 the AIDS death rate,12 and also to predict the transmission and prevalence of drug-resistant strains.13 Here, we have used this model to derive an analytical expression for R0ARV; where we define R0ARV as the average number of new HIV-infections that one infected individual will generate during his/her lifetime in a community where ARV is available and where both drug-sensitive and ARV-resistant strains are co-circulating. Hence, R0ARV functions as a single outcome measure that provides a summary estimate of the overall epidemic-level impact of ARV. We calculate the values of R0ARV that are generated due to a variety of different treatment rates; hence we assessed whether ARV has an overall beneficial or detrimental impact at the epidemiclevel.
Section snippets
Methods
We first calculated an analytical expression for R0ARV. To calculate R0ARV we used the next-generation operator methodology.14 We set the right-hand side of the model differential equations (given in reference 12) to zero and made a standard change of variables to find the disease-free equilibrium in terms of the forces of infection of the resistant (λR) and sensitive (λS) strains. The problem was then reduced to a system of two nonlinear algebraic equations given in equation 1.
(1) λS=F (λS, λR
Results
The analytical expression for R0ARV is very complex and hence is not shown.
Discussion
Our findings have four significant clinical and public health implications. First, increasing the percentage of cases receiving ARV would substantially reduce the severity of the HIV epidemic (ie, the value of R0ARV), even in the presence of high levels of ARV resistance and increases in risky behaviour. However, ARV should not be used as an epidemic control strategy to improve public health unless increasing usage rates would also produce clinical benefits for the treated individuals. Second,
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