Forecasting the future of HIV epidemics: the impact of antiretroviral therapies & imperfect vaccines.

Mathematical models can be used as health policy tools and predictive tools. Here we review how mathematical models have been used both to predict the consequences of specific epidemic control strategies and to design epidemic control strategies. We review how models have been used to evaluate the potential impact on HIV epidemics of (i) combination antiretroviral therapies (ART) and (ii) imperfect vaccines. In particular, we discuss how models have been used to predict the potential effect of ART on incidence rates, and to predict the evolution of an epidemic of drug-resistant HIV. We also discuss, in detail, how mathematical models have been used to evaluate the potential impact of prophylactic, live-attenuated and therapeutic HIV vaccines. We show how HIV vaccine models can be used to evaluate the epidemic-level impact of vaccine efficacy, waning in vaccine-induced immunity, vaccination coverage level, and changes (increases or decreases) in risky behavior. We also discuss how mathematical models can be used to determine the levels of cross-immunity that vaccines will need to attain if they are to be used to control HIV epidemics in countries where more than one subtype is being transmitted.

Could widespread use of combination antiretroviral therapy eradicate HIV epidemics?

Current combination antiretroviral therapies (ARV) are widely used to treat HIV. However drug-resistant strains of HIV have quickly evolved, and the level of risky behaviour has increased in certain communities. Hence, currently the overall impact that ARV will have on HIV epidemics remains unclear. We have used a mathematical model to predict whether the current therapies: are reducing the severity of HIV epidemics, and could even lead to eradication of a high-prevalence (30%) epidemic. We quantified the epidemic-level impact of ARV on reducing epidemic severity by deriving the basic reproduction number (R(0)(ARV)). R(0)(ARV) specifies the average number of new infections that one HIV case generates during his lifetime when ARV is available and ARV-resistant strains can evolve and be transmitted; if R(0)(ARV) is less than one epidemic eradication is possible. We estimated for the HIV epidemic in the San Francisco gay community (using uncertainty analysis), the present day value of R(0)(ARV), and the probability of epidemic eradication. We assumed a high usage of ARV and three behavioural assumptions: that risky sex would (1) decrease, (2) remain stable, or (3) increase. Our estimated values of R(0)(ARV) (median and interquartile range [IQR]) were: 0.90 (0.85-0.96) if risky sex decreases, 1.0 (0.94-1.05) if risky sex remains stable, and 1.16 (1.05-1.28) if risky sex increases. R(0)(ARV) decreased as the fraction of cases receiving treatment increased. The probability of epidemic eradication is high (p=0.85) if risky sex decreases, moderate (p=0.5) if levels of risky sex remain stable, and low (p=0.13) if risky sex increases. We conclude that ARV can function as an effective HIV-prevention tool, even with high levels of drug resistance and risky sex. Furthermore, even a high-prevalence HIV epidemic could be eradicated using current ARV.

Problems and solutions for the Stop TB partnership.

Recent international efforts for global control of tuberculosis have resulted in a new movement: the Stop TB partnership. One of the operational goals of this movement is based on WHO-determined targets to detect, by 2005, 70% of new smear-positive cases under DOTS, and to successfully treat 85% of these cases. In a paper in the Bulletin of the World Health Organization, Dye and colleagues present data that show the current case-detection rate to be low (only 27%), and that in many areas treatment-success rates are still below the WHO target level. Dye and colleagues predict, by linear extrapolation of these data, that the WHO target of a 70% case detection rate will be achieved by 2013. Here, we discuss why it is unlikely that the WHO global targets for either case detection or treatment success will be reached by 2013, and we also offer some potential solutions.

Amplification dynamics: predicting the effect of HIV on tuberculosis outbreaks.

HIV affects the pathogenesis and the transmission of Mycobacterium tuberculosis. We used a discrete event simulation model to predict the potential impact of HIV on increasing the probability and the expected severity of tuberculosis outbreaks. Our predictions reveal that an HIV epidemic can significantly increase the frequency and severity of tuberculosis outbreaks, but that this amplification effect of HIV on tuberculosis outbreaks is very sensitive to the tuberculosis treatment rate. At moderate or low treatment rates, even a moderate HIV epidemic can cause the average size of tuberculosis outbreaks to almost double in comparison with the expected outbreak size when HIV is absent. However, we determined that the amplification effect of HIV can be substantially reduced if the treatment rate of tuberculosis is very high. We discuss the significant implications of these results for the global control of tuberculosis. Our results also reveal that occasionally a "normal-virulence" strain of M. tuberculosis can be expected to generate a large outbreak. We discuss the implications of these results in understanding the virulence of M. tuberculosis and in the planned elimination of tuberculosis in the United States.

Predicting the unpredictable: transmission of drug-resistant HIV.

We use a mathematical model to understand (from 1996 to 2001) and to predict (from 2001 to 2005) the evolution of the epidemic of drug-resistant HIV in San Francisco. We predict the evolutionary trajectories for 1,000 different drug-resistant strains with each strain having a different fitness relative to a drug-sensitive strain. We calculate that the current prevalence of resistance is high, and predict it will continue to rise. In contrast, we calculate that transmission of resistance is currently low, and predict it will remain low. We show that the epidemic of resistance is being generated mainly by the conversion of drug-sensitive cases to drug-resistant cases, and not by the transmission of resistant strains. We also show that transmission of resistant strains has not increased the overall number of new HIV infections. Our results indicate that transmission of resistant strains is, and will remain, a relatively minor public health problem.

The continuing HIV epidemic among men who have sex with men.

OBJECTIVES: This study characterized the AIDS epidemic among urban men who have sex with men (MSM). METHODS: A probability sample of MSM was obtained in 1997 (n = 2881; 18 years and older) from New York, Los Angeles, Chicago, and San Francisco, and HIV status was determined through self-report and biological measures. RESULTS: HIV prevalence was 17% (95% confidence interval = 15%, 19%) overall, with extremely high levels in African Americans (29%), MSM who used injection drugs (40%), "ultraheavy" noninjection drug users (32%), and less educated men (< high school, 37%). City-level HIV differences were non-significant once these other factors were controlled for. In comparing the present findings with historical data based on public records and modeling, HIV prevalence appears to have declined as a result of high mortality (69%) and stable, but high, incidence rates (1%-2%). CONCLUSIONS: Although the findings suggest that HIV prevalence has declined significantly from the mid-1980s, current levels among urban MSM in the United States approximate those of sub-Saharan countries (e.g., 14%-25%) and are extremely high in many population subsegments. Despite years of progress, the AIDS epidemic continues unabated among subsegments of the MSM community.

Live attenuated HIV vaccines: predicting the tradeoff between efficacy and safety.

The utility of live attenuated vaccines for controlling HIV epidemics is being debated. Live attenuated HIV vaccines (LAHVs) could be extremely effective in protecting against infection with wild-type strains, but may not be completely safe as the attenuated strain could cause AIDS in some vaccinated individuals. We present a theoretical framework for evaluating the consequences of the tradeoff between vaccine efficacy (in terms of preventing new infections with wild-type strains) and safety (in terms of vaccine-induced AIDS deaths). We use our framework to predict, for Zimbabwe and Thailand, the epidemiological impact of 1,000 different (specified by efficacy and safety characteristics) LAHVs. We predict that paradoxically: (i) in Zimbabwe (where transmission is high) LAHVs would significantly decrease the AIDS death rate, but (ii) in Thailand (where transmission is low) exactly the same vaccines (in terms of efficacy and safety characteristics) would increase the AIDS death rate. Our results imply that a threshold transmission rate exists that determines whether any given LAHV has a beneficial or a detrimental impact. We also determine the vaccine perversity point, which is defined in terms of the fraction of vaccinated individuals who progress to AIDS as a result of the vaccine strain. Vaccination with any LAHV that causes more than 5% of vaccinated individuals to progress to AIDS in 25 years would, even 50 years later, lead to perversity (i.e., increase the annual AIDS death rate) in Thailand; these same vaccines would lead to decreases in the annual AIDS death rate in Zimbabwe.

Early therapy for latent tuberculosis infection.

The risk of developing active tuberculosis is highest within the first 2 years of infection. Therefore, an intervention that targets persons with recent infection, such as identifying contacts of active cases, could be particularly effective as an epidemic control measure. A mathematical model of a tuberculosis epidemic is formulated and used to evaluate the strategy of targeting therapy to persons with recently acquired latent tuberculosis infection. The model is used to quantify the effectiveness of therapy for early latent tuberculosis infection in reducing the prevalence of active tuberculosis. The model is also used to demonstrate how effective therapy for early latent tuberculosis infection has to be to eliminate tuberculosis, when used in conjunction with therapy for active tuberculosis. Analysis of the model suggests that programs such as contact investigations, which identify and treat persons recently infected with Mycobacterium tuberculosis, may have a substantial effect on controlling tuberculosis epidemics.

Potential impact of tuberculosis vaccines as epidemic control agents.

We use 2 simple mathematical models (one a preexposure vaccine model and the other a postexposure vaccine model) to provide general insight into the effects of vaccination on tuberculosis epidemics. We discuss how these models can be used as health policy tools: to identify which vaccines are "equivalent," to design control strategies, and to predict the epidemiological impact of different vaccination strategies. Our results show that even moderately effective vaccines could have a significant effect on reducing tuberculosis epidemics if they can be coupled with moderate to high treatment rates. We suggest that both preexposure and postexposure tuberculosis vaccines can be used to help eliminate tuberculosis in developing countries. In developed countries, only a preexposure vaccine (used in combination with a high level of treatment) would be necessary to eliminate tuberculosis.

Impact of antivirals and emergence of drug resistance: HSV-2 epidemic control.

Genital herpes, caused by herpes simplex virus type-2 (HSV-2), affects more people world-wide than any other sexually transmitted disease (STD). Antivirals are effective in decreasing the duration of symptoms and in reducing viral shedding; however, currently antiviral usage is extremely low. Increased usage of antivirals would have a beneficial epidemic-level effect (due to the decreased transmission of drug-sensitive strains) as well as potentially a detrimental epidemic-level effect (if drug-resistant strains emerge and are transmitted). Previously, we have developed a mathematical model that we have used to predict (with a degree of uncertainty) the beneficial and the potential detrimental epidemic-level effects of increased antiviral usage. Here, we use our model to make further predictions about the impact of increasing antiviral usage. We calculate the effect, on individual patients, of antiviral usage in terms of: (1) the decrease in the average number of infectious days per year and (2) an individual's lifetime probability of acquiring permanent drug resistance. We also use our model: (1) to determine the probability of eliminating herpes by antivirals and (2) to quantify the effect of increasing antiviral usage on decreasing HSV-2 prevalence. Our results show that theoretically it would be possible to eliminate herpes epidemics by using a drug that does not cure.

A tale of two futures: HIV and antiretroviral therapy in San Francisco.

The effect of antiretroviral therapy (ART) in preventing human immunodeficiency virus (HIV) infections and averting acquired immunodeficiency syndrome (AIDS) deaths in the San Francisco gay community over the next 10 years was predicted. A transmission model was coupled with a statistical approach that enabled inclusion of a high degree of uncertainty in the potential treatment effects of ART (in terms of infectivity and survival), increase in risky behavior, and rate of emergence of drug resistance. Increasing the usage of ART in San Francisco would decrease the AIDS death rate and could substantially reduce the incidence rate.

Global elimination of trachoma: how frequently should we administer mass chemotherapy?

The World Health Organization has recommended repeat mass drug administration as part of their global initiative to eliminate blinding trachoma by the year 2020. The efficacy of repeat treatment will be tested empirically, but the results will not be available for many years, and recommendations for the necessary frequency of treatment are needed immediately. We have developed a mathematical model that uses available epidemiological data from a variety of countries. We recommend, based on our analysis, that in areas where trachoma is moderately prevalent (<35% in children), it should be treated annually, but hyperendemic areas (>50% in children), it should be treated biannually.

Quantifying the intrinsic transmission dynamics of tuberculosis.

Previously we have formulated transmission models of untreated tuberculosis epidemics (Blower et al., Nature, Medicine 1 (1995), 815-821); in this paper, we present time-dependent uncertainty and sensitivity analyses in order to quantitatively understand the transmission dynamics of tuberculosis epidemics in the absence of treatment. The time-dependent uncertainty analysis enabled us to evaluate the variability in the epidemiological outcome variables of the model during the progression of a tuberculosis epidemic. Calculated values (from the uncertainty analysis) for the disease incidence, disease prevalence, and mortality rates were approximately consistent with historical data. The time-dependent sensitivity analysis revealed that only a few of the model's input parameters significantly affected the severity of a tuberculosis epidemic; these parameters were the disease reactivation rate, the fraction of infected individuals who develop tuberculosis soon after infection, the number of individuals that an infectious individual infects per year, the disease death rate, and the population recruitment rate. Our analysis demonstrates that it is possible to improve our understanding of the behavior of tuberculosis epidemics by applying time-dependent uncertainty and sensitivity analysis to a transmission model.

Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework.

The high prevalence of tuberculosis in developing countries and the recent resurgence of tuberculosis in many developed countries suggests that current control strategies are suboptimal. The increase in drug-resistant cases exacerbates the control problems. Currently employed epidemic control strategies are not devised on the basis of a theoretical understanding of the transmission dynamics of Mycobacterium tuberculosis. We describe and discuss a theoretical framework based upon mathematical transmission models that can be used for understanding, predicting, and controlling tuberculosis epidemics. We illustrate how the theoretical framework can be used to predict the temporal dynamics of the emergence of drug resistance, to predict the epidemiological consequences of epidemic control strategies in developing and developed countries, and to design epidemic control strategies.