On transient effects in the HIV/AIDS epidemic

During the initially exponential spread of the human immunodeficiency virus (HIV—the causative agent of AIDS) the growth rate of the number of AIDS cases decreases from plus infinity to the growth rate of HIV infections. A sensitivity analysis shows that for all reasonable values of the parameters of the HIV epidemic (incubation period, initial doubling time, etc.) the effect of this positive transient becomes negligible when the annual number of AIDS cases reaches a few dozen. Necessary and sufficient conditions are given for the growth rate of the number of AIDS cases to be monotonically decreasing during the positive transient. A mildly pathological density function for the incubation period of AIDS provides an example of a growth rate of AIDS that does not decrease monotonically, even though HIV is spreading exponentially. A negative transient occurs when the growth rate of HIV begins to decrease. In this context a somewhat surprising result emerges under the assumption that the growth rate of HIV is non-increasing: the growth rate of AIDS is at all times larger than the growth rate of HIV. A logistic HIV epidemic illustrates this result, and implications for the growth of the HIV epidemic in the United States and Europe are discussed. In particular, it is shown that the positive transient must have passed by 1982 in the United States and by 1986 or 1987 for the five European countries with the largest caseloads.     

Epidemiological and statistical aspects of the AIDS epidemic: introduction

In 1988, a government working party studied estimates of incidence and prevalence of numbers of acquired immunodeficiency syndrome (AIDS) cases. They investigated a series of epidemiological, statistical and mathematical problems associated with predicting trends in incidences of AIDS. This paper introduces a series of papers that give a fuller and more technical exposition of the appendixes of that working party report. The papers provide a brief background to the current state of knowledge on the epidemiology of the infection and the disease; a deterministic model for human immunodeficiency virus (HIV) transmission in the male homosexual community in England and Wales is introduced. Back-projection methods are studied in two papers, following the distribution of the incubation period of the disease. The concept of minimum size of the epidemic is introduced. Mathematical functions to describe the spread of HIV infection are refined by using past trends in the incidence of AIDS to estimate values for some parameters. Survival times for AIDS patients from the point of diagnosis are considered and evidence for changes in male homosexual sexual behaviour is studied; lag-time from the point of diagnosis to the report of the case is also examined. There is a comparative analysis of the AIDS epidemic in various European countries. The incubation period of HIV in patients with haemophilia A and B infections and the problems associated with making predictions for different at-risk groups or small subgroups based on geographical area are discussed. Reasons for fluctuation between the number of reported cases from month to month are provided.     

Estimation of the incidence of HIV infection

The aim of the method of 'back projection' is to provide estimates of the number of new infections with the human immunodeficiency virus (HIV) as a function of time, by using the numbers of diagnoses of the acquired immune deficiency syndrome (AIDS) together with information on the distribution of the incubation period between infection and diagnosis. Here, the method is investigated with particular reference to cases of HIV infection and AIDS in the United Kingdom.     

Assessing the effects of drug misuse on HIV/AIDS prevalence

Drug misuse (injecting drug users-IDU) has been recognized to have a significant effect on the spread of HIV/AIDS epidemic. A deterministic model to assess the contribution of drug misuse and sex in the spread of HIV/AIDS is investigated. The threshold parameters of the model are determined and stabilities are analysed. Analysis of the reproduction number has shown that increase in drug misuse results in an increase in HIV infections. Furthermore, numerical simulations of the model show that drug misuse enhances HIV transmission and progression to AIDS. Thus, in a population with intravenous drug users, advocating for safe sex alone will not be enough to control the HIV/AIDS epidemic.     

Through a glass, darkly: data and uncertainty in the AIDS debate

The HIV/AIDS epidemic is the greatest threat to development in much of Africa. It is already the main cause of death in many countries, especially those in Southern Africa. However there is an absence of solid data on the scale and scope of the disease and how it is evolving. In this article we discuss the data on the epidemic – where it comes from and how it is presented. We note the limitations of the use of antenatal clinic surveys – which provide the bulk of our information.
We then turn to the evidence of impact. The paper shows that the long incubation period between infection and illness means that it takes time for HIV infections to turn into AIDS cases, and AIDS cases to translate into deaths with all the consequences of orphaning, poverty and changing population structures. Furthermore it means that once the HIV prevalence has peaked, AIDS impact will take years to work through – this epidemic is a 'long-wave' event.
The paper is premised on the view that HIV causes AIDS and AIDS causes death. It notes that insufficient and/or unreliable data have allowed leaderships to deny the scope and scale of the problem and that this is unacceptable. However it is incumbent on all to accept the moral responsibility for and the moral consequences of their work, and this includes those who gather, interpret and use the data.     

Statistical modelling of the AIDS epidemic for forecasting health care needs

The objective of this paper is to develop statistical methods for estimating current and future numbers of individuals in different stages of the natural history of the human immunodeficiency (AIDS) virus infection and to evaluate the impact of therapeutic advances on these numbers. The approach is to extend the method of back-calculation to allow for a multistage model of natural history and to permit the hazard functions of progression from one stage to the next to depend on calendar time. Quasi-likelihood estimates of key quantities for evaluating health care needs can be obtained through iteratively reweighted least squares under weakly parametric models for the infection rate. An approach is proposed for incorporating into the analysis independent estimates of human immunodeficiency virus (HIV) prevalence obtained from epidemiologic surveys. The methods are applied to the AIDS epidemic in the United States. Short-term projections are given of both AIDS incidence and the numbers of HIV-infected AIDS-free individuals with CD4 cell depletion. The impact of therapeutic advances on these numbers is evaluated using a change-point hazard model. A number of important sources of uncertainty must be considered when interpreting the results, including uncertainties in the specified hazard functions of disease progression, in the parametric model for the infection rate, in the AIDS incidence data, in the efficacy of treatment, and in the proportions of HIV-infected individuals receiving treatment.     

The AIDS epidemic: profiles of development

As all HIV-infected subjects become virus carriers, the epidemic will not attain a "steady state" until the number of deletions (from death and other factors) equals or outnumbers that of new cases, i.e. each HIV-infected subject transmits the infection to only one subject in the course of his lifespan. A full stop of all spreading of HIV will most likely require worldwide vaccination. By simple mathematical models it is shown that calculation of the number of HIV infected individuals based on the number of AIDS cases is very uncertain. The ratio of HIV infected subjects to AIDS cases is greatly influenced by the length of the incubation period and the case doubling time. Since the growth of the epidemic is exponential, all efforts to control the epidemic should be continuously intensified as single measures will only retard the rate of spread. The effect of saturation/deletion on the number of susceptible individuals is insignificant in this phase of the epidemic, except in small groups at special risk.     

A mathematical model of comprehensive test-and-treat services and HIV incidence among men who have sex with men in the United States

Background

Early diagnosis and treatment of HIV infection and suppression of viral load are potentially powerful interventions for reducing HIV incidence. A test-and-treat strategy may have long-term effects on the epidemic among urban men who have sex with men (MSM) in the United States and may achieve the 5-year goals of the 2010 National AIDS Strategy that include: 1) lowering to 25% the annual number of new infections, 2) reducing by 30% the HIV transmission rate, 3) increasing to 90% the proportion of persons living with HIV infection who know their HIV status, 4) increasing to 85% the proportion of newly diagnosed patients linked to clinical care, and 5) increasing by 20% the proportion of HIV-infected MSM with an undetectable HIV RNA viral load.

Methods and Findings

We constructed a dynamic compartmental model among MSM in an urban population (based on New York City) that projects new HIV infections over time. We compared the cumulative number of HIV infections in 20 years, assuming current annual testing rate and treatment practices, with new infections after improvements in the annual HIV testing rate, notification of test results, linkage to care, initiation of antiretroviral therapy (ART) and viral load suppression. We also assessed whether five of the national HIV prevention goals could be met by the year 2015. Over a 20-year period, improvements in test-and-treat practice decreased the cumulative number of new infections by a predicted 39.3% to 69.1% in the urban population based on New York City. Institution of intermediate improvements in services would be predicted to meet at least four of the five goals of the National HIV/AIDS Strategy by the 2015 target.

Conclusions

Improving the five components of a test-and-treat strategy could substantially reduce HIV incidence among urban MSM, and meet most of the five goals of the National HIV/AIDS Strategy.     

Trends in incidence of AIDS associated with transfusion of blood and blood products in Europe and the United States, 1985-93.

OBJECTIVE--To quantify patterns and trends in incidence of AIDS associated with transfusion of blood and its products in 14 European countries and the United States. DESIGN--Data were derived from the World Health Organisation''s European non-aggregate AIDS dataset and, for the United States, from the Centers for Disease Control AIDS public information dataset. Rates were standardised by using the world standard populations and adjusted for reporting delays in each country. SUBJECTS--Cases of AIDS in patients with haemophilia and recipients of transfusions. RESULTS--Overall, between 1985 and 1993 almost 6000 cases of AIDS associated with transfusions were registered in the 14 European countries considered and over 8000 in the United States between 1985 and 1992. Most European countries had annual age adjusted rates lower than 0.5 per million children aged 12 or less and between 1 and 2 per million adults. The United States had rates around 1 per million children and 5 per million adults in the most recent period. For children, the highest rates were generally reached in 1985-7, whereas in adults the highest rates were in the late 1980s. France had the highest overall incidence of AIDS related to transfusion in Europe (3.3 per million). Romania had a major epidemic in children (over 30 cases per million children in 1988-90). Incidence rates of AIDS associated with transfusion were still increasing in some southern European countries in the early 1990s. CONCLUSIONS--Apart from in France and Romania it is clear that rates of bloodborne AIDS in European countries are lower than those registered in the United States.     

Is the United States country zero for the First-World AIDS epidemic?

The incidence for AIDS per hundred thousand is several times higher in the United States than in the rest of the First World. Earlier work by Thompson (1984, 1989a, b, 1990, 1998) indicated that a relatively small proportion of gay males frequenting the bathhouses in the United States, drove AIDS over the epidemiological threshold in the U.S. It is shown that the rate of growth of AIDS is essentially the same for the United States and other First-World countries. An argument is advanced, based on WHO AIDS data, to the effect that it is contact with the pool of infectives in the United States that drives the epidemic in other First-World Countries.     

Predictions of the AIDS epidemic in the U.K.: the use of the back projection method

Back projection methods are used to predict the yearly number of new AIDS diagnoses and the number of new HIV infections, to the end of 1992. The AIDS, but not the HIV, predictions are insensitive to the choice of incubation period distribution. A wide range of predictions is consistent with the AIDS diagnoses in years up to 1987, but limited ancillary information on the relative rates of new HIV infection in 1984 to 1987 can be used to narrow this range. The range of prediction based on AIDS reports to the end of 1988 is lower and narrower than the range based on reports to the end of 1987. The number of new AIDS cases in 1992 appears likely to fall in the range 1000-3000.     

A review of vaccines for HIV prevention

HIV/AIDS has become the most devastating pandemic in recorded history. It has killed 40 million people in the last 20 years and the World Health Organisation estimated that at least 14,000 new infections occurred daily in 2001. There will be up to 100 million new infections in the next 10 years (for current updates, visit http://www.unaids.org/epidemic_update/). Most HIV infections occur in the developing world, and the adverse social and economic impact of the HIV/AIDS pandemic, particularly in the developing world, is unprecedented. Highly active antiretroviral therapy (HAART) has had significant effects on HIV/AIDS in the developed world. The drugs have acted to prolong survival, reduce the viral load, and to alleviate suffering. However, the incidence of side effects and resistance is high and the drugs are unaffordable and unavailable in the developing world. HAART regimens are difficult to comply with. Public health efforts to modify the behaviour, attitude and culture that accelerate the spread of HIV/AIDS have had only modest success. There is urgent need for a prophylactic and/or therapeutic HIV vaccine. This is a review of the obstacles and current trends in HIV vaccine development.     

Understanding the scourge of HIV/AIDS in sub-Saharan Africa

Sub-Saharan Africa is the part of the world that has been hit hardest by the HIV epidemic. To fight the spread of HIV in the continent, it is necessary to know and effectively address the factors that drive the spread of HIV. The purpose of this article is to review the factors associated with the spread of the HIV epidemic in sub-Saharan Africa and to propose 6 essential activities, which we refer to by the acronym "ESCAPER," to help curb the spread of HIV/AIDS in Africa.     

HIV/AIDS epidemic in Eastern Europe: Recent developments in the Russian Federation and Ukraine among women

Background: The Russian Federation and the Ukraine are among the Eastern European countries with the fastest growing number of cases of HIV. According to data from the Joint United Nations Program on HIV/AIDS, nearly 90% of newly reported HIV diagnoses in Eastern Europe in 2006 were from the Russian Federation (66%) and the Ukraine (21%). A growing number of women are infected with HIV. The impact of gender on HIV/AIDS is an important factor in understanding the development and evolution of the HIV/AIDS epidemic in Eastern Europe.Objective: The aim of this study was to assess the importance of integrating gender consideration into the creation of HIV programs and to examine the effect of gender on HIV/AIDS.Methods: Reported HIV/AIDS cases from the official epidemiological register of the Ukrainian Centre for AIDS Prevention alongside data from the Russian Federal AIDS Center were analyzed. Joint United Nations Program on HIV/AIDS country fact sheets were reviewed and analyzed, and this information was supplemented with published HIV prevalence and sexually transmitted disease case reporting information, unpublished reports, and expert evaluations.Results: Of the newly registered cases of HIV, the proportion of women rose from 13.0% in 1995 to 44.0% in 2006 in the Russian Federation, and from 37.2% in 1995 to 41.9% in 2006 in the Ukraine. There has also been a considerable increase in mother-to-child transmission of HIV since 1995. Between 1987 and 1994, the proportion of children among the people newly infected with HIV in the Ukraine was 2.2%; in 2006 it was 17.6%. In 2006, 16,078 new HIV cases were registered in the Ukraine and 39,652 new HIV cases in the Russian Federation. Large increases in the number of HIV-infected women were reported from both countries.Conclusions: The data examined in this study suggest subregional differences in the magnitude of the HIV/AIDS epidemic in the Russian Federation and the Ukraine and the importance of the impact of gender on the rapid spread of the HIV/AIDS epidemic among women and women of child-bearing age. To protect women from HIV infection, it is important to find ways to empower them by implementing policies and specific prevention measures that increase their access to knowledge about HIV/AIDS; the empowerment of women is vital to reversing the HIV/AIDS epidemic.     

Guidelines for the Control of Human Immunodeficiency Virus Infection in Adolescents

Although adolescents account for only 0.4% of reported cases of the acquired immunodeficiency syndrome (AIDS) in the United States, they are sexually active and, therefore, at risk of acquiring human immunodeficiency virus (HIV) infection. To address issues of HIV control in adolescents, we developed guidelines that emphasize education and medical care and deemphasize antibody testing. For adolescents known to be infected with HIV, we recommend no restrictions on access to educational or treatment programs except when their health providers recommend such restrictions to protect them from exposure to opportunistic infections. For adolescents of unknown antibody status with a possible previous exposure to HIV, we recommend that as long as the incidence of HIV infection and clinical AIDS remains low, there should be no restrictions on residential placements and no routine antibody testing.     

Epidemic human immunodeficiency virus (HIV) infection among intravenous drug users (IVDU)

Human immunodeficiency virus (HIV) infection is epidemic among intravenous drug users (IVDU), particularly in the northeastern United States. IVDU are playing a critical role in the spread of HIV by infecting their heterosexual partners and children, as well as their needle-sharing partners. The epidemiology of HIV infection among IVDU is reviewed here, including a compilation of seroprevalence data. Relevant determinants of the future spread of HIV among IVDU are discussed, including the major risk factors for HIV seropositivity, the modes of HIV transmission, and aspects of the natural history of HIV infection in IVDU. The public health policy implications of these issues include the need for education of adolescents and the general public about the risks of drug injection and heterosexual intercourse with IVDU, as well as motivation of IVDU to stop injecting, never share injection paraphernalia, or, at least, clean needles effectively.     

Estimation of HIV infection and incubation via state space models

By using the state space model (Kalman filter model) of the HIV epidemic, in this paper we have developed a general Bayesian procedure to estimate simultaneously the HIV infection distribution, the HIV incubation distribution, the numbers of susceptible people, infective people and AIDS cases. The basic approach is to use the Gibbs sampling method combined with the weighted bootstrap method. We have applied this method to the San Francisco AIDS incidence data from January 1981 to December 1992. The results show clearly that both the probability density function of the HIV infection and the probability density function of the HIV incubation are curves with two peaks. The results of the HIV infection distribution are clearly consistent with the finding by Tan et al. [W.Y. Tan, S.C. Tang, S.R. Lee, Estimation of HIV seroconversion and effects of age in San Francisco homosexual populations, J. Appl. Stat. 25 (1998) 85]. The results of HIV incubation distribution seem to confirm the staged model used by Satten and Longini [G. Satten, I. Longini, Markov chain with measurement error: estimating the 'true' course of marker of the progression of human immunodeficiency virus disease, Appl. Stat. 45 (1996) 275].     

The HIV epidemic: medical and social challenges

The sudden appearance, rapid spread, and devastating clinical impact of HIV infection in Africa, Europe and North America has created a medical problem unprecedented in the modern era. HIV is sexually transmitted, afflicts sexual and racial minorities in developed countries, and appears likely to be fatal and incurable in a majority of infected people. Its epidemiology (transmission and natural history) and clinical manifestations have been well described, but treatment of HIV remains minimally effective, creating only a short respite from progressive deterioration. In the absence of effective vaccination, HIV will continue to spread, abetted by a long period of asymptomatic carriage during which carriers are infectious. It has spread internationally to most undeveloped countries aided by fear and ignorance. The problem will resist simple technological solutions and adversely impact the lives of tens of millions of people in these areas over the next several decades. In developed countries HIV will strain medical resources and kill several million people before the end of the century. Despite the tremendous problems created by the AIDS epidemic, it has driven a remarkable expansion of virologic and immunologic understanding which promises to ultimately lead to control of not only AIDS, but a variety of other serious diseases. The following reviews of pivotal issues in AIDS research document this progress.     

Allocating HIV prevention funds in the United States: recommendations from an optimization model

The Centers for Disease Control and Prevention (CDC) had an annual budget of approximately $327 million to fund health departments and community-based organizations for core HIV testing and prevention programs domestically between 2001 and 2006. Annual HIV incidence has been relatively stable since the year 2000 and was estimated at 48,600 cases in 2006 and 48,100 in 2009. Using estimates on HIV incidence, prevalence, prevention program costs and benefits, and current spending, we created an HIV resource allocation model that can generate a mathematically optimal allocation of the Division of HIV/AIDS Prevention's extramural budget for HIV testing, and counseling and education programs. The model's data inputs and methods were reviewed by subject matter experts internal and external to the CDC via an extensive validation process. The model projects the HIV epidemic for the United States under different allocation strategies under a fixed budget. Our objective is to support national HIV prevention planning efforts and inform the decision-making process for HIV resource allocation. Model results can be summarized into three main recommendations. First, more funds should be allocated to testing and these should further target men who have sex with men and injecting drug users. Second, counseling and education interventions ought to provide a greater focus on HIV positive persons who are aware of their status. And lastly, interventions should target those at high risk for transmitting or acquiring HIV, rather than lower-risk members of the general population. The main conclusions of the HIV resource allocation model have played a role in the introduction of new programs and provide valuable guidance to target resources and improve the impact of HIV prevention efforts in the United States.