Determination of the spread of HIV from the AIDS incidence history

The relation between the incidence of HIV in the general population, the number of AIDS cases, and the incubation period for the disease is examined. The number of AIDS cases can be expressed in terms of a convolution integral over the incubation period distribution and the temporal history of HIV incidence. In order to determine the level of HIV incidence it is necessary to invert the convolution. In this manner, it is possible to determine the spread of HIV up to the present time from knowledge of the AIDS incidence history and the incubation period. We describe the inversion of the convolution in terms of a Laplace transform technique that is applicable for any given incubation period distribution. Substantial simplifications in the technique are found in the case of an Erlang distribution for the probability density. The spread of HIV infections in the United States is charted through 1988 using AIDS incidence data that are corrected for both the revised AIDS case definition and reporting time delays. The results are consistent with current estimates of the HIV incidence in the United States and show no evidence of saturation in the rate of new infections. Indeed, the rate of new infections still appears to be climbing as of that date. While the technique is unable to predict the future course of the epidemic, it may provide a useful benchmark for comparison with mathematical models of the epidemic. The techniques are conceptually applicable to diseases other than AIDS.     

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 modeled time-varying density function for the incubation period of AIDS

Building on the Weibull distribution, we develop a modeled time-varying density function of the incubation time between exposure to HIV infection and full-blown AIDS. This approach leads to a series of cohort-specific density functions that take into account the increasing impact of new therapies such as zidovudine (AZT). The resulting modeled density functions are studied in detail, particularly with regard to their modes and medians. The mode is sensitive to changes in the period incubation time distribution, with even a possibility of a bimodal distribution for certain combinations of the parameters that determine the rate at which the period median incubation time changes. An important substantive result is that when a period median incubation period slowly increases to some leveling off value, say m(x _c ), then it is surprisingly early on that cohorts of infected individuals have a median incubation period very close to that ultimate value m(x _c ).     

On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS)

In this study, we investigate systematically the role played by the reproductive number (the number of secondary infections generated by an infectious individual in a population of susceptibles) on single group populations models of the spread of HIV/AIDS. Our results for a single group model show that if R 1, the disease will die out, and strongly suggest that if R > 1 the disease will persist regardless of initial conditions. Our extensive (but incomplete) mathematical analysis and the numerical simulations of various research groups support the conclusion that the reproductive number R is a global bifurcation parameter. The bifurcation that takes place as R is varied is a transcritical bifurcation; in other words, when R crosses 1 there is a global transfer of stability from the infection-free state to the endemic equilibrium, and vice versa. These results do not depend on the distribution of times spent in the infectious categories (the survivorship functions). Furthermore, by keeping all the key statistics fixed, we can compare two extremes: exponential survivorship versus piecewise constant survivorship (individuals remain infectious for a fixed length of time). By choosing some realistic parameters we can see (at least in these cases) that the reproductive numbers corresponding to these two extreme cases do not differ significantly whenever the two distributions have the same mean. At any rate a formula is provided that allows us to estimate the role played by the survivorship function (and hence the incubation period) in the global dynamics of HIV. These results support the conclusion that single population models of this type are robust and hence are good building blocks for the construction of multiple group models. Our understanding of the dynamics of HIV in the context of mathematical models for multiple groups is critical to our understanding of the dynamics of HIV in a highly heterogeneous population.     

Modeling the AIDS epidemic in Mexico City

To study the future course of the AIDS epidemic in Mexico City, we use an open compartmental model to forecast new AIDS cases among homosexual and bisexual males and among heterosexual males and females. For each group three compartments are defined: uninfected persons, infected but asymptomatic persons, and persons diagnosed with AIDS. It is assumed that the AIDS epidemic will follow the propagation of infectious disease model, where spread of infection is proportional to the product of the number of healthy persons and the number of infected ones. The compartmental model is represented by a system of nonlinear differential equations describing the rate of change in the number of persons in each compartment. The impact of preventive measures is explored by decreasing the probability of HIV transmission, which is one of the model parameters representing behavioral patterns. By April 1989, 491 AIDS cases had been reported in Mexico City and classified as sexually related. Our model predicts that the AIDS incidence will continue to rise in Mexico City for the foreseeable future and will spread among the heterosexual population. Decreasing the transmission probability by 10% in all groups (through education programs) will result in a decrease of 18.1% in the number of accumulated cases over a 5-year period. A 20% decrease would prevent more than 31% of the cases. We conclude that mathematical models can be valuable in predicting the spread of the AIDS epidemic and the impact of behavioral change on its spread.     

HIV and HCV： from Co-infection to Epidemiology, Transmission, Pathogenesis, and Treatment

Human immunodeficiency virus (HIV) is the infectious agent causing acquired immu-nodeficiency syndrome (AIDS),a deadliest scourge of human society. Hepatitis C virus (HCV) is a major causative agent of chronic liver disease and infects an estimated 170 million people worldwide,resulting in a serious public health burden. Due to shared routes of transmission,co-infection with HIV and HCV has become common among individuals who had high risks of blood exposures. Among hemophiliacs the co-infection rate accounts for 85%; while among injection drug users (IDU) the rate can be as high as 90%. HIV can accelerate the progression of HCV-related liver disease,particularly when immunodeficiency has developed. Although the effect of HCV on HIV infection is controversial,most studies showed an increase in mortality due to liver disease. HCV may act as a direct cofactor to fasten the progression of AIDS and decrease the tolerance of highly active antiretroviral therapy (HARRT). Conversely,HAART-related hepatotoxicity may enhance the progression of liver fibrosis. Due to above complications,co-infection with HCV and HIV-1 has imposed a critical challenge in the management of these patients. In this review,we focus on the epidemiology and transmission of HIV and HCV,the impact of the two viruses on each other,and their treatment.     

HIV and HCV: from Co-infection to epidemiology, transmission, pathogenesis, and treatment

Human immunodeficiency virus (HIV) is the infectious agent causing acquired immunodeficiency syndrome (AIDS), a deadliest scourge of human society. Hepatitis C virus (HCV) is a major causative agent of chronic liver disease and infects an estimated 170 million people worldwide, resulting in a serious public health burden. Due to shared routes of transmission, co-infection with HIV and HCV has become common among individuals who had high risks of blood exposures. Among hemophiliacs the co-infection rate accounts for 85%; while among injection drug users (IDU) the rate can be as high as 90%. HIV can accelerate the progression of HCV-related liver disease, particularly when immunodeficiency has developed. Although the effect of HCV on HIV infection is controversial, most studies showed an increase in mortality due to liver disease. HCV may act as a direct cofactor to fasten the progression of AIDS and decrease the tolerance of highly active antiretroviral therapy (HARRT). Conversely, HAART-related hepatotoxicity may enhance the progression of liver fibrosis. Due to above complications, co-infection with HCV and HIV-1 has imposed a critical challenge in the management of these patients. In this review, we focus on the epidemiology and transmission of HIV and HCV, the impact of the two viruses on each other, and their treatment.      

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.     

吸毒人群中HIV/HCV核酸和抗体关系的分析

研究了高危人群中HIV/HCV核酸和抗体的关系。从新疆地区采集吸毒人群的血样,并对其进行HIV/ HCV核酸和抗体的检测。320例吸毒人员血浆样品中HCV抗体阳性为80．3％,HIV抗体阳性率为41．9％,HIV 和HCV共感染者为38．3％。HIV RNA与抗体的总符合率为98．8%,在186例HIV抗体阴性样品中可能有2例 为HIV感染的窗口期。HCV抗体和HCV RNA的阳性符合率为92．6％,HCV RNA与HCV抗体的总符合率为 90．0％,以上结果说明在HIV／HCV的高流行区进行HIV／HCV核酸检测可以发现病毒感染的窗口期,而约8% 的HCV抗体阳性样品为病毒核酸阴性,也值得进一步研究。     

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.     

HIV(+)/AIDS并发肺结核与单纯肺结核患者临床对照分析

提高对HIV(+)/AIDS并发肺结核临床表现的认识。方法:选取1998年以来我院收治的HIV(+)/AIDS并发肺结核的病例共47例为观察组(A组),及同期住院的HIV(-)单纯肺结核病例50例为对照组(B组)进行回顾性对照分析。结果:(1)A组发烧和体重下降较B组更常见,而咳嗽和咯血较B组少见;(2)A组痰抗酸杆菌阳性率显著低于B组;(3)A组结核杆菌培养阳性率显著低于B组,而耐多药结核(MDR-TB)所占比率显著高于B组;(4)肺结核的X线表现为弥漫性浸润或粟粒性阴影的,A组多于B组,而A组影像学空洞率显著低于B组;(5)A组合并肺外结核较B组多见,A组淋巴系统较B组常发生结核病变,A组全身血液播散性结核病的发病率明显高于B组;(6)PPD结核菌素反应阳性率A组显著低于B组,A组PPD阳性率与外周CD4+T淋巴细胞数相关。结论:HIV(+)/AIDS患者并发肺结核临床表现不典型。     

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.     

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.     

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.     

Monitoring the trend of the transmission rate of vertically acquired HIV infection: a simple method applied to Italian data.

The objective of this study was to develop and validate a method for estimating and monitoring over time the transmission rate of vertically acquired HIV infection at the population level. We estimated the annual number of children born to HIV-infected women in Italy in 1991-1994 by multiplying the seroprevalence rates, provided by Anonymous Unlinked HIV Serosurveys among Italian Newborns, by the annual number of births, provided by the Italian National Institute of Statistics. The number of HIV-infected children was estimated by applying a simplified back-calculation method to the incident cases of vertically acquired AIDS reported to the AIDS surveillance registry, using seven different estimates of the distribution of the incubation period identified through a literature search. The annual vertical transmission rates were estimated by dividing the estimated number of children with vertically acquired HIV infection by the estimated number of births to an HIV-infected mother. Depending on the chosen distribution of the incubation period, the estimated transmission rate for the four-year period ranges from 0.10 to 0.30. Five of the seven incubation distributions provided a rate falling within the very narrow interval 0.18-0.20. The method provided estimates of vertical transmission rates consistent with those of longitudinal studies performed in European countries. The method presented here could be useful for monitoring the impact of interventions aimed at reducing HIV vertical transmission rate.     

Three-stage stochastic epidemic model: an application to AIDS.

A three-stage stochastic epidemic model extending the so-called classical epidemic process to one that includes time-dependent transition probabilities is described, and a solution to the appropriate set of forward differential-difference equations is given. When an individual can move from being a susceptible to one infected with the HIV virus to one diagnosed as having AIDS, we can use this general model to describe an AIDS epidemic process. We obtain expressions for the mean and variance of the number of AIDS cases for some special cases. By comparing these with actual data, it is suggested that, for some categories of cases (in particular, children), this model might be a plausible model to describe the underlying mechanism of the AIDS epidemic.     

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.     

A different disease: HIV/AIDS and health care for women in poverty

The goal of this paper is to demonstrate that HIV/AIDS for poor women is a qualitatively different disease than the one first defined in the United States in the 1980s. HIV/AIDS for poor women is not a new disease; it is only another life-threatening condition which parallels serious health problems already experienced by these populations. A time-honored and broad continuum of disease and death for poor women is linked to such factors as poverty, self-medication, infant morbidity, infant mortality and cervical cancer. The programmatic responses to HIV/AIDS in poor women have been grafted onto existing services established by and for homosexual men or onto the obstetrical-gynecological and prenatal systems already in place. Furthermore, the primary socio-psychological mechanisms of denial and dependency that characterize poor women are far more salient than notions of risk-taking or sexual lifestyles. These conclusions lead to somber predictions for the course of the epidemic and the prognosis for treatment and care for poor women with HIV.     

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.