Mathematical Study of a Staged-Progression HIV Model with Imperfect Vaccine

A staged-progression HIV model is formulated and used to investigate the potential impact of an imperfect vaccine. The vaccine is assumed to have several desirable characteristics such as protecting against infection, causing bypass of the primary infection stage, and offering a disease-altering therapeutic effect (so that the vaccine induces reversal from the full blown AIDS stage to the asymptomatic stage). The model, which incorporates HIV transmission by individuals in the AIDS stage, is rigorously analyzed to gain insight into its qualitative features. Using a comparison theorem, the model with mass action incidence is shown to have a globally-asymptotically stable disease-free equilibrium whenever a certain threshold, known as the vaccination reproduction number, is less than unity. Furthermore, the model with mass action incidence has a unique endemic equilibrium whenever this threshold exceeds unity. Using the Li-Muldowney techniques for a reduced version of the mass action model, this endemic equilibrium is shown to be globally-asymptotically stable, under certain parameter restrictions. The epidemiological implications of these results are that an imperfect vaccine can eliminate HIV in a given community if it can reduce the reproduction number to a value less than unity, but the disease will persist otherwise. Furthermore, a future HIV vaccine that induces the bypass of primary infection amongst vaccinated individuals (who become infected) would decrease HIV prevalence, whereas a vaccine with therapeutic effect could have a positive or negative effect at the community level.     

Bayesian Estimation of the Time‐Varying Sensitivity of a Diagnostic Test with Application to Mother‐to‐Child Transmission of HIV

Summary We present a Bayesian model to estimate the time‐varying sensitivity of a diagnostic assay when the assay is given repeatedly over time, disease status is changing, and the gold standard is only partially observed. The model relies on parametric assumptions for the distribution of the latent time of disease onset and the time‐varying sensitivity. Additionally, we illustrate the incorporation of historical data for constructing prior distributions. We apply the new methods to data collected in a study of mother‐to‐child transmission of HIV and include a covariate for sensitivity to assess whether two different assays have different sensitivity profiles.     

The Role of HIV Replicative Fitness in Perinatal Transmission of HIV

Perinatal transmission of Human immunodeficiency virus(HIV),also called mother-to-child transmission(MTCT),accounts for 90% of infections in infants worldwide and occurs in 30%-45% of children born to untreated HIV-1 infected mothers.Among HIV-1 infected mothers,some viruses are transmitted from mothers to their infants while others are not.The relationship between virologic properties and the pathogenesis caused by HIV-1 remains unclear.Previous studies have demonstrated that one obvious source of selectiv...     

人免疫缺陷病毒母婴传播研究进展

随着抗逆转录病毒药物和抗蛋白酶抑制剂的联合应用,人免疫缺陷病毒(HIV)的垂直传播率可降至2%以下。尽管如此,据估计全世界每天仍有1600名婴儿感染HIV。因此,研究HIV母婴传播中的危险因素和干预措施,仍然是极为重要的防治垂直传播的课题。我们就HIV母婴传播的最新进展做简要综述。     

Modeling the synergy between HSV-2 and HIV and potential impact of HSV-2 therapy

Mounting evidence indicates that genital HSV-2 infection may increase susceptibility to HIV infection and that co-infection may increase infectiousness. Accordingly, antiviral treatment of people with HSV-2 may mitigate the incidence of HIV in populations where both pathogens occur. To better understand the epidemiological synergy between HIV and HSV-2, we formulate a deterministic compartmental model that describes the transmission dynamics of these pathogens. Unlike earlier models, ours incorporates gender and heterogeneous mixing between activity groups. We derive explicit expressions for the reproduction numbers of HSV-2 and HIV, as well as the invasion reproduction numbers via next generation matrices. A qualitative analysis of the system includes the local and global behavior of the model. Simulations reinforce these analytical results and demonstrate epidemiological synergy between HSV-2 and HIV. In particular, numerical results show that HSV-2 favors the invasion of HIV, may dramatically increase the peak as well as reducing the time-to-peak of HIV prevalence, and almost certainly has exacerbated HIV epidemics. The potential population-level impact of HSV-2 on HIV is demonstrated by calculating the fraction of HIV infections attributable to HSV-2 and the difference between HIV prevalence in the presence and absence of HSV-2. The potential impact of treating people with HSV-2 on HIV control is demonstrated by comparing HIV prevalence with and without HSV-2 therapy. Most importantly, we illustrate that the aforementioned aspects of the population dynamics can be significantly influenced by the sexual structure of the population.     

Ethical issues associated with HIV phylogenetics in HIV transmission dynamics research: A review of the literature using the Emanuel Framework

The reduced costs of DNA sequencing and the use of such data for HIV‐1 clinical management and phylogenetic analysis have led to a massive increase of HIV‐1 sequences in the last few years. Phylogenetic analysis has shed light on the origin, spread and characteristics of HIV‐1 epidemics and outbreaks. Phylogenetic analysis is now also being used to advance our knowledge of the drivers of HIV‐1 transmission in order to design effective interventions. However, HIV phylogenetic analysis presents unique ethical challenges, which have not been fully explored. This review presents an analysis of what appear to be key ethical issues in HIV phylogenetics in the hope of stimulating further conceptual and empirical work in this rapidly emerging area. We structure the review using the Emanuel Framework, a systematic, holistic framework, which has been adapted for use in developing countries, which bear the brunt of the HIV‐1 pandemic.     

Repetitive exposures with simian/human immunodeficiency viruses: strategy to study HIV pre-clinical interventions in non-human primates

BACKGROUND: Non-human primate models for human immunodeficiency virus (HIV) infection represent a valuable pre-clinical tool to evaluate interventions (e.g., topical microbicides, vaccines, and chemoprophylaxis) designed to prevent transmission or slow disease progression after infection. Standard transmission models use a single-dose exposure with high, non-physiologic levels of virus to approach 100% infection rates of control animals. These single-exposure models do not represent the circumstances of mucosal HIV transmission in humans and may result in misleading data with regard to intervention efficacy. Therefore, we have developed a repetitive mucosal exposure model using doses of virus that better reflects human exposures. METHODS: The virus used for these evaluations was simian-human immunodeficiency virus [SHIVSF162P3 (R5-using, subtype B HIV-1 envelope)] and the virus dose used (approximately 10(5)-10(6) viral particle equivalents or approximately 10 tissue culture infectious doses per exposure) approximates viral loads observed in the semen during acute HIV-1 infection. Using the repeated mucosal exposure approach, we have evaluated a candidate vaginal microbicide (cellulose acetate phthalate, CAP) given 15 minutes prior to each weekly virus exposure. Pig-tailed macaques were exposed weekly by vaginal inoculations with and without microbicide until systemic viral RNA was detected. RESULTS: Groups of na?ve control monkeys were infected after an average of three to four exposures for the vaginal route of inoculation. Data from the first application of this monkey model to evaluate the topical microbicide CAP suggested that protection from SHIV infection was possible with three of four CAP-treated monkeys remaining uninfected after 12 exposures (P = 0.015). CAP efficacy was markedly improved from 66% in a previous single-dose virus exposure study to 92% in this repeated exposure system. CONCLUSIONS: Our experience with using repetitive virus exposures to study topical microbicides and the findings to date from this study provides a basis to refine monkey models to more closely resemble human exposure during HIV transmission. This model may be highly relevant to pre-clinical evaluation for a variety of therapeutic interventions which is discussed here.     

Estimating the Accuracy of Anal Cytology in the Presence of an Imperfect Reference Standard

Background

The study aim is to estimate sensitivity and specificity of anal cytology for histologic HSIL in analyses adjusted for the imperfect biopsy reference standard.

Methods and Principal Findings

Retrospective cohort study of an anal dysplasia screening program for HIV infected adults. We estimated the prevalence of histologic HSIL by concurrent cytology category and the associated cytology ROC area. Cytology operating characteristics for HSIL were estimated and adjusted for the imperfect reference standard by 3 methodologies. The study cohort included 261 patients with 3 available measures: (1) referral cytology; (2) HRA cytology; and (3) HRA directed biopsy. The prevalence of biopsy HSIL varied according to the concurrent HRA cytology result: 64.5% for HSIL or ASC-H, 12.6% for LSIL, 10.9% for ASCUS, and 6.3% for no abnormality. The cytology ROC area was 0.78. The observed prevalence of HSIL was 37% (referral cytology), 24% (HRA cytology), and 24% (HRA biopsy). Unadjusted estimates of sensitivity and specificity of cytology were 0.66 and 0.90, respectively. Adjusted estimates varied from 0.47–0.89 (sensitivity) and 0.89—1.0 (specificity).

Conclusions

Analysis of a single dataset yields widely different estimates of anal cytology operating characteristics that depend on difficult to verify assumptions regarding the accuracy of the imperfect reference standard.     

Influence of Irradiation on the Risk of Transmission of HIV in Bone Grafts Obtained from Appropriately Screened Donors and Followed by Radiation Sterilization

We studied the effects of radiation (electrons of 6.2 MeV) at different temperatures with respect to the inactivation of the human immunodeficiency virus to determine the radiosensitivity of the virus. Using a mathematical model describing the dependence on radiation dose of the proportion of sterile items in a population of bone allografts contaminated by HIV, and subjected to irradiation, we have commented on and explained the calculation of the sterility assurance level in bone transplantation according to different doses of irradiation at different temperatures. Simultaneous application of heat and radiation increases inactivation of HIV. Given the relative imprecision of viral sensitivity curves and the impossibility of knowing the number of viral particles in a patient at a given moment of the disease, irradiation does not authorize bone transplantation without screening. However, irradiation can be considered as a serious adjuvent to decrease the risk of contamination after screening.     

Estimation of the Timing of Perinatal Transmission of HIV

Knowledge of the timing of perinatal transmission of HIV would be valuable for the determination and evaluation of preventive treatments and would shed light on the mechanism of transmission. Estimation of the distribution of the time of perinatal transmission is difficult, however, because tests of infection status can only be undertaken after birth. DNA and RNA polymerase chain reaction (PCR) assays and HIV culture have been the most commonly used diagnostic tests for perinatal HIV infection. Such tests have high sensitivity and specificity, except when they are given shortly after infection. In this paper we use the time-dependent sensitivity of these diagnostic tests to make nonparametric and semiparametric inferences about the distribution of the time of perinatal HIV transmission as well as the cumulative probability of perinatal transmission. The methods are illustrated with data from a clinical trial conducted by the AIDS Clinical Trials group.     

ROC Curve Analysis in the Presence of Imperfect Reference Standards

The receiver operating characteristic (ROC) curve is an important tool for the evaluation and comparison of predictive models when the outcome is binary. If the class membership of the outcomes is known, ROC can be constructed for a model, and the ROC with greater area under the curve indicates better performance. However in practice, imperfect reference standards often exist, in which class membership of every data point is not fully determined. This situation is especially prevalent in high-throughput biomedical data because obtaining perfect reference standards for all data points is either too costly or technically impractical. To construct ROC curves for these data, the common practice is to either ignore the uncertainties in references or remove data points with high uncertainties. Such approaches may cause bias to the ROC curves and generate misleading results in method evaluation. Here we present a framework to incorporate membership uncertainties into the construction of ROC curve, termed the expected ROC or “eROC” curve. We develop an efficient procedure for the estimation of eROC curve. The advantages of using eROC are demonstrated using simulated and real data.     

一类总人口在变化的HIV/AIDS传播的动力学模型

建立了HIV/AIDS传播的具有常数移民和指数出生的SI型模型,其中易感人群按照有无不良行为被分为两组.分别对具双线性传染率和具标准传染率的模型讨论了其无病平衡点和地方病平衡点的存在性,并就某些重要的特殊情况进行了平衡点和稳定性的分析.     

Modeling the joint epidemics of TB and HIV in a South African township

We present a simple mathematical model with six compartments for the interaction between HIV and TB epidemics. Using data from a township near Cape Town, South Africa, where the prevalence of HIV is above 20% and where the TB notification rate is close to 2,000 per 100,000 per year, we estimate some of the model parameters and study how various control measures might change the course of these epidemics. Condom promotion, increased TB detection and TB preventive therapy have a clear positive effect. The impact of antiretroviral therapy on the incidence of HIV is unclear and depends on the extent to which it reduces sexual transmission. However, our analysis suggests that it will greatly reduce the TB notification rate.     

Mother-to-child transmission of HIV in Botswana: an ethical perspective on mandatory testing

Mother-to-child transmission (MTCT) of HIV represents a particularly dramatic aspect of the HIV epidemic with an estimated 600,000 newborns infected yearly, 90% of them living in sub-Saharan Africa. Since the beginning of the HIV epidemic, an estimated 5.1 million children worldwide have been infected with HIV. MTCT is responsible for 90% of these infections. Two-thirds of the MTCT are believed to occur during pregnancy and delivery, and about one-third through breastfeeding. As the number of women of child bearing age infected with HIV rises, so does the number of infected children. It is apparent that voluntary testing in Botswana has made some valuable inroads in decreasing perinatal HIV transmission, but the statistics showing the increased rate of HIV infection among women 15-24 years of age are not very promising. After reviewing all the pertinent scientific data it is clear that mandatory HIV testing of all pregnant women in conjunction with the implementation of a full package of interventions would save thousands of lives -- mothers, newborns and others who could be infected as a result of these women not being aware of their HIV status. If the protection and preservation of human life is a priority in Botswana, then it is time to allow for mandatory HIV testing of all pregnant women, before it is too late for those who are the most vulnerable. To do less would be medically inappropriate and ethically irresponsible.     

Direct stringency comparison of two macaque models (single-high vs. repeat-low) for mucosal HIV transmission using an identical anti-HIV chemoprophylaxis intervention

BACKGROUND: In our previous work, oral chemoprophylaxis with tenofovir disoproxil fumarate (TDF) provided partial protection in rhesus macaques against repeated low-dose (RL) intrarectal SHIV162p3 exposure. METHODS: Here, we make a direct comparison of these previous findings with data generated using a single high (SH)-dose challenge strategy. RESULTS: All 5 (100%) control macaques were infected after a SH challenge and only three of five (60%) TDF-treated macaques became infected. The remaining two TDF-treated macaques remained virus-negative and were susceptible to virus infection upon re-challenge in the absence of oral TDF. Thus, two of five (40%) TDF-treated macaques were protected by the pre-exposure chemoprophylaxis regimen. By comparison with the RL challenge system, only one of four (25%) of TDF-treated macaques were protected from infection, whereas four of four (100%) control macaques became infected using RL challenges. CONCLUSION: Taken together, these findings indicate that the stringency of the RL challenge model for testing antiretroviral interventions is not lower and possibly greater than that of the SH challenge model.     

传播的人群生态动力学模型

研究了HIV传播的动力学模型,描述了流行性传染病区域的人群传播规律,特别是利用摄动理论对艾滋病的传播动力学非线性方程作了定量、定性的讨论。     

Comparative prevalence of plasma human herpesvirus 8 DNA in sexual contact and intravenous injection routes of HIV transmission

Detection of plasma human herpesvirus (HHV)-8 DNA correlates with antibodies to lytic HHV-8 antigens, being predictive of Kaposi's sarcoma in HIV-infected patients. We show that the prevalence of plasma HHV-8 DNA was 10.6% for HIV infection through sexual contact and 7.1% for HIV infection through intravenous injection. In addition, the prevalence of plasma HHV-8 DNA was significantly associated with male gender (9.4%) and HIV viral load below 1000 copies mL(-1) (12.1%), but not age or CD4 cell count in HIV-infected patients. The study suggested that detection of plasma HHV-8 DNA could be important for monitoring replicating HHV-8 in HIV-infected patients, and may have use as a marker for the diagnosis of HHV-8 infection in blood-borne transmission.     

Mathematical Analysis of the Transmission Dynamics of HIV Syphilis Co-infection in the Presence of Treatment for Syphilis

The re-emergence of syphilis has become a global public health issue, and more persons are getting infected, especially in developing countries. This has also led to an increase in the incidence of human immunodeficiency virus (HIV) infections as some studies have shown in the recent decade. This paper investigates the synergistic interaction between HIV and syphilis using a mathematical model that assesses the impact of syphilis treatment on the dynamics of syphilis and HIV co-infection in a human population where HIV treatment is not readily available or accessible to HIV-infected individuals. In the absence of HIV, the syphilis-only model undergoes the phenomenon of backward bifurcation when the associated reproduction number (\({\mathcal {R}}_{T}\)) is less than unity, due to susceptibility to syphilis reinfection after recovery from a previous infection. The complete syphilis–HIV co-infection model also undergoes the phenomenon of backward bifurcation when the associated effective reproduction number (\({\mathcal {R}}_{C}\)) is less than unity for the same reason as the syphilis-only model. When susceptibility to syphilis reinfection after treatment is insignificant, the disease-free equilibrium of the syphilis-only model is shown to be globally asymptotically stable whenever the associated reproduction number (\({\mathcal {R}}_{T}\)) is less than unity. Sensitivity and uncertainty analysis show that the top three parameters that drive the syphilis infection (with respect to the associated response function, \({\mathcal {R}}_{T}\)) are the contact rate (\(\beta _S\)), modification parameter that accounts for the increased infectiousness of syphilis-infected individuals in the secondary stage of the infection (\(\theta _1\)) and treatment rate for syphilis-only infected individuals in the primary stage of the infection (\(r_1\)). The co-infection model was numerically simulated to investigate the impact of various treatment strategies for primary and secondary syphilis, in both singly and dually infected individuals, on the dynamics of the co-infection of syphilis and HIV. It is observed that if concerted effort is exerted in the treatment of primary and secondary syphilis (in both singly and dually infected individuals), especially with high treatment rates for primary syphilis, this will result in a reduction in the incidence of HIV (and its co-infection with syphilis) in the population.     

Modelling HIV/AIDS in the presence of an HIV testing and screening campaign

Preventing and managing the HIV/AIDS epidemic in South Africa will dominate the next decade and beyond. Reduction of new HIV infections by implementing a comprehensive national HIV prevention programme at a sufficient scale to have real impact remains a priority. In this paper, a deterministic HIV/AIDS model that incorporates condom use, screening through HIV counseling and testing (HCT), regular testing and treatment as control strategies is proposed with the objective of quantifying the effectiveness of HCT in preventing new infections and predicting the long-term dynamics of the epidemic. It is found that a backward bifurcation occurs if the rate of screening is below a certain threshold, suggesting that the classical requirement for the basic reproduction number to be below unity though necessary, is not sufficient for disease control in this case. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number R₀. Numerical simulations are performed and the model is fitted to data on HIV prevalence in South Africa. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long-term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed.