Global Stability of Equilibria in a Two-Sex HPV Vaccination Model

Human papillomavirus (HPV) is the primary cause of cervical carcinoma and its precursor lesions, and is associated with a variety of other cancers and diseases. A prophylactic quadrivalent vaccine against oncogenic HPV 16/18 and warts-causing genital HPV 6/11 types is currently available in several countries. Licensure of a bivalent vaccine against oncogenic HPV 16/18 is expected in the near future. This paper presents a two-sex, deterministic model for assessing the potential impact of a prophylactic HPV vaccine with several properties. The model is based on the susceptible-infective-removed (SIR) compartmental structure. Important epidemiological thresholds such as the basic and effective reproduction numbers and a measure of vaccine impact are derived. We find that if the effective reproduction number is greater than unity, there is a locally unstable infection-free equilibrium and a unique, globally asymptotically stable endemic equilibrium. If the effective reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable, and HPV will be eliminated.     

HIV Testing and Tolerance to Gender Based Violence: A Cross-Sectional Study in Zambia

This paper explores the effect of social relations and gender-based conflicts on the uptake of HIV testing in the South and Central provinces of Zambia. We conducted a community-based cross-sectional study of 1716 randomly selected individuals. Associations were examined using mixed-effect multivariable logistic regression. A total of 264 men (64%) and 268 women (56%) had never tested for HIV. The strongest determinants for not being tested were disruptive couple relationships (OR = 2.48 95% CI = 1.00–6.19); tolerance to gender-based violence (OR = 2.10 95% CI = 1.05–4.32) and fear of social rejection (OR = 1.48 95% CI = 1.23–1.80). In the Zambian context, unequal power relationships within the couple and the community seem to play a pivotal role in the decision to test which until now have been largely underestimated. Policies, programs and interventions to rapidly increase HIV testing need to urgently address gender-power inequity in relationships and prevent gender-based violence to reduce the negative impact on the lives of couples and families.     

Turnaround Time for Early Infant HIV Diagnosis in Rural Zambia: A Chart Review

Background

Early infant HIV diagnosis is challenging in sub-Saharan Africa, particularly in rural areas where laboratory capacity is limited. Specimens must be transported to central laboratories for testing, leading to delays in diagnosis and initiation of antiretroviral therapy. This study was undertaken in rural Zambia to measure the turnaround time for confirmation of HIV infection and identify delays in diagnosis.

Methods

Chart reviews were conducted from 2010–2012 for children undergoing early infant HIV diagnosis at Macha Hospital in Zambia. Relevant dates, receipt of drugs by mother and child for the prevention of mother-to-child transmission (PMTCT), and test results were abstracted.

Results

403 infants provided 476 samples for early infant diagnosis. The median age at the “6-week” and “6-month” assessments was 8.1 weeks and 7.0 months, respectively. The majority of mothers (80%) and infants (67%) received PMTCT. The median time between sample collection and arrival at the central laboratory in Lusaka was 17 days (IQR: 10, 28); arrival at the central laboratory to testing was 6 days (IQR: 5, 11); testing to return of results to the clinic was 29 days (IQR: 17, 36); arrival of results at the clinic to return of results to the caregiver was 45 days (IQR: 24, 79). The total median time from sample collection to return of results to the caregiver was 92 days (IQR: 84, 145). The proportion of HIV PCR positive samples was 12%. The total median turnaround time was shorter for HIV PCR positive as compared to negative or invalid samples (85 vs. 92 days; p = 0.08).

Conclusions

Delays in processing and communicating test results were identified, particularly in returning results from the central laboratory to the clinic and from the clinic to the caregiver. A more efficient process is needed so that caregivers can be provided test results more rapidly, potentially resulting in earlier treatment initiation and better outcomes for HIV-infected infants.     

A Population-Structured HIV Epidemic in Israel: Roles of Risk and Ethnicity

Background

HIV in Israel started with a subtype-B epidemic among men who have sex with men, followed in the 1980s and 1990s by introductions of subtype C from Ethiopia (predominantly acquired by heterosexual transmission) and subtype A from the former Soviet Union (FSU, most often acquired by intravenous drug use). The epidemic matured over the last 15 years without additional large influx of exogenous infections. Between 2005 and 2013 the number of infected men who have sex with men (MSM) increased 2.9-fold, compared to 1.6-fold and 1.3-fold for intravenous drug users (IVDU) and Ethiopian-origin residents. Understanding contemporary spread is essential for effective public health planning.

Methods

We analyzed demographic and virologic data from 1,427 HIV-infected individuals diagnosed with HIV-I during 1998–2012. HIV phylogenies were reconstructed with maximum-likelihood and Bayesian methods.

Results

Subtype-B viruses, but not A or C, demonstrated a striking number of large clusters with common ancestors having posterior probability ≥0.95, including some suggesting presence of transmission networks. Transmitted drug resistance was highest in subtype B (13%). MSM represented a frequent risk factor in cross-ethnic transmission, demonstrated by the presence of Israeli-born with non-B virus infections and FSU immigrants with non-A subtypes.

Conclusions

Reconstructed phylogenetic trees demonstrated substantial grouping in subtype B, but not in non-MSM subtype-A or in subtype-C, reflecting differences in transmission dynamics linked to HIV transmission categories. Cross-ethnic spread occurred through multiple independent introductions, with MSM playing a prevalent role in the transmission of the virus. Such data provide a baseline to track epidemic trends and will be useful in informing and quantifying efforts to reduce HIV transmission.     

A Mathematical Model of the Tuberculosis Epidemic

Acta Biotheoretica - Tuberculosis has continued to retain its title as “the captain among these men of death”. This is evident as it is the leading cause of death globally from a single...     

An HIV Epidemic Model Based on Viral Load Dynamics: Value in Assessing Empirical Trends in HIV Virulence and Community Viral Load

Trends in HIV virulence have been monitored since the start of the AIDS pandemic, as studying HIV virulence informs our understanding of HIV epidemiology and pathogenesis. Here, we model changes in HIV virulence as a strictly evolutionary process, using set point viral load (SPVL) as a proxy, to make inferences about empirical SPVL trends from longitudinal HIV cohorts. We develop an agent-based epidemic model based on HIV viral load dynamics. The model contains functions for viral load and transmission, SPVL and disease progression, viral load trajectories in multiple stages of infection, and the heritability of SPVL across transmissions. We find that HIV virulence evolves to an intermediate level that balances infectiousness with longer infected lifespans, resulting in an optimal SPVL∼4.75 log₁₀ viral RNA copies/mL. Adaptive viral evolution may explain observed HIV virulence trends: our model produces SPVL trends with magnitudes that are broadly similar to empirical trends. With regard to variation among studies in empirical SPVL trends, results from our model suggest that variation may be explained by the specific epidemic context, e.g. the mean SPVL of the founding lineage or the age of the epidemic; or improvements in HIV screening and diagnosis that results in sampling biases. We also use our model to examine trends in community viral load, a population-level measure of HIV viral load that is thought to reflect a population''s overall transmission potential. We find that community viral load evolves in association with SPVL, in the absence of prevention programs such as antiretroviral therapy, and that the mean community viral load is not necessarily a strong predictor of HIV incidence.     

A Two-Sex Polygenic Model for the Evolution of Premating Isolation. II. Computer Simulation of Experimental Selection Procedures

A Monte-Carlo simulation program is described for a polygenic mating model introduced in the first paper in this series (Sved 1981). The program is used to simulate the situation in laboratory experiments in which two strains are allowed to mass-mate, hybrids are artificially eliminated and the establishment of mating isolation is studied. It is shown that, if mating choice is sufficiently precise, a combination of chance fluctuation and selection can lead to divergence in mating behavior. However, for small population sizes, the variability would usually be considerably reduced by the time some divergence is established, leading to low eventual levels of isolation. For larger population sizes, on the other hand, it may take many generations for any divergence to be established.-A dissection of the selective forces involved in the divergence shows that the major force potentially responsible for initial selective response is the tendency for divergent females and males to reject mates from the wrong strain. However, this is nullified in mixed-strain matings by the tendency of such individuals equally to reject mates from the correct strain. To overcome this problem, it is suggested that the usual mixed-strain mating procedure be replaced by procedures specifically designed to select for rejection of interstrain matings. Two procedures are suggested for this, and computer simulation shows that one or other of the procedures will work under the assumptions of the mating model. Other possible outcomes of selection, including asymmetrical divergence, are discussed for cases in which the assumptions of the mating model are invalid.     

Evaluating the Impact of Test-and-Treat on the HIV Epidemic among MSM in China Using a Mathematical Model

Background

Various studies have modeled the impact of test-and-treat policies on the HIV epidemics worldwide. However, few modeling studies have taken into account China’s context. To understand the potential effect of test-and-treat on the HIV epidemic among men who have sex with men (MSM) in China, we developed a mathematical model to evaluate the impact of the strategy.

Method

Based on the natural history of the CD4 count of people living with HIV and AIDS (PLWHA), we constructed a dynamic compartmental model of HIV transmission among Chinese MSM to project the number of HIV new infections and prevalence over 10 years. We predicted the annual number of HIV new infections and the total number of MSM living with HIV and AIDS (based on Beijing data) between 2010 and 2022 under the following conditions: (1) current practice (testing rate of 50% and ART coverage of 39%); (2) both testing rate and ART coverage increasing to 70% in 2013; (3) both testing rate and ART coverage increasing to 90% in 2013; and (4) both testing rate and ART coverage increasing gradually every year until 90% since 2013.

Results

Based on our model, if the HIV test-and-treat policy was implemented among Chinese MSM, the total number of HIV new infections over 10 years (2013-2022) would be reduced by 50.6-70.9% compared with the current policy. When ART coverage for PLWHA increased to 58% since 2013, the ‘turning point’ would occur on the curve of HIV new infections by 2015. A 25% reduction in annual number of HIV new infections by 2015 might be achieved if the testing rate increased from 50% to 70% and treatment coverage for PLWHA increased to 55% since 2013.

Conclusion

Implementation of the test-and-treat strategy may significantly reduce HIV new infections among MSM in China. Great efforts need to be made to scale up HIV testing rate and ART coverage among Chinese MSM.     

Antiretroviral therapy and demand for HIV testing: Evidence from Zambia

This paper examines the effects of antiretroviral therapy (ART) on demand for HIV testing and of ART-induced testing on demand for risky sexual behavior. I provide a model of sexual behavior decision-making under uncertainty and estimate the structural parameters of the model using nationally representative survey data from Zambia on HIV testing decisions before and after the introduction of ART. The empirical results indicate that although the introduction of ART appears to have increased HIV testing rates by upwards of 50 percent, the ART allocation process may have limited the prevention benefit of ART-induced testing. Simulation results show that eliminating this prevention inefficiency while holding the supply of ART constant would increase the prevention impact of ART-induced testing more than four-fold. More generally, the analysis indicates that existing studies which examine “universal” testing or quasi-experimental testing programs understate the efficacy of standard voluntary counseling and testing programs.     

Impact of HIV on tuberculosis in Zambia: a cross sectional study.

OBJECTIVE--To examine the contribution of HIV infection to the apparently increasing incidence of tuberculosis in central Africa. DESIGN--Cross sectional study. SETTING--Outpatient clinic in teaching hospital, Lusaka, Zambia. PATIENTS--346 Adult patients with tuberculosis. RESULTS--Overall, 206 patients (60%; 95% confidence interval 54% to 65%) were positive for HIV--in one or both assays used. The peaks for both tuberculosis and HIV infection were among men aged 25-34 years and women aged 14-24 years. Of patients with confirmed pulmonary tuberculosis, 73/149 (49%; 41% to 57%) were positive for HIV; 67/83 (81%; 70% to 89%) patients with pleural disease and 16/19 (84%; 60% to 97%) patients with pericardial disease were positive. HIV positive patients with positive sputum culture were less likely to have had a positive sputum smear, and their chest x ray films less often showed classic upper zone disease or cavitation. Of 72 patients who fulfilled clinical criteria for AIDS, 17 were negative for HIV. CONCLUSIONS--The high prevalence of HIV in patients with tuberculosis suggests that an epidemic of reactivating tuberculosis is arising in those who are infected with HIV. The redirection of public health priorities towards tuberculosis would focus on a major treatable and preventable complication of the AIDS epidemic.     

A Susceptible-infected Epidemic Model with Voluntary Vaccinations

An susceptible-infected epidemic model with endogenous behavioral changes is presented to analyze the impact of a prophylactic vaccine on disease prevalence. It is shown that, with voluntary vaccination, whether an endemic equilibrium exists or not does not depend on vaccine efficacy or the distribution of agent-types. Although an endemic equilibrium is unique in the absence of a vaccine, the availability of a vaccine can lead to multiple endemic equilibria that differ in disease prevalence and vaccine coverage. Depending on the distribution of agent-types, the introduction of a vaccine or, if one is available, a subsidy for vaccination can increase disease prevalence by inducing more risky behavior.I would like to thank one of the editors of the journal, Alan Hastings, for his comments and suggestions.     

Size Matters: Concurrency and the Epidemic Potential of HIV in Small Networks

Background

Generalized heterosexual epidemics are responsible for the largest share of the global burden of HIV. These occur in populations that do not have high rates of partner acquisition, and research suggests that a pattern of fewer, but concurrent, partnerships may be the mechanism that provides the connectivity necessary for sustained transmission. We examine how network size affects the impact of concurrency on network connectivity.

Methodology/Principal Findings

We use a stochastic network model to generate a sample of networks, varying the size of the network and the level of concurrency, and compare the largest components for each scenario to the asymptotic expected values. While the threshold for the growth of a giant component does not change, the transition is more gradual in the smaller networks. As a result, low levels of concurrency generate more connectivity in small networks.

Conclusions/Significance

Generalized HIV epidemics are by definition those that spread to a larger fraction of the population, but the mechanism may rely in part on the dynamics of transmission in a set of linked small networks. Examples include rural populations in sub-Saharan Africa and segregated minority populations in the US, where the effective size of the sexual network may well be in the hundreds, rather than thousands. Connectivity emerges at lower levels of concurrency in smaller networks, but these networks can still be disconnected with small changes in behavior. Concurrency remains a strategic target for HIV combination prevention programs in this context.     

Female Sex Workers,Male Circumcision and HIV: A Qualitative Study of Their Understanding,Experience, and HIV Risk in Zambia

Several sub-Saharan African countries, including Zambia, have initiated national voluntary medical male circumcision (MC) programs to reduce HIV incidence. In-depth interviews were conducted with twenty female sex workers (FSWs) in Lusaka to examine their understanding of MC and experiences with circumcised clients. Knowledge of MC was derived primarily through informal sources, with very few FSWs reporting exposure to MC educational campaigns. MC was not widely believed to be protective against HIV, however it was viewed by some as protective against STIs. Three FSWs reported having sex with recently circumcised clients, and most reported that men often used their MC status to try to convince FSWs to forego condoms. Findings suggest that FSWs, already at high risk for HIV infection, may face additional pressure toward higher risk behavior as a result of MC. As MC services are expanded, programs should support FSWs'' efforts to protect themselves by providing information about what MC can - and cannot - offer for HIV/STI infection prevention.     

Estimating HIV pre-exposure prophylaxis need and impact in Malawi,Mozambique and Zambia: A geospatial and risk-based analysis

BackgroundPre-exposure prophylaxis (PrEP), a WHO-recommended HIV prevention method for people at high risk for acquiring HIV, is being increasingly implemented in many countries. Setting programmatic targets, particularly in generalised epidemics, could incorporate estimates of the size of the population likely to be eligible for PrEP using incidence-based thresholds. We estimated the proportion of men and women who would be eligible for PrEP and the number of HIV infections that could be averted in Malawi, Mozambique, and Zambia using prioritisation based on age, sex, geography, and markers of risk.Methods and findingsWe analysed the latest nationally representative Demographic and Health Surveys (DHS) of Malawi, Mozambique, and Zambia to determine the proportion of adults who report behavioural markers of risk for HIV infection. We used prevalence ratios (PRs) to quantify the association of these factors with HIV status. Using a multiplier method, we combined these proportions with the number of new HIV infections by district, derived from district-level modelled HIV estimates. Based on these numbers, different scenarios were analysed for the minimum number of person-years on PrEP needed to prevent 1 HIV infection (NNP).An estimated total of 38,000, 108,000, and 46,000 new infections occurred in Malawi, Mozambique, and Zambia in 2016, corresponding with incidence rates of 0.43, 0.63, and 0.57 per 100 person-years. In these countries, 9%–20% of new infections occurred among people with a sexually transmitted infection (STI) in the past 12 months and 40%–42% among people with either an STI or a non-regular sexual partner (NP) in the past 12 months (STINP). The models estimate that around 50% of new infections occurred in districts with incidence rates ≥1.0% in Mozambique and Zambia and ≥0.5% in Malawi. In Malawi, Mozambique, and Zambia, 35.1%, 21.9%, and 12.5% of the population live in these high-incidence districts. In the most parsimonious scenario, if women aged 15–34 years and men 20–34 years with an STI in the past 12 months living in high-incidence districts were to take PrEP, it would take a minimum of 65.8 person-years on PrEP to avert 1 HIV infection per year in Malawi, 35.2 in Mozambique, and 16.4 in Zambia. Our findings suggest that 3,300, 5,200, and 1,700 new infections could be averted per year in the 3 countries, respectively. Limitations of our study are that these values are based on modelled estimates of HIV incidence and self-reported behavioural risk factors from national surveys.ConclusionsA large proportion of new HIV infections in these 3 African countries were estimated to occur among people who had either an STI or an NP in the past year, providing a straightforward means to set PrEP targets. Greater prioritisation of PrEP by district, sex, age, and behavioural risk factors resulted in lower NNPs thereby increasing PrEP cost-effectiveness, but also diminished the overall impact on reducing new infections

Dominik Stelzle and co-workers estimate impact of antiretroviral pre-exposure prophylaxis use on HIV infections in 3 African countries.