Mathematical formulation and studies of the risk parameters involved in HIV transmission

The probability of becoming infected with HIV is formulated in terms of the total number of sexual contacts (N), the probability that a sexual act is infectious (r) and the prevalence (p). Using the appropriate equations we studied the effect of reducing each of the risk factors on lowering the probability of infection. We show that for many realistic situations the probability of becoming infected by multiple partners is equal to the probability of becoming infected by one partner in a monogamous relationship given that the prevalence is the same in both cases; however if the multiple partners are chosen over time from a pool of a growing prevalence, then one is better off in a monogamous relationship where that partner is chosen early in the epidemic.     

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.     

Development,Calibration and Performance of an HIV Transmission Model Incorporating Natural History and Behavioral Patterns: Application in South Africa

Understanding HIV transmission dynamics is critical to estimating the potential population-wide impact of HIV prevention and treatment interventions. We developed an individual-based simulation model of the heterosexual HIV epidemic in South Africa and linked it to the previously published Cost-Effectiveness of Preventing AIDS Complications (CEPAC) International Model, which simulates the natural history and treatment of HIV. In this new model, the CEPAC Dynamic Model (CDM), the probability of HIV transmission per sexual encounter between short-term, long-term and commercial sex worker partners depends upon the HIV RNA and disease stage of the infected partner, condom use, and the circumcision status of the uninfected male partner. We included behavioral, demographic and biological values in the CDM and calibrated to HIV prevalence in South Africa pre-antiretroviral therapy. Using a multi-step fitting procedure based on Bayesian melding methodology, we performed 264,225 simulations of the HIV epidemic in South Africa and identified 3,750 parameter sets that created an epidemic and had behavioral characteristics representative of a South African population pre-ART. Of these parameter sets, 564 contributed 90% of the likelihood weight to the fit, and closely reproduced the UNAIDS HIV prevalence curve in South Africa from 1990–2002. The calibration was sensitive to changes in the rate of formation of short-duration partnerships and to the partnership acquisition rate among high-risk individuals, both of which impacted concurrency. Runs that closely fit to historical HIV prevalence reflect diverse ranges for individual parameter values and predict a wide range of possible steady-state prevalence in the absence of interventions, illustrating the value of the calibration procedure and utility of the model for evaluating interventions. This model, which includes detailed behavioral patterns and HIV natural history, closely fits HIV prevalence estimates.     

The initialization and sensitivity of multigroup models for the transmission of HIV

We study two multigroup mathematical models of the spread of HIV. In the differential infectivity model, the infected population is divided into groups according to their infectiousness, and HIV is primarily spread by a small, highly infectious, group of superspreaders. In the staged-progression model, every infected individual goes through a series of infection stages and the virus is primarily spread by individuals in an initial highly infectious stage or in the late stages of the disease. We demonstrate the importance of choosing appropriate initial conditions, and define a new approach to distributing the initial population among the subgroups so as to minimize the artificial transients in the solutions due to unbalanced initial conditions. We demonstrate that the rate of removal in and out of a population is an important, yet often neglected, effect. We also illustrate the importance of distinguishing between the number of partners a person has and the number of contacts per partner. By assuming that people with many partners have fewer contacts per partner than people with few partners, we found that the epidemic is less sensitive to the partner acquisition rate than one might expect. However, because the probability of transmission of HIV per contact is low, the epidemic is very sensitive to the number of contacts per partner. Modeling this distinction is particularly important when estimating the impact of programs which encourage people to have fewer sexual partners.     

The migratory activity of HIV-infected people in the northwestern region and the routes of the possible spread of the infection]

The epidemic situation in HIV infection in the northwestern region of this country has been analyzed. The ways of the spread of HIV infection among the infected persons, residents of the St. Petersburg region, Kaliningrad, Novgorod and Murmansk, have been studied. The infection is transmitted mainly through sexual contacts, both homosexual and heterosexual. High migration activity of HIV-infected persons, homo- and heterosexuals, has been established, and a great number of unknown (casual) sexual contacts among them was noted. The results of these observations may be useful in the prognostication of the epidemic situation in HIV infection not only in the northwestern region, but also beyond its boundaries, and later in the optimization of screening.     

Comparison of female to male and male to female transmission of HIV in 563 stable couples. European Study Group on Heterosexual Transmission of HIV.

OBJECTIVE--To identify risk factors for heterosexual transmission of HIV and to compare the efficiency of male to female and female to male transmission. DESIGN--Cohort study of heterosexual couples. Regular partners of HIV infected subjects were tested and both members of the couples interviewed every six months. HIV prevalence in partners was analysed according to the characteristics of the couples. SETTING--Nine European countries. SUBJECTS--563 couples comprising 156 female index patients with their 159 male partners and 400 male index patients with their 404 female partners. Partners reporting risk factors other than sexual contacts with the index patient were excluded. MAIN OUTCOME MEASURES--HIV infection in partners and high risk sexual behaviour. RESULTS--Overall, 19 (12%) male partners and 82 (20%) female partners were infected with HIV, suggesting that male to female transmission is 1.9 (95% confidence interval 1.1 to 3.3) times more effective than female to male transmission. An advanced stage of HIV infection in the index patient (odds ratio 17.6; 4.9 to 62.7) and sexual contacts during menses (3.4; 1.0 to 11.1) increased the risk of female to male transmission and stage of infection (2.7; 1.5 to 4.9), anal sex (5.1; 2.9 to 8.9), and age of the female partner (3.9; 1.2 to 13.0 for age > 45 years) increased the risk of male to female transmission. None of the 24 partners who had used condoms systematically since the first sexual contact was infected. CONCLUSIONS--Several factors which potentiate the risk of transmission through unprotected vaginal intercourse have been identified. Knowledge of these factors could be helpful for counselling patients infected with HIV and their sexual partners.     

Effects of public health educational campaigns and the role of sex workers on the spread of HIV/AIDS among heterosexuals

This paper presents a sex-structured model for heterosexual transmission of HIV/AIDS in which the population is divided into three subgroups: susceptibles, infectives and AIDS cases. The subgroups are further divided into two classes, consisting of individuals involved in high-risk sexual activities and individuals involved in low-risk sexual activities. The model considers the movement of individuals from high to low sexual activity groups as a result of public health educational campaigns. Thus, in this case public health educational campaigns are resulting in the split of the population into risk groups. The equilibrium and epidemic threshold, which is known as the basic reproductive number (R0), are obtained, and stability (local and global) of the disease-free equilibrium is investigated. The model is extended to incorporate sex workers, and their role in the spread of HIV/AIDS in settings with heterosexual transmission is explored. Comprehensive analytic and numerical techniques are employed in assessing the possible community benefits of public health educational campaigns in controlling HIV/AIDS. From the study, we conclude that the presence of sex workers enlarges the epidemic threshold R0, thus fuels the epidemic among the heterosexuals, and that public health educational campaigns among the high-risk heterosexual population reduces R0, thus can help slow or eradicate the epidemic.     

HIV infection in patients attending clinics for sexually transmitted diseases in England and Wales. Collaborative Study by Consultants in Genitourinary Medicine and the Public Health Laboratory Service.

A national study of the prevalence of HIV antibody designed to monitor sexual spread of HIV infection in England and Wales was made of homosexual and heterosexual patients attending sexually transmitted disease clinics in four districts in 1985, seven in 1986, and 14 in 1987. Patients were invited to participate and were counselled. Among homosexual men in two clinics in south east England, HIV antibody was found in 92 (12.9%) of 711 in 1985, 65 (15.2%) of 428 in 1986, and 81 (14.6%) of 556 in 1987: corresponding findings in the other regions were 16 (5.0%) of 321, 41 (6.3%) of 654, and 21 (3.1%) of 678. The prevalence of HIV antibody was higher in homosexual than bisexual men, in patients aged 25 years or more, or with one or more specified minor complaints. Among heterosexual patients in the south east in 1986, HIV antibody was found in seven (3.0%) of 230 men and three (1.3%) of 233 women and in 1987 in 10 (1.0%) of 962 men and seven (0.7%) of 949 women. In other areas corresponding findings in 1986 were two (0.2%) of 950 men and three (0.4%) of 752 women and in 1987 were three (0.06%) of 5312 men and one (0.02%) of 4778 women. All but one of the heterosexual patients with the antibody were intravenous drug abusers or had had sexual contacts in or were from an area abroad with a high prevalence of AIDS. Failure to identify a heterosexual patient with HIV antibody not in a risk group (other than that of being an attender at the clinic) or who did not have a sexual partner in a risk group suggests that their prevalence in the patient population of the clinics in the south east is less than one in 700 and in the other regions less than one in 3000. Refusals to participate increased during the study but comparisons of patients who agreed and refused in terms of age, the presence of symptoms suggesting AIDS, travel abroad, and number of sexual partners a month showed little evidence of selective bias.     

Increasing Adolescent HIV Prevalence in Eastern Zimbabwe – Evidence of Long-Term Survivors of Mother-to-Child Transmission?

Recent data from the Manicaland HIV/STD Prevention Project, a general-population open HIV cohort study, suggested that between 2004 and 2007 HIV prevalence amongst males aged 15–17 years in eastern Zimbabwe increased from 1.20% to 2.23%, and in females remained unchanged at 2.23% to 2.39%, while prevalence continued to decline in the rest of the adult population. We assess whether the more likely source of the increase in adolescent HIV prevalence is recent sexual HIV acquisition, or the aging of long-term survivors of perinatal HIV acquisition that occurred during the early growth of the epidemic. Using data collected between August 2006 and November 2008, we investigated associations between adolescent HIV and (1) maternal orphanhood and maternal HIV status, (2) reported sexual behaviour, and (3) reporting recurring sickness or chronic illness, suggesting infected adolescents might be in a late stage of HIV infection. HIV-infected adolescent males were more likely to be maternal orphans (RR = 2.97, p<0.001) and both HIV-infected adolescent males and females were more likely to be maternal orphans or have an HIV-infected mother (male RR = 1.83, p<0.001; female RR = 16.6, p<0.001). None of 22 HIV-infected adolescent males and only three of 23 HIV-infected females reported ever having had sex. HIV-infected adolescents were 60% more likely to report illness than HIV-infected young adults. Taken together, all three hypotheses suggest that recent increases in adolescent HIV prevalence in eastern Zimbabwe are more likely attributable to long-term survival of mother-to-child transmission rather than increases in risky sexual behaviour. HIV prevalence in adolescents and young adults cannot be used as a surrogate for recent HIV incidence, and health systems should prepare for increasing numbers of long-term infected adolescents.     

Age and Sex Structured Model for Assessing the Demographic Impact of Mother-to-Child Transmission of HIV/AIDS

Age and sex structured HIV/AIDS model with explicit incubation period is proposed as a system of delay differential equations. The model consists of two age groups that are children (0–14 years) and adults (15–49 years). Thus, the model considers both mother-to-child transmission (MTCT) and heterosexual transmission of HIV in a community. MTCT can occur prenatally, at labour and delivery or postnatally through breastfeeding. In the model, we consider the children age group as a one-sex formulation and divide the adult age group into a two-sex structure consisting of females and males. The important mathematical features of the model are analysed. The disease-free and endemic equilibria are found and their stabilities investigated. We use the Lyapunov functional approach to show the local stability of the endemic equilibrium. Qualitative analysis of the model including positivity and boundedness of solutions, and persistence are also presented. The basic reproductive number (ℛ₀) for the model shows that the adult population is responsible for the spread HIV/AIDS epidemic, thus up-to-date developed HIV/AIDS models to assess intervention strategies have focused much on heterosexual transmission by the adult population and the children population has received little attention. We numerically analyse the HIV/AIDS model to assess the community benefits of using antiretroviral drugs in reducing MTCT and the effects of breastfeeding in settings with high HIV/AIDS prevalence ratio using demographic and epidemiological parameters for Zimbabwe.     

A policy to control the spread of HIV infection

Prevention of transmission of HIV infection is the most important public health concern of the AIDS epidemic. To date, unfortunately, we have failed to contain the epidemic. The increasingly rapid spread of HIV into the IV drug-abusing population and subsequent heterosexual transmission represent a further failure of the public health system. Current organization of the public health programs, especially the lack of independence and adequate financial and personnel support, is an extremely serious problem. More funding may not be the answer, unless there is better organization. Identification of infected individuals and a vigorous education program must be implemented. HIV antibody-positive individuals should be followed carefully in order to evaluate the risk factors for AIDS and efficacy of specific interventions.     

Age-dependent choice of sexual partners and the transmission dynamics of HIV in Sub-Saharan Africa.

A mathematical model of the transmission of HIV-1 within heterosexual populations in Sub-Saharan Africa is described and its properties analysed. The model incorporates epidemiological and demographic processes and extends previous work in this area via the inclusion of age and sex dependency in rates of sexual partner change, and sexual partner choice dependent on age. Parameter assignments are made on the basis of current data on the transmission dynamics of HIV-1 and the demography of human populations in Africa. Both age-dependent rates of sexual activity and the sexual contact of males with females younger than themselves act to enhance the predicted demographic impact. With realistic parameter values, the model suggests AIDS is able to reverse the sign of population growth rates from positive to negative values over a timescale of a few decades. The sensitivity of this prediction is examined in relation to changes in the pattern of sexual contact between different age classes of females and males, different patterns of change in the age-dependent rate of sexual partner change, different assumptions concerning the doubling time of the epidemic in its early stages, and the relative efficiencies of viral transmission between men and women, and vice versa. The impact AIDS is predicted to have on the number of young and elderly persons as a fraction of the number of productive adults (the dependancy ratio) is examined under various assumptions concerning the weighting to be applied to mirror the burden imposed by the care of those with AIDS. The paper includes an assessment of the influence of the timing of changes in sexual behaviour, or the promotion of the use of condoms, on the predicted course of the epidemic. The paper concludes with a discussion of data needs and the model refinements required to more accurately mirror current understanding of the epidemiology of HIV-1.     

The influence of concurrent partnerships on the dynamics of HIV/AIDS.

Most models of the spread of HIV/AIDS assume that the probability of transmission from an infected individual to a susceptible partner has some constant value per sexual act, compounding independently randomly (so that ten acts with one person chosen from a particular group has, on average, the same risk as one act with each of ten different people from that group). Guided by available data, other models treat the transmission process as being some characteristic (but highly variable) value per partnership, independent of the number of acts. This latter approach does not allow for the possible effects of concurrent partnerships, and therefore does not take account of the possibility that an initially uninfected partner of a given susceptible individual may become infected over the duration of their partnership. We present a new model, based on transmission per partnership, that takes account of partnership duration. If the number of overlapping partnerships is high enough (so that R0 greater than 1 among "standing crops" of partners), any initial infection will spread very fast--on the time scale of a few times the latent interval (a few months)--among existing networks of partners. After this initial "fast phase," the subsequent epidemic proceeds more slowly along conventional lines as new partnerships are formed. These properties of the model are illustrated numerically and by analytic studies (using singular perturbation theory). The possibility of such "two time-scale" phenomena could have implications for data analysis based on statistical back-projection.     

National cross sectional study of views on sexual violence and risk of HIV infection and AIDS among South African school pupils

Objective To investigate the views of school pupils on sexual violence and on the risk of HIV infection and AIDS and their experiences of sexual violence.Design National cross sectional study.Setting 5162 classes in 1418 South African schools.Participants 269 705 school pupils aged 10-19 years in grades 6-11.Main outcome measure Answers to questions about sexual violence and about the risk of HIV infection and AIDS.Results Misconceptions about sexual violence were common among both sexes, but more females held views that would put them at high risk of HIV infection. One third of the respondents thought they might be HIV positive. This was associated with misconceptions about sexual violence and about the risk of HIV infection and AIDS. Around 11% of males and 4% of females claimed to have forced someone else to have sex; 66% of these males and 71% of these females had themselves been forced to have sex. A history of forced sex was a powerful determinant of views on sexual violence and risk of HIV infection.Conclusions The views of South African youth on sexual violence and on the risk of HIV infection and AIDS were compatible with acceptance of sexual coercion and “adaptive” attitudes to survival in a violent society. Views differed little between the sexes.     

Twenty years of human immunodeficiency virus infection in Croatia--an epidemic that is still in an early stage

Croatia has a low-level HIV epidemic; 553 persons were diagnosed with HIV infection in the period 1985-2005. The principal mode of transmission was sex between men (40% of cases) and heterosexual contact (40%). Only about 10% of cases were injecting drug users. Testing data also suggest a low prevalence of HIV infection in Croatia, even in vulnerable groups. Behavioral data indicate risky sexual behaviors, with the clear need for interventions. National policy towards HIVIAIDS is operated through the National Committee on HIV/AIDS, a multisectorial advisory body to the Government of Croatia. Croatia applied to the Global Fund to fight AIDS, tuberculosis and malaria in 2002 which resulted in a 4,9 million USD grant for scaling up prevention interventions. Croatia has a centralized system of treatment and care which is provided at the University Hospital for Infectious Diseases in Zagreb. Highly active antiretroviral treatment is provided free of charge from April 1998.     

Sexually transmitted disease and the evolution of mating systems

Sexually transmitted diseases (STDs) have been shown to increase the costs of multiple mating and therefore favor relatively monogamous mating strategies. We examine another way in which STDs can influence mating systems in species in which female choice is important. Because more popular males are more likely to become infected, STDs can counteract any selective pressure that generates strong mating skews. We build two models to investigate female mate choice when the sexual behavior of females determines the prevalence of infection in the population. The first model has no explicit social structure. The second model considers the spatial distribution of matings under social monogamy, when females mated to unattractive males seek extrapair fertilizations from attractive males. In both cases, the STD has the potential to drastically reduce the mating skew. However, this reduction does not always happen. If the per contact transmission probability is low, the disease dies out and is of no consequence. In contrast, if the transmission probability is very high, males are likely to be infected regardless of their attractiveness, and mating with the most attractive males imposes again no extra cost for the female. We also show that optimal female responses to the risk of STDs can buffer the prevalence of infection to remain constant, or even decrease, with increasing per contact transmission probabilities. In all cases considered, the feedback between mate choice strategies and STD prevalence creates frequency-dependent fitness benefits for the two alternative female phenotypes considered (choosy vs. randomly mating females or faithful vs. unfaithful females). This maintains mixed evolutionarily stable strategies or polymorphisms in female behavior. In this way, a sexually transmitted disease can stabilize the populationwide proportion of females that mate with the most attractive males or that seek extrapair copulations.     

Kunyenga, "real sex," and survival: assessing the risk of HIV infection among urban street boys in Tanzania

This article examines possible avenues of HIV infection among urban street boys in Tanzania. In doing so, it questions the ways that AIDS researchers have defined and approached the phenomenon of "survival sex" in East and Central Africa. The article specifically examines the boys' sexual networks, sexual practices, and attitudes regarding their own sexual behavior, including their perceived risk of HIV/AIDS infection. Seventy-five street boys aged eight to 20 from the city of Mwanza were interviewed. Results suggest that almost all street boys are involved in a sexual network in which homosexual and heterosexual behavior occurs. Homosexual practices are rooted in a complex set of behaviors and ideologies known as kunyenga, which is a situated aspect of life on the streets and helps maintain the boys' strong dependence on one another. A key aspect of the boys' sexual careers involves a decrease in kunyenga activity as they approach the age of 18 and an increase in heterosexual encounters after the age of 11. There appears to be a critical period between these ages in which heterosexual and kunyenga activities overlap. It is suggested that boys between these ages represent a potential bridge for HIV/AIDS infection between the general population and the relatively enclosed sexual network of street boys.     

The determinants of the spread of HIV among injection drug addicts in Ukraine

The main tendencies in the development of drug addiction in the Ukraine, the dynamics of the spread of HIV among drug addicts introducing drugs intravenously, epidemiological data on HIV, AIDS and drug addiction, as well as prognoses on the development of HIV infection are presented. Since 1995 the number of HIV-infected persons grew 34-fold, the number of cases of HIV infection resulting from the intravenous use drugs rose to 70% simultaneously with the rise (about 34-fold) of the number of persons infected with HIV through sexual contacts (about 13 fold). In 1996-1997 such tendency increased. On the whole, the proportion of drug addicts introducing drugs by intravenous injection was 83% in the Ukraine. By April 1, 1998, official registration covered 18,800 HIV-infected persons, including 270 foreign nationals, as well as 499 AIDS patients, including 487 Ukrainian citizens, among them 28 children. Out of 18,800 HIV-infected persons, 78.3% were drug addicts, most of them young people aged 15-30 years; about 18% were young people under 20 years of age, 80% being males. According to the model the rapid spread of HIV from the group of drug addicts to the heterosexual population, the total number of HIV-infected persons reaching 1,500,000 is expected in the country by 2014.     

Uncertainties in predicting the demographic impact of AIDS

A model giving the demographic impact of AIDS is analysed to examine the sensitivity of the projections when various complicating features are included. The model deals with age and sexual partner change rate as continuous variables and uses a device to specify arbitrary correlations between the ages of the people who form sexual partnerships. The device ensures consistency, in that the amount of partner formation is the same regardless of whether the partnerships are counted from the point of view of males or females. Arbitrary correlation between partner change rate and fertility is also permitted. The results show the uncertainty in model predictions that population growth will reduce over the next 20 years to approximately zero in parts of East Africa severely affected by the AIDS epidemic. The main sources of uncertainty in the model predictions are assumptions concerning the correlation between ages in a partnership, the correlation between partner change rate and fertility, the incubation period of AIDS, and the variability of the female partner change rate.     

Risk factors for infection with human immmunodeficiency virus among European expatriates in Africa.

The pattern of cases of AIDS in Belgium suggests that Europeans infected with human immunodeficiency virus (HIV) acquired the infection in Africa. The prevalence of infection was assessed in Belgian advisers and European expatriates and risk factors for infection defined in a case-control study of expatriate men. Fifteen (1.1%) of 1401 Belgian advisers working in Africa and 41 (0.9%) of 4564 European expatriates living in Africa, were positive for antibody to HIV in a voluntary screening programme in Belgium. Among subjects with antibody to HIV the ratio of men to women was 3:1. These subjects did not have a history of intravenous drug abuse or blood transfusion and only one was homosexual. In a case-control study of 33 expatriate men who had antibody to HIV and 119 controls the men with antibody reported significantly more female sexual partners, who were more commonly local; and significantly more sexual contact with prostitutes in Africa. They had a significantly higher prevalence of history of sexually transmitted disease and had received significantly more injections by unqualified staff in Africa during the previous five years. No specific sexual practices were associated with having antibody to HIV. After multivariate analysis sexual contact with local women (adjusted odds ratio 14.7; 95% confidence interval 2.81 to 76.9), sexual contact with prostitutes (adjusted odds ratio 10.8 (1.6 to 71.9), and injections by unqualified staff (adjusted odds ratio 13.5 (3.7 to 49.8) remained independent risk factors for infection. European expatriates in Africa were at increased risk from infection with HIV and were a means of introducing HIV into the heterosexual population in Europe. Transmission from women to men by vaginal intercourse seemed to be the most probable route of infection.