Basic Reproduction Number for HIV Model Incorporating Commercial Sex and Behavior Change

The basic reproduction number is obtained for an HIV epidemic model incorporating direct and indirect commercial sex as well as behavior change by the female commercial sex workers (CSWs) and their male customers in response to the proliferation of the disease in the community. A recent result by van den Driessche P., and Watmough J. (Math. Biosci. 180:29–48, 2002) is utilized to compute the threshold parameters for the local asymptotic stability of the Disease-Free Equilibrium (DFE), by considering the transfers in and out of the infective classes. Numerical examples are used to describe the uniqueness and global properties of the endemic equilibrium when DFE is unstable. Biological interpretation of the results obtained in this work is discussed, as are the implications of our results for the design of public health policies such as targeting strategy to target intervention and control measures toward specific high-risk population groups in order to reduce infections. We show that targeting any one sector of the commercial sex alone for prevention will be difficult to have a decided effect on eradicating the epidemic. However, if the aim of the targeted intervention policy is not eradication of the epidemic but decrease in HIV incidence of a particular high-risk group, then concentrated targeting strategy could be sufficient, if properly implemented. This work also demonstrates the usefulness of the theorem of van den Driessche and Watmough (Math. Biosci. 180:29–48, 2002) in obtaining threshold parameters for complicated infectious diseases models.     

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.     

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

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

Fitting the HIV Epidemic in Zambia: A Two-Sex Micro-Simulation Model

Background

In describing and understanding how the HIV epidemic spreads in African countries, previous studies have not taken into account the detailed periods at risk. This study is based on a micro-simulation model (individual-based) of the spread of the HIV epidemic in the population of Zambia, where women tend to marry early and where divorces are not frequent. The main target of the model was to fit the HIV seroprevalence profiles by age and sex observed at the Demographic and Health Survey conducted in 2001.

Methods and Findings

A two-sex micro-simulation model of HIV transmission was developed. Particular attention was paid to precise age-specific estimates of exposure to risk through the modelling of the formation and dissolution of relationships: marriage (stable union), casual partnership, and commercial sex. HIV transmission was exclusively heterosexual for adults or vertical (mother-to-child) for children. Three stages of HIV infection were taken into account. All parameters were derived from empirical population-based data. Results show that basic parameters could not explain the dynamics of the HIV epidemic in Zambia. In order to fit the age and sex patterns, several assumptions were made: differential susceptibility of young women to HIV infection, differential susceptibility or larger number of encounters for male clients of commercial sex workers, and higher transmission rate. The model allowed to quantify the role of each type of relationship in HIV transmission, the proportion of infections occurring at each stage of disease progression, and the net reproduction rate of the epidemic (R ₀ = 1.95).

Conclusions

The simulation model reproduced the dynamics of the HIV epidemic in Zambia, and fitted the age and sex pattern of HIV seroprevalence in 2001. The same model could be used to measure the effect of changing behaviour in the future.     

Assessing the effects of drug misuse on HIV/AIDS prevalence

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

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.     

Are general practitioners ready to prevent the spread of HIV?

General practitioners are excellently placed to assess a person''s risk of being infected with the human immunodeficiency virus (HIV) and to give advice on reducing that risk. Their attitudes to the acquired immune deficiency syndrome (AIDS) and infection with HIV are, however, unknown. A questionnaire survey of 196 general practitioners in East Berkshire Health District was used to assess general practitioners'' readiness to undertake opportunistic health education to prevent the spread of infection with HIV. Altogether 132 replied. Sixty four of them expressed little interest in health education about HIV, and one in six would not dissent from the notion that AIDS could be controlled only by criminalising homosexuality. Only 75 of them had initiated discussions about HIV with patients. Moreover, many underestimated the risks from heterosexual sex while exaggerating the risks from non-sexual contact.Advice from general practitioners if given extensively might reduce the spread of infection with HIV. How best this may be achieved needs to be considered urgently.     

Transitions from injection-drug-use-concentrated to self-sustaining heterosexual HIV epidemics: patterns in the international data

Background

Injecting drug use continues to be a primary driver of HIV epidemics in many parts of the world. Many people who inject drugs (PWID) are sexually active, so it is possible that high-seroprevalence HIV epidemics among PWID may initiate self-sustaining heterosexual transmission epidemics.

Methods

Fourteen countries that had experienced high seroprevalence (<20%) HIV epidemics among PWID and had reliable data for injection drug use (IDU) and heterosexual cases of HIV or AIDS were identified. Graphs of newly reported HIV or AIDS cases among PWID and heterosexuals were constructed to identify temporal relationships between the two types of epidemics. The year in which newly reported cases among heterosexuals surpassed newly reported cases among PWID, aspects of the epidemic curves, and epidemic case histories were analyzed to assess whether it was “plausible” or “highly unlikely” that the HIV epidemic among PWID might have initiated the heterosexual epidemic in each country.

Results

Transitions have occurred in 11 of the 14 countries. Two types of temporal relationships between IDU and heterosexual HIV epidemics were identified, rapid high incidence transitions vs. delayed, low incidence transitions. In six countries it appears “plausible” that the IDU epidemic initiated a heterosexual epidemic, and in five countries it appears “highly unlikely” that the IDU epidemic initiated a heterosexual epidemic. A rapid decline in incidence among PWID after the peak year of new cases and national income were the best predictors of the “highly unlikely” initiation of a heterosexual epidemic.

Discussion

Transitions from IDU concentrated epidemics to heterosexual epidemics are common in countries with high seroprevalence among PWID though there are distinct types of transitions. Interventions to immediately reduce HIV incidence among PWID may reduce the likelihood that an IDU epidemic may initiate a heterosexual epidemic.     

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.     

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.     

Slowing of the HIV Epidemic in Ukraine: Evidence from Case Reporting and Key Population Surveys, 2005–2012

Background

Ukraine developed Europe''s most severe HIV epidemic due to widespread transmission among persons who inject drugs (PWID). Since 2004, prevention has focused on key populations; antiretroviral therapy (ART) coverage has increased. Recent data show increases in reported HIV cases through 2011, especially attributed to sexual transmission, but also signs of potential epidemic slowing. We conducted a data triangulation exercise to better analyze available data and inform program implementation.

Methods and Findings

We reviewed data for 2005 to 2012 from multiple sources, primarily national HIV case reporting and integrated biobehavioral surveillance (IBBS) studies among key populations. Annually reported HIV cases increased at a progressively slower rate through 2011 with recent increases only among older, more immunosuppressed individuals; cases decreased 2.7% in 2012. Among women <25 years of age, cases attributed to heterosexual transmission and HIV prevalence in antenatal screening declined after 2008. Reported cases among young PWID declined by three-fourths. In 2011, integrated biobehavioral surveillance demonstrated decreased HIV prevalence among young members of key populations compared with 2009. HIV infection among female sex workers (FSW) remains strongly associated with a personal history of injecting drug use (IDU).

Conclusions

This analysis suggests that Ukraine''s HIV epidemic has slowed, with decreasing reported cases and older cases predominating among those diagnosed. Recent decreases in cases and in prevalence support decreased incidence among young PWID and women. Trends among heterosexual men and men who have sex with men (MSM) are less clear; further study and enhanced MSM prevention are needed. FSW appear to have stable prevalence with risk strongly associated with IDU. Current trends suggest the Ukrainian epidemic can be contained with enhanced prevention among key populations and increased treatment access.     

Unequal evolutionary rates in the human immunodeficiency virus type 1 (HIV-1) pandemic: the evolutionary rate of HIV-1 slows down when the epidemic rate increases

HIV-1 sequences in intravenous drug user (IDU) networks are highly homogenous even after several years, while this is not observed in most sexual epidemics. To address this disparity, we examined the human immunodeficiency virus type 1 (HIV-1) evolutionary rate on the population level for IDU and heterosexual transmissions. All available HIV-1 env V3 sequences from IDU outbreaks and heterosexual epidemics with known sampling dates were collected from the Los Alamos HIV sequence database. Evolutionary rates were calculated using phylogenetic trees with a t test root optimization of dated samples. The evolutionary rate of HIV-1 subtype A1 was found to be 8.4 times lower in fast spread among IDUs in the former Soviet Union (FSU) than in slow spread among heterosexual individuals in Africa. Mixed epidemics (IDU and heterosexual) showed intermediate evolutionary rates, indicating a combination of fast- and slow-spread patterns. Hence, if transmissions occur repeatedly during the initial stage of host infection, before selective pressures of the immune system have much impact, the rate of HIV-1 evolution on the population level will decrease. Conversely, in slow spread, where HIV-1 evolves under the pressure of the immune system before a donor infects a recipient, the virus evolution at the population level will increase. Epidemiological modeling confirmed that the evolutionary rate of HIV-1 depends on the rate of spread and predicted that the HIV-1 evolutionary rate in a fast-spreading epidemic, e.g., for IDUs in the FSU, will increase as the population becomes saturated with infections and the virus starts to spread to other risk groups.     

Altered Platelet Monoamine Oxidase-B Activity in Idiopathic Parkinson’s Disease

A case-control study was undertaken to investigate the status of platelet monoamine oxidase-B (MAO-B) activity in Indian cases of idiopathic Parkinson’s disease. A significant increase in the activity of platelet MAO-B was observed in Parkinson’s cases (n = 26) as compared to controls (n = 26). No significant change in the activity of the enzyme was observed while the data was analysed with respect to age, sex and duration of disease. A trend of decrease in platelet MAO-B activity was observed in Parkinson’s cases with respect to stage although the change was not significant. No correlation in platelet MAO-B activity was observed with respect to age and sex in the control subjects. Parkinson’s cases treated with L-DOPA and MAO-B inhibitor exhibited decreased platelet MAO-B activity as compared to drug naive cases and those treated with L-DOPA alone. Interestingly, Parkinson’s cases treated with L-DOPA and amantadine also had lower platelet MAO-B activity as compared to drug naive cases and those treated with L-DOPA alone. Activity of platelet MAO-B in Parkinson’s patients was increased in naive cases and those treated with L-DOPA alone or in combination with other drugs compared to controls. The results of the present study indicate that phenotypic activity of platelet MAO-B is high in Indian Parkinson’s cases. Further, action mechanism of drugs used in the treatment of Parkinson’s disease could be understood by assay of platelet MAO-B activity. It is an interesting observation and may be looked further in large number of cases.     

Controlling the number of HIV infectives in a mobile population

The spread of the human immunodeficiency virus (HIV) depends prominently on the migration of people between different regions. An important consequence of this population mobility is that HIV control strategies that are optimal in a regional sense may not be optimal in a national sense. We formulate various mathematical control problems for HIV spread in mobile heterosexual populations, and show how optimal regional control strategies can be obtained that minimize the national spread of HIV. We apply the cross-entropy method to solve these highly multi-modal and non-linear optimization problems. We demonstrate the effectiveness of the method via a range of experiments and illustrate how the form of the optimal control function depends on the mathematical model used for the HIV spread.     

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.     

The effect of structural behavior change on the spread of HIV in a one-sex population.

Within a preferred mixing type of model for the spread of HIV in a one-sex population, the effects of structural behavior change, that is movements of individuals from one activity class to another, with accompanying changes of contact pattern are investigated. It is concluded that such behavior change makes it more difficult for an epidemic to arise if the contact pattern is of the restricted type, whereas the effect is indeterminate in the proportional mixing case. Some of the problems in analyzing sexual activity data from a population within which this behavior change mechanism is at work are also commented upon.     

Cyclic variation in women’s preferences for masculine traits

Women’s preferences for several male traits, including voices, change over the menstrual cycle, but the proximate causes of these changes are unknown. This paper explores relationships between levels of estradiol, progesterone, luteinizing hormone, follicle stimulating hormone, prolactin, and testosterone (estimated using menstrual cycle information) and women’s preferences for male vocal masculinity in normally cycling and hormonally contracepting heterosexual females. Preferences for vocal masculinity decreased with predicted progesterone levels and increased with predicted prolactin levels in normally cycling—but not hormonally contracepting—women. Adaptive explanations for menstrual variation in women’s preferences for masculine traits are discussed and evaluated in light of these findings.     

Transposable element-medicated evolution of sex: A population genetic model

For a population made up of individuals capable of sexual as well as asexual modes of reproduction, conditions for the spread of a transposable element are explored using a one-locus, two-haplotype model. The analysis is then extended to include the possibility that the transposable element can modulate the probability of sexual reproduction, thus casting Hickey’s (1982,Genetics 101: 519–531) suggestion in a population genetics framework. The model explicitly includes the cost of sexual reproduction, fitness disadvantage to the transposable element, probability of transposition, and the predisposition for sexual reproduction in the presence and absence of the transposable element. The model predicts several kinds of outcome, including initial frequency dependence and stable polymorphism. More importantly, it is seen that for a wide range of parameter values, the transposable element can go to fixation. Therefore it is able to convert the population from a predominantly asexual to a predominantly sexual mode of reproduction. Viewed in conjunction with recent results implicating short stretches of apparently non-coding DNA in sex determination (McCoubreyet al. 1988,Science 242: 1146–1151), the model hints at the important role this mechanism could have played in the evolution of sexuality.     

HIV infection: increase in public awareness and anxiety.

Between the end of September and mid-November 1986 the number of patients who requested antibody testing for human immunodeficiency virus (HIV) at this department increased by over 300%. This increase followed a media campaign that emphasised the potential heterosexual spread of HIV. After pretest counselling roughly one quarter of the women and of the heterosexual men decided not to be tested. The reason given most often by women for testing was previous sexual intercourse with bisexual or possibly bisexual men. Heterosexual men were most often concerned about previous casual encounters or contact with prostitutes. Of the 641 tests for HIV antibody performed during the last three months of 1986, 37 (5-8%) were positive. Because an increasing number of patients are attending sexually transmitted diseases clinics for HIV antibody testing staffing levels in these clinics need to be reappraised now.