Predicting and preventing the emergence of antiviral drug resistance in HSV-2.

Genital herpes, caused by herpes simplex virus, is the most prevalent sexually transmitted disease worldwide. In many developing countries genital herpes is untreated, and in the United States only 10% of cases are treated. We present a mathematical model that we use as a health policy tool to predict the levels of antiviral drug resistance that would emerge, if treatment rates were increased, and to identify the key factors in determining the emergence of drug resistance. We use our results to suggest control measures for herpes epidemics that would prevent the emergence of substantial levels of antiviral drug resistance.

Predicting the unpredictable: transmission of drug-resistant HIV.

We use a mathematical model to understand (from 1996 to 2001) and to predict (from 2001 to 2005) the evolution of the epidemic of drug-resistant HIV in San Francisco. We predict the evolutionary trajectories for 1,000 different drug-resistant strains with each strain having a different fitness relative to a drug-sensitive strain. We calculate that the current prevalence of resistance is high, and predict it will continue to rise. In contrast, we calculate that transmission of resistance is currently low, and predict it will remain low. We show that the epidemic of resistance is being generated mainly by the conversion of drug-sensitive cases to drug-resistant cases, and not by the transmission of resistant strains. We also show that transmission of resistant strains has not increased the overall number of new HIV infections. Our results indicate that transmission of resistant strains is, and will remain, a relatively minor public health problem.

The intrinsic transmission dynamics of tuberculosis epidemics.

In developed countries the major tuberculosis epidemics declined long before the disease became curable in the 1940s. We present a theoretical framework for assessing the intrinsic transmission dynamics of tuberculosis. We demonstrate that it takes one to several hundred years for a tuberculosis epidemic to rise, fall and reach a stable endemic level. Our results suggest that some of the decline of tuberculosis is simply due to the natural behaviour of an epidemic. Although other factors must also have contributed to the decline, these causal factors were constrained to operate within the slow response time dictated by the intrinsic dynamics.

Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco.

Theory is linked with data to assess the probability of eradicating human immunodeficiency virus (HIV) in San Francisco through the use of prophylactic vaccines. The necessary vaccine efficacy levels and population coverage levels for eradication are quantified. The likely impact of risk behavior changes on vaccination campaigns is assessed. The results show it is unlikely that vaccines will be able to eradicate HIV in San Francisco unless they are combined with considerable reductions in risk behaviors. Furthermore, if risk behavior increases as the result of a vaccination campaign, then vaccination could result in a perverse outcome by increasing the severity of the epidemic.

A tale of two futures: HIV and antiretroviral therapy in San Francisco.

The effect of antiretroviral therapy (ART) in preventing human immunodeficiency virus (HIV) infections and averting acquired immunodeficiency syndrome (AIDS) deaths in the San Francisco gay community over the next 10 years was predicted. A transmission model was coupled with a statistical approach that enabled inclusion of a high degree of uncertainty in the potential treatment effects of ART (in terms of infectivity and survival), increase in risky behavior, and rate of emergence of drug resistance. Increasing the usage of ART in San Francisco would decrease the AIDS death rate and could substantially reduce the incidence rate.

Control strategies for tuberculosis epidemics: new models for old problems.

Tuberculosis, although preventable and curable, causes more adult deaths than any other infectious disease. A theoretical framework for designing effective control strategies is developed and used to determine treatment levels for eradication, to assess the effects of noneradicating control, and to examine the global goals of the World Health Organization. The theory is extended to assess how suboptimal control programs contribute to the evolution of drug resistance. A new evaluation criterion is defined and used to suggest how control strategies can be improved. In order to control tuberculosis, treatment failure rates must be lower in developing countries than in developed countries.

Modelling HIV vaccination.

Relatively recently, mathematical models have been applied to issues r elated to HIV vaccination. Significant progress has been made towards understanding how rather ineffective vaccines will perform in trials and in the community, but some areas still need research.

Adaptation at specific loci. IV. Differential mating success among glycolytic allozyme genotypes of Colias butterflies.

Male mating success as a function of genotype is an important fitness component. It can be studied in wild populations, in species for which a given group of progeny has exactly one father, by determining genotypes of wildcaught mothers and of sufficient numbers of their progeny. Here, we study male mating success as a function of allozyme genotype at two glycolytic loci in Colias butterflies, in which sperm precedence is complete, so that the most recent male to mate fathers all of a female's subsequent progeny.--For the phosphoglucose isomerase, PGI, polymorphism, we predict mating advantage and disadvantage of male genotypes based on evaluation of their biochemical functional differences in the context of thermal-physiological-ecological constraints on the insects' flight activity. As predicted, we find major, significant advantage in mating success for kinetically favored genotypes, compared to the genotype distribution of males active with the sampled females in the wild. These effects are repeatable among samples and on different semispecies' genetic backgrounds.--Initial study of the phosphoglucomutase, PGM, polymorphism in the same samples reveals heterozygote advantage in male-mating success, compared to males active with the females sampled. This contrasts with a lack of correspondence between PGI and PGM genotypes in other fitness index or component differences.--Epistatic interactions in mating success between the two loci are absent.--There is no evidence for segregation distortion associated with the alleles of either primary locus studied, nor is there significant assortative mating.--These results extend our understanding of the specific variation studied and suggest that even loci closely related in function may have distinctive experience of evolutionary forces. Implications of the specificity of the effects seen are briefly discussed.

Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework.

The high prevalence of tuberculosis in developing countries and the recent resurgence of tuberculosis in many developed countries suggests that current control strategies are suboptimal. The increase in drug-resistant cases exacerbates the control problems. Currently employed epidemic control strategies are not devised on the basis of a theoretical understanding of the transmission dynamics of Mycobacterium tuberculosis. We describe and discuss a theoretical framework based upon mathematical transmission models that can be used for understanding, predicting, and controlling tuberculosis epidemics. We illustrate how the theoretical framework can be used to predict the temporal dynamics of the emergence of drug resistance, to predict the epidemiological consequences of epidemic control strategies in developing and developed countries, and to design epidemic control strategies.

The supply and demand dynamics of sexual behavior: implications for heterosexual HIV epidemics.

This article investigates the supply and demand dynamics of sexual behavior in a simple epidemiological model of heterosexual transmission of human immunodeficiency virus (HIV). The supply and demand dynamics of sexual behavior are modeled by specifying implicit sexual behavior change (ISBC) mechanisms. These mechanisms specify how males and females modify their rates of sex partner change in response to changes in the availability of the opposite sex. During an epidemic, the availability of both sexes will change owing to recruitment and mortality; consequently, implicit sexual behavior changes will be induced. These behavior changes will be independent of any explicit sexual behavioral changes that may occur as a result of intervention strategies. We investigate four different ISBC mechanisms: the two extremes of the continuum of possible mechanisms (where only one sex changes behavior), as well as two intermediate possibilities (where both sexes change behavior). The results show that the epidemiological effects of these ISBC mechanisms depend upon the transmission speed of the virus. If HIV transmission is slow, the epidemiological effects of the four ISBC mechanisms cannot be differentiated. If HIV transmission is fast, the four ISBC mechanisms differ considerably in the degree to which they modify the gender-specific rates of sex partner change, but the sexual behavioral changes occur too late to significantly decrease the cumulative number of infected persons. However, if HIV transmission is moderately fast, the four different ISBC mechanisms produce significantly different epidemics. The differences between the epidemics, produced by the four ISBC mechanisms, are magnified as the degree of asymmetry between the heterosexual transmission efficiencies increases. We discuss the implications of our results for both the future number of AIDS cases that will be observed in the "real world" and the number of AIDS cases that will be predicted from mathematical models. We also discuss the implications for studies that evaluate the causation of sexual behavior changes.

Sex acts, sex partners, and sex budgets: implications for risk factor analysis and estimation of HIV transmission probabilities.

Many epidemiological studies have identified the number of sex partners as a risk factor for the acquisition of HIV, but few studies have identified the number of sex acts as a risk factor. The seeming lack of importance of the number of sex acts as a risk factor has yet to be explained. In this report we conduct an exploratory data analysis to evaluate the relationship between the number of sex acts and the number of sex partners for heterosexuals. Our results indicate that it may be most appropriate to view sexual activity within a sex budget and resource allocation framework. We use the results (a) to suggest an explanation for why the results from some of the risk factor analysis studies have identified a per partnership but not a per act risk, and (b) to assess the implications of the relationship for the estimation of heterosexual transmission probabilities for HIV.

Effect of differential mortality on risk behavior change in cohort studies.

Recent theoretical work suggests that reductions in aggregate measures of risk behaviors are to be expected during a human immunodeficiency virus epidemic, because mortality is likely to be differential with respect to the level of the risk behavior. We present and apply a methodology for quantifying the effects of differential mortality on risk behavior changes in closed cohort studies. We demonstrate that differential mortality has caused 21% of the observed reduction in the mean, 29% of the observed reduction in the effective average, and 33% of the observed reduction in the variance of a risk behavior in a cohort of gay men.

Loglinear models, sexual behavior and HIV: epidemiological implications of heterosexual transmission.

An analysis is presented of sexual behaviour data from a "random" sample (n = 780) of the adult population of England and Wales. Sex stratified frequency distributions of the reported number of sex partners/time were analysed for heterosexuals, demographic characteristics associated with the number of sex partners/time were identified, and epidemiological parameters (the basic reproductive rate of HIV and the doubling time of the epidemic) were calculated. These analyses suggest that the size of the group at risk for acquiring the virus by heterosexual transmission may be large and that the age of first sexual intercourse (for males and females) is decreasing in younger cohorts. Members of the potential heterosexual at-risk group may be identified by demographic variables such as marital status (males and females) and age (females only), but not by socioeconomic class. The epidemiological implications of our results for the heterosexual transmission of HIV are discussed.

Problems and solutions for the Stop TB partnership.

Recent international efforts for global control of tuberculosis have resulted in a new movement: the Stop TB partnership. One of the operational goals of this movement is based on WHO-determined targets to detect, by 2005, 70% of new smear-positive cases under DOTS, and to successfully treat 85% of these cases. In a paper in the Bulletin of the World Health Organization, Dye and colleagues present data that show the current case-detection rate to be low (only 27%), and that in many areas treatment-success rates are still below the WHO target level. Dye and colleagues predict, by linear extrapolation of these data, that the WHO target of a 70% case detection rate will be achieved by 2013. Here, we discuss why it is unlikely that the WHO global targets for either case detection or treatment success will be reached by 2013, and we also offer some potential solutions.

Could widespread use of combination antiretroviral therapy eradicate HIV epidemics?

Current combination antiretroviral therapies (ARV) are widely used to treat HIV. However drug-resistant strains of HIV have quickly evolved, and the level of risky behaviour has increased in certain communities. Hence, currently the overall impact that ARV will have on HIV epidemics remains unclear. We have used a mathematical model to predict whether the current therapies: are reducing the severity of HIV epidemics, and could even lead to eradication of a high-prevalence (30%) epidemic. We quantified the epidemic-level impact of ARV on reducing epidemic severity by deriving the basic reproduction number (R(0)(ARV)). R(0)(ARV) specifies the average number of new infections that one HIV case generates during his lifetime when ARV is available and ARV-resistant strains can evolve and be transmitted; if R(0)(ARV) is less than one epidemic eradication is possible. We estimated for the HIV epidemic in the San Francisco gay community (using uncertainty analysis), the present day value of R(0)(ARV), and the probability of epidemic eradication. We assumed a high usage of ARV and three behavioural assumptions: that risky sex would (1) decrease, (2) remain stable, or (3) increase. Our estimated values of R(0)(ARV) (median and interquartile range [IQR]) were: 0.90 (0.85-0.96) if risky sex decreases, 1.0 (0.94-1.05) if risky sex remains stable, and 1.16 (1.05-1.28) if risky sex increases. R(0)(ARV) decreased as the fraction of cases receiving treatment increased. The probability of epidemic eradication is high (p=0.85) if risky sex decreases, moderate (p=0.5) if levels of risky sex remain stable, and low (p=0.13) if risky sex increases. We conclude that ARV can function as an effective HIV-prevention tool, even with high levels of drug resistance and risky sex. Furthermore, even a high-prevalence HIV epidemic could be eradicated using current ARV.

Imperfect vaccines and herd immunity to HIV.

A number of prophylactic vaccines against human immunodeficiency virus (HIV) have passed through phase I clinical trials, and phase II clinical trials are now being planned. These vaccines are not expected to be perfect and might fail in a number of different ways. This paper shows how to equate different aspects of imperfection in a prophylactic vaccine in terms of impact upon levels of herd immunity, and hence upon the vaccine coverage required for eradication. Such comparisons reveal that an otherwise perfect vaccine that gives protection which wanes with a half-life of 10 years is only as good as a vaccine that works in 30% of people giving them complete, lifelong protection. The paper goes on to compare predicted patterns of seroconversion that would be observed in clinical trials and in community-wide vaccination campaigns for vaccines that confer the same levels of herd immunity but are imperfect in different ways.

HIV transmission in sexual networks: an empirical analysis.

Risk behaviour and egocentric sexual network data collected from a large random sample of young gay men in San Francisco were analysed to assess the importance of sexual mixing (i.e. sexual networks) in the acquisition of HIV. These data were collected in 1993, during wave one of a longitudinal cohort study of HIV transmission in gay men; the seroprevalence level in the sample was 18%. We identify recent sexual mixing patterns and we demonstrate that seropositives and seronegatives have very different age-stratified sexual mixing patterns. We show that sexual mixing can explain the current seroprevalence patterns in the young gay community; seroprevalence levels in risk groups reflect the degree of sexual mixing with the older (and more heavily infected) age group. Our results suggest that seropositives became infected with HIV not simply owing to an increased rate of acquisition of sex partners, but also as a result of their sexual mixing pattern. We develop and apply a simple methodology that uses the sexual network data in combination with risk behaviour data to estimate the future number of seroconverters. Our methodology is validated by testing our predictions against the observed seroconversion data collected during wave two of the cohort study in 1994. Our analyses empirically demonstrate (for the first time) the significance of sexual mixing as a risk factor for HIV transmission.

Mixing ecology and epidemiology.

Mixing matrices can be used to describe subgroup interactions in mathematical models which have heterogeneity in population structure. A discussion is presented of two different approaches to the formulation of such mixing matrices. The relation between the two different methods is discussed, using examples based upon models of the transmission dynamics of HIV. There follows a discussion of the application of the mixing matrix approach to other areas in population biology, and a complementary overview of recent advances in theoretical ecology that may have applications in theoretical epidemiology.

Parasitic castration: host species preferences, size-selectivity and spatial heterogeneity.

This study investigates host-parasite population dynamics in a marine intertidal community of three barnacle host species (Balanus glandula, Chthamalus fissus andC. dalli). Our paper addresses the following questions: (1) Does prevalence (percentage parasitism) differ among the three host species? (2) What are the spatial and temporal population dynamics within the community? and (3) Does the parasite exhibit size-selective behaviour in any of the three host species? Significant differences in prevalence were found among the three host species; the parasitic castrator (Hemioniscus balani) most heavily infected the least abundant host. Parasitism occurred throughout the year and also showed significant spatial variation.H. balani showed size-selective parasitism inC. fissus, but not inC. dalli. Consequently, the population effects of parasitic castration inC. fissus depend both upon the host population size structure and the intensity of the parasite's size-selectivity.

Impact of antivirals and emergence of drug resistance: HSV-2 epidemic control.

Genital herpes, caused by herpes simplex virus type-2 (HSV-2), affects more people world-wide than any other sexually transmitted disease (STD). Antivirals are effective in decreasing the duration of symptoms and in reducing viral shedding; however, currently antiviral usage is extremely low. Increased usage of antivirals would have a beneficial epidemic-level effect (due to the decreased transmission of drug-sensitive strains) as well as potentially a detrimental epidemic-level effect (if drug-resistant strains emerge and are transmitted). Previously, we have developed a mathematical model that we have used to predict (with a degree of uncertainty) the beneficial and the potential detrimental epidemic-level effects of increased antiviral usage. Here, we use our model to make further predictions about the impact of increasing antiviral usage. We calculate the effect, on individual patients, of antiviral usage in terms of: (1) the decrease in the average number of infectious days per year and (2) an individual's lifetime probability of acquiring permanent drug resistance. We also use our model: (1) to determine the probability of eliminating herpes by antivirals and (2) to quantify the effect of increasing antiviral usage on decreasing HSV-2 prevalence. Our results show that theoretically it would be possible to eliminate herpes epidemics by using a drug that does not cure.