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Sexually Transmitted Diseases:
doi: 10.1097/01.olq.0000258486.81492.a2
Article

Suppressive Valacyclovir Therapy: Impact on the Population Spread of HSV-2 Infection

Williams, John R. DPhil*; Jordan, Jamie C. PharmD†; Davis, E Anne PharmD†; Garnett, Geoffrey P. PhD*

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Author Information

From the *Division of Epidemiology, Public Health and Primary Care, Imperial College London, United Kingdom; and †GlaxoSmithKline, Research Triangle Park, North Carolina

The authors thank Josephine Mauskopf for her assistance in preparing the manuscript.

This study was supported by a grant from GlaxoSmithKline.

Correspondence: John R. Williams, DPhil, Division of Epidemiology, Public Health and Primary Care, Imperial College London, St. Mary’s Campus, Norfolk Place, W2 1PG, London, United Kingdom. E-mail: jr.williams@imperial.ac.uk.

Received for publication December 6, 2005, and accepted November 28, 2006.

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Abstract

Objectives: Recent trial results demonstrate that the transmission probability of HSV-2 in monogamous couples is nearly halved by the use of valacyclovir as suppressive therapy.

Goal: The goal of this study is to understand the potential impact of suppressive valacyclovir therapy on the transmission of HSV-2 within a population.

Study Design: A mathematical model of HSV-2 epidemiology was developed which included suppressive therapy with the efficacy observed in the clinical trial. The model represented HSV-2 spread in an age and sexual activity stratified population where rates of viral shedding declined based on time since infection. The model tested the impact of a range of suppression coverage levels.

Results: Suppressive therapy reduces the population incidence of HSV-2. With coverage rates of 3.2%, the incidence of HSV-2 would be reduced by between 1.8% and 2.8%. Higher coverage rates were estimated to reduce the incidence of new cases up to 13%. Starting suppression closer to the time of infection also reduces the incidence of new cases.

Conclusion: The impact of suppressive therapy on the HSV-2 epidemic is modest at current coverage levels but could be substantially increased with higher rates of diagnosis and a focus on coverage soon after infection.

WITH GLOBALLY INCREASING PREVALENCE1 herpes simplex virus type 2 (HSV-2) currently infects one in four US adults.2,3 As recurrent episodes of viral shedding frequently remain undiagnosed,4–6 85% to 90% of those infected unknowingly place their sexual partners at risk.4 In addition to morbidity caused by HSV-2 lesions, awareness of the condition may cause social and psychological distress.7 Adult treatment patterns may be either episodic in response to symptomatic outbreaks, or continual suppressive therapy may be used to reduce frequency and severity of episodes8 although only 2% of those infected in the USA presently receive suppressive therapy.

Valacylovir suppressive therapy was recently observed to reduce both symptomatic episodes and sexual transmission.9 A randomized controlled trial in HSV-2 discordant couples compared incidence of transmission from infected partners on valacyclovir suppressive therapy and on placebo. A significant reduction in the incidence of HSV-2 seroconversion and subsequent genital herpes disease was demonstrated: over an 8-month period 3.6% of the partners of placebo recipients acquired infection compared with 1.9% of the partners of those treated with suppressive therapy, a reduction of 47%.9 While these data are encouraging, the further question arises regarding the extent to which HSV-2 suppressive therapy can reduce the population incidence and prevalence of infection. This question could be explored either through wide scale observational studies or, as here, using a theoretical framework describing the transmission dynamics of HSV-2 and the predicted impact of changes in the patterns of infectivity brought about by the use of suppressive therapy.

Several such modeling studies have explored the impact of genital herpes treatment or suppression on HSV-2 epidemiology: Blower and colleagues,10 assuming a population homogeneous in sexual behavior, found a substantial impact from widespread treatment of lesions. In a more recent study, Blower et al.11 expanded their epidemiologic model to include subgroups of people with high rates of reactivation and showed a substantial impact on HSV-2 infection rates when a high proportion of people in this subgroup received suppressive therapy. White and Garnett,12 additionally incorporating behavioral heterogeneity, found long-term suppressive therapy for a very high proportion of all those infected was required to observe a major impact on incidence. These models incorporated assumptions that therapy was initiated immediately upon infection, that transmission risk did not vary with age and that risk of acquiring and transmitting infection was independent of partnership duration and therefore greatest in those with many sexual partnerships.

A more recent model by Garnett et al. exploring the impact of an HSV-2 vaccine13 suggests that the assumption that likelihood of transmission to a partner is independent of partnership duration may not be appropriate. This model implicitly included patterns of symptomatic and asymptomatic viral shedding and assumed transmission probability within a partnership depended upon the fraction of time shedding virus and the number of sex acts within the partnership.13 Because of the low transmission probability per act, infected individuals with few partners but many acts per partnership will be more likely to spread infection to each partner than those with many partners but few acts per partner.14 The relative importance of those with many partners but few acts per partner and those with few partners and many acts per partner in the epidemiology of HSV-2 will be dependent upon the transmission probability per act and the distribution of acts per partner. HSV-2 with its low transmission probability per act but long duration of infectiousness will be more greatly influenced by those with a few partners than will an infection like gonorrhea or syphilis, which have high per act transmission probabilities and short durations of infectiousness.14

In this article, we use the model of Garnett et al.,13 with the addition of age structure and suppressive antiviral therapy, to explore the impact of suppressive therapy on the population epidemiology of HSV-2 under reasonably plausible levels of coverage.

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Materials and Methods

Model Structure

A deterministic mathematical model of the spread of HSV-2 was developed and solved numerically. The incidence and prevalence of HSV-2 infection in the presence of different levels and patterns of use of suppressive therapy was compared with the incidence or prevalence in its absence. The mathematical model is illustrated with a flow diagram in Figure 1a, and the equations are presented in Appendix A.

Fig. 1
Fig. 1
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The model assumes the following lifecycle of HSV-2 infection. Upon infection a proportion of the newly infected population, depending upon sex and HSV-1 status, develop primary genital herpes lesions from which they progress to an early, asymptomatic or “latent” stage; the remainder of the newly infected population, enter the “latent” stage directly. To allow for the observed reduction in frequency of symptomatic and asymptomatic episodes of viral shedding as an infection progresses, the course of an infection is divided into 20 consecutive “stages” (Fig. 1a). Symptomatic and asymptomatic shedding episodes are assumed to occur at stage dependent rates, and mean duration of symptomatic episodes is assumed to be longer than asymptomatic episodes.5 In each stage, the amount of time with viral shedding is the product of the frequency of such episodes and mean episode duration.

The model population is stratified by sex, age, and four sexual activity classes. It uses partial differential equations to represent changes in the pattern and spread of infection through age and time. A risk of transmission of HSV-2 infection to noninfected individuals is assumed to be present for sex acts during symptomatic or asymptomatic viral shedding. People with HSV-2 infection are allowed to take viral suppressive therapy for a specified time period at some point in their disease course. The frequency and duration of viral shedding is assumed to be less during suppressive therapy. The model can be run assuming varying degrees of assortative behavior (changing partners across sexual activity groups). The influence of HSV-1 on HSV-2 transmission dynamics is included in the model by assuming that a fraction of the population has experienced HSV-1 infection and hence has a different probability of experiencing a primary disease episode.15 Thus, where diagnosis and delivery of suppressive therapy is in response to such episodes, prior HSV-1 infection will reduce delivery of suppressive therapy and consequently impact on further transmission.

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Model Parameters

The risk of acquiring HSV-2 infection experienced by each susceptible person was assumed to depend on their sexual behavior, the fraction of sexual partners who are infected, the risk of infection with each sex act with an infected partner shedding virus and the fraction of time each partner is shedding virus; this fraction depends on whether the partner is taking suppressive therapy. The data sources and values for each of these model parameters are described below.

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Sexual Behavior

The per susceptible risk of acquiring HSV-2 infection depended, in part, on sexual behavior measured as number of new partners per year, partner preference in terms of age and activity group, and number of sex acts with each partner.

Both male and female populations were subdivided into four different sexual activity classes defined by rates of partner acquisition and numbers of sex acts per sexual partnership. The average numbers of new sexual partnerships formed each year by age group for men and women in the US population16 and in a Newark, NJ population17 were used as a basis to derive mean number of new sexual partnerships per year (Table 1). In addition, the population was divided into four sexual activity groups within each age group according to rates of partner change; those with the highest rate formed the smallest group16, 17 (Table 2). Although the mean rate of partner change varied according to age group (Table 1), for each of the activity groups the rates of partner change remained as the same multiple of the lowest activity class (Class 4) rate for every age group (Table 2).

Table 1
Table 1
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Table 2
Table 2
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Patterns of sexual partnership formation between the different age and activity classes were allowed to vary between the extremes of assortative mixing (choosing a partner within the same age or activity class) and random mixing according to age and activity class.13 For the base-case analysis, degree of assortativeness in the pattern of sexual mixing by sexual activity class was assumed to be nearly random (0.8), and that by age, moderately assortative (0.2).18–21

The number of sex acts over the full duration of a partnership varied according to sexual activity class, with those in the highest activity class, defined according to number of new partners per year, having fewer acts per partner and those with fewer new partners per year more acts with each (Table 3). In the model, transmission is assumed to be instantaneous, collapsing all the acts during a partnership to a particular point in time. The number of sex acts per partner for those with fewer partners was chosen so that model HSV-2 prevalence estimates matched the observed prevalence of HSV-2 in the US while maintaining the observed distribution of number of new partners per year. The use of condoms within a sexual partnership was not modeled explicitly. Condom use was implicitly assumed to be at the same rate as was observed during the clinical trial for valacyclovir.9

Table 3
Table 3
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Fraction of Sexual Partners Who Are Infected

The probability of a sexual partner of a susceptible person being infected was derived from the US prevalence of HSV-2 and was assumed to be 25.6% for women and 17.8% for men2 before suppressive therapy is introduced into the model.

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Fraction of Time Partner Is Shedding Virus

The risk of developing primary HSV-2 disease for a newly infected individual depended on sex and prior HSV-1 status with an average risk of 40%15 (Table 4). The duration of a primary disease episode was assumed to be longer than a subsequent episode. A value of 14 symptomatic or asymptomatic days was used in the model.22,23

Table 4
Table 4
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Mean time since the partner’s infection, as represented by their “stage of infection,” was used to determine the likelihood and duration of viral shedding each year after infection. Twenty-two disease stages were included in the model. Stages 1 and 2 represent the susceptible and primary symptomatic infection periods. The remaining twenty stages are variable in length to allow the model to differentiate between the effects of starting therapy at different time points after the start of the latent infection (see Appendix A).

For each disease stage, the fraction of the time that an individual was shedding virus was assumed to be a function of time since infection. In the first year following initial infection, we assumed that there were six episodes with clinical lesions and that this decayed exponentially with a reduction of 0.8 episodes per year after the first year (a decay rate of 0.22) in line with the initial years in the cohort studied by Benedetti et al.24; the same decay rate was assumed for subsequent years. We assumed that the incidence of asymptomatic shedding episodes was four times that of clinical reactivation episodes (based on fraction of time that shedding is detected by PCR4) but that they are of much shorter duration than symptomatic episodes. The mean duration of symptomatic recurrences was assumed to be 6 days and asymptomatic shedding episodes were assumed to last for on average 2 days.5,25

Suppressive therapy coverage rates were included in the model by assuming a certain percentage of people entering each disease stage were started and remained on suppressive therapy through ensuing stages for a mean period of 3 years. In the base case, the percentage starting on suppressive therapy was assumed to be constant over time since infection and was chosen to match current observed coverage rates and their projection into the future. In sensitivity analyses, the percentage starting on suppressive therapy was assumed to be weighted towards earlier stages and away from later stages so that the percentage for those in the first treated stage was as much as twice as high in earlier disease stages than in the base case.

Suppressive therapy was assumed to reduce the fraction of time the partner is shedding virus by 47% based on the reduction in transmission probability observed in the valacyclovir discordant partners suppression trial.9

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Risk of Transmission per Sex Act During Viral Shedding

The parameter estimates of the risk of transmission per sexual contact during viral shedding were derived from the results of the trial of the impact of suppressive therapy on transmission in HSV-2 discordant couples who were followed for an average of 240 days. During this time, 3.6% of control partners acquired HSV-2 infection compared to 1.9% of those in the treatment arm whose partners were on suppressive therapy, a reduction of 47%.9 Since the trial couples were in longstanding monogamous relationships, the results represent the risk of transmission over a part, not all, of the duration of the sexual partnership, and possibly reflects periods when infected individuals are no longer at their most infectious.

The data from the transmission clinical trial, along with assumptions about the frequency of viral shedding within the trial and number of sex acts, were used to estimate the transmission probability per sex act during viral shedding used in the epidemic model (see steps described in Appendix C). First, based upon the risk of infection within the partnerships during the trial period and the reported number of sex acts, the transmission probability per sex act without suppressive therapy was estimated.

On the basis of an average of 54 sex acts per partnership9 over the duration of follow-up, the transmission probability per act was estimated to be 0.068% without suppressive therapy. This per sex act transmission probability is independent of whether virus is being shed (i.e., it is averaged over all sex acts).

The average per sex act transmission probability was next converted into an estimate of the transmission probability per sex act when virus is being shed. For the trial control population not on suppressive therapy, the fraction of sex acts during which virus is shed (9.18%) was estimated based on average time since diagnosis for the control population and an exponential decay in viral shedding with time since infection as described above. The fraction of time that virus was shed was then used to convert the per sex act transmission probability to a transmission probability per sex act when virus is being shed (0.74%). Based on earlier analyses, it was assumed in the model that the transmission probability from men to women was four times that from women to men.13

For those on suppressive therapy, the reduction in the fraction of time shedding virus that would generate the observed reduction in transmission risk (47%) was estimated. Those on suppressive therapy were assumed to have the same probability of transmission per sex act when virus is being shed (0.74%). Suppressive therapy was, therefore, estimated to reduce the percent of sex acts during which viral shedding occurs to 4.80%.

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Influence of HSV-1

The influence of HSV-1 on the incidence of a primary HSV-2 disease episode was also incorporated in the model with a proportion, 60%, of the US population assumed to be infected with HSV-1.25

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Model Runs

The primary outcome from the model is the percentage change in incidence of new cases of HSV-2 after the introduction of viral suppressive therapy. The impact of suppression with valacyclovir on this primary model outcome was determined using the model for both base-case and alternative scenarios.

In our base-case analyses, we explored possible patterns of coverage of suppressive therapy including maximum feasible coverage. Patterns of coverage depend upon the fraction of infections diagnosed and the fraction of those who are diagnosed starting therapy. The lowest estimate of coverage is 3.2% of all persons who are HSV-2 positive, irrespective of whether serostatus is known, with this level of coverage being reached by 5 years after the introduction of suppressive therapy. This assumes that 19% of infections are diagnosed, 51% of these cases are treated, of which 94% receive some kind of antiviral treatment with 35% of the latter receiving suppressive therapy. It is possible to consider increasing both the diagnosis of infection and the fraction of those infected on treatment that is suppressive. We illustrate in Figure 1b the coverages of suppressive therapy achieved by different diagnosis and treatment targets. Moderate levels of diagnosis and treatment are required to take coverage up to 15%, whereas very high levels are required if coverage is to reach 60%. These higher levels of coverage are included in our exploration of the impact of suppressive therapy.

For the base-case analyses, the model was run assuming that population coverage rates ranged between 3.2% and 15%, the probability of starting suppressive treatment each year was constant, and total suppression duration was for 3 years.

One-way sensitivity analyses were performed changing 1) number of years on suppressive therapy (1–5 years), and 2) probability of starting on suppressive therapy by time since the onset of infection where the probability of starting suppressive therapy was assumed to be higher (either 1.5 or 2 times higher than the base case) in the early years of the infection and correspondingly lower than the base case in the later years (either down to 0.5 times lower than the base case or zero).

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Results

Base Case Results

Results of the base-case US scenario for different percentage coverage with suppressive therapy are shown in Figures 2 and 3; these assume a start time on suppression that is evenly distributed since start of infection and 3 years on suppressive therapy. Figure 2 shows the projected absolute reductions, while Figure 3 shows percentage reductions in the incidence (new cases) of adult HSV-2 infection. A marked initial immediate impact is shown for the first year as a result of the step change in the force of infection arising from the instantaneous application of suppressive therapy for the specified proportion of HSV-2 positive individuals. In ensuing years, as all eligible individuals are already receiving suppressive therapy, any further reductions in incidence will arise simply as a result of the time lag before a new equilibrium is attained in the population as a result of the lowered force of infection. The percentage reduction in new cases ranges from 1.8% after 5 years15 from the start of use of suppressive therapy with a coverage level of 3.2% to a percentage reduction in new cases of 6% after 5 years15 with a coverage level of 15%. Higher levels of coverage provide a higher impact, with a 30% coverage reducing incidence by 30% after 25 years and a 60% coverage reducing incidence by 65% after 25 years.

Fig. 2
Fig. 2
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Fig. 3
Fig. 3
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Early Use of Suppressive Therapy

In Figure 4, the results are presented of a comparison of the percent reduction in incidence rates for a population coverage rate of 3.2% when those starting suppressive therapy each year are evenly distributed across all disease stages (our base case) with alternative scenarios where the distribution of therapy use is weighted moderately (up to 1.5 times more likely) or strongly (up to 2 times more likely) towards patients in the earlier disease stages. Here achieving higher suppressive therapy coverage early in the disease reduces the incidence of HSV-2 by up to 3.4% by year 25 of the program compared with 2.8% when suppression is given uniformly throughout the disease duration.

Fig. 4
Fig. 4
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Increased Duration of Suppressive Therapy

The projected effects on adult HSV-2 incidence rates in the US of changing the duration of suppressive therapy are shown in Figure 5. Increasing the mean time spent on suppression to 5 years for each person starting suppression is a mechanism for maintaining a larger pool of individuals on suppressive therapy, and thus increases overall suppression coverage; the converse applies if the mean time spent on suppression is reduced. With a 5 year mean duration of suppression, the incidence of HSV-2 infection is reduced by 3.5% by year 25 of the program instead of 2.8% (Fig. 5). In contrast, if the mean duration of suppression is reduced to 1 year, the incidence at 25 years is reduced only by 1.3%. Incidence levels were significantly more sensitive to the mean duration of suppressive therapy than to the degree of weighting of suppression towards the early stages of infection.

Fig. 5
Fig. 5
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Discussion

The efficacy of suppressive therapy with valacyclovir at preventing the transmission of HSV-2 infection has been demonstrated in a clinical trial.9 The impact of viral suppressive therapy on the incidence of new cases of HSV-2 in the US population has been calculated in this paper using a mathematical model of the epidemiology of HSV-2. In the base case, which employs a 3.2% coverage rate to reflect the current state of medical treatment in the US, the model estimates little impact on population incidence. In alternative scenarios, increasing suppression coverage targeting suppression earlier in the disease and keeping people on suppression for longer were shown to increase the impact of suppressive therapy on the population incidence of HSV-2.

At first sight, the results may seem unsurprising, with the proportion of cases averted similar to the coverage rate. However, as suppressive therapy provides an estimated 47% reduction rather than complete cessation in transmission, the achievement of, for example 2.8% reduction after 25 years with 3.2% coverage is perhaps more notable than it might seem. The less than 100% efficacy in reducing infectiousness is counteracted by the “herd immunity” provided by reducing infections in the population. It is possible to compare the ratio of infections averted to coverage at a given time after the introduction of suppressive therapy. The optimum impact to coverage ratio of around 1.0 occurs when coverage is in the region of 60%. At coverage levels higher than 60%, the time lag between the starting point of widespread suppressive therapy and maximum impact increases substantially and efficiency is decreased. As coverage approaches 99%, the impact to coverage ratio at 25 years is only about 0.8 to 0.85.

A coverage of 60% requires nearly universal diagnosis of infections combined with very high penetration of treatment, the majority of which is suppressive. A coverage rate of 60% is thus unrealistic. However, with a major effort placed on improving diagnosis and proportion of patients who receive treatment, a coverage rate of approximately 30% might be more feasible and is projected by our model to achieve commensurate reductions in infection.

A number of questions remain about whether the efficacy of the suppressive therapy in reducing transmission in the trial could be higher or lower in clinical practice. First, the average time since diagnosis for the valacyclovir trial population was 8.9 years. Thus, the trial population might have passed the period when they were most likely to have viral shedding and, thus, past when the efficacy of suppression would be at a maximum. In the general population with earlier suppression, where a fraction would be in the more active phase, the results may be improved. Second, the HSV-2 trial inclusion requirement that participants have repeated symptomatic episodes may have selected participants with higher levels of recognition of symptomatic viral shedding and greater concern about transmission to their partner. Efficacy of suppression might be greater in those with lower levels of recognition of HSV-2 symptoms. Third, efficacy of suppressive therapy might be lower in the general population if compliance with suppressive therapy was not as high as in the clinical trial.

In addition, the benefits of suppression in the clinical trial were obtained despite the repeated emphasis on use of condoms for sex acts in the monogamous couples enrolled in the clinical trial. Clearly in nonmonogamous couples, opportunities for infection are greater for the seronegative partner, although this may be balanced by reduced transmission from the seropositive partner. To the extent that condom use is lower in the overall sexually active US population than in the clinical trial population, the benefits of suppressive therapy might be greater.25

The benefits of suppression targeted to people with high levels of viral shedding have recently been shown by Blower et al.11 The authors state that high frequency testing of mucosal sites would be required to identify individuals who have high levels of viral shedding. They suggest as an alternative method of identification, the criterion of recent infection with HSV-2. Our model, illustrates the greater effectiveness at reducing the HSV-2 incidence when starting suppressive therapy in newly infected individuals based on the assumption of more frequent viral shedding at this time.

In the US population, the epidemic of HSV-2 has been extensive leading to a relatively high risk of infection per susceptible person. This is a challenge that suppressive therapy would have to counter. In other countries, with lower prevalence and in combination with other strategies such as increased symptom recognition and condom use the impact of viral suppressive therapy may be greater.

Epidemic models are a valuable way to estimate the long-term impacts of alternative genital herpes disease management strategies. However, they are limited by the scarcity of data on sexual activity and viral shedding patterns.

Based on estimates that only one in five infections is diagnosed and only half of these treated, our model estimates that the impact of suppressive therapy on HSV-2 epidemic in the US will be small. The magnitude of benefit is limited by the low suppressive therapy coverage rate, which is primarily driven by the percent of patients who are diagnosed and who receive some kind of treatment. Were the medical community able to place significant effort on improving diagnosis and treatment rates and in turn make it possible to achieve coverage rates closer to 30%, our model estimates that a commensurate and meaningful reduction in HSV-2 incidence would result. Though intrinsically unlikely to exceed that of an effective vaccine, clearly, the epidemiologic impact of valacyclovir suppressive therapy could be substantially increased by using suppressive therapy in as many infections as possible, as early as possible after infection onset, and for as long as possible.

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Appendix A
Equations Defining the Epidemic Model

The sex, age, and activity structured model is defined by the following set of partial differential equations in which the first superscript corresponds to HSV-1 status, the second to infection stage, the third to therapy status, the first subscript to sex, and the second to sexual activity class:

Susceptible unvaccinated

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Primary infection

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Initial latent stage

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Stage at which treatment can start

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Further progression

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Final stage qmax

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Boundary conditions

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Force of infection with age as a continuous variable

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However, for simplicity in parameterizing patterns of sexual partner change and mixing about age we discretize age into 5-year age blocks represented by the subscript i. Thus, the force of infection is calculated in the following expression:

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Where

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with jB and jT and iB and iT the lower and upper bounds of the age group respectively.

The incidence of vertical transmission can be derived from the age specific fertility and the infectiousness of women:

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The proportion of acts during postprimary infection which transmit is

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Model Parameter List

α Rate of recovery per year by sex and HSV-1 status etc.

β Transmission probability per sex act from sex k′ to sex k

γ Rate per year of reactivation by sex and HSV-1 status

ϵ Proportion of assortative mixing

θ Rate of transition from latent stage q to stage q + 1

λ Force of infection

μ Mortality rate

π Proportion entering sexually active population with HSV-1 infection (h = 1) and without HSV-1 infection (h = 2)

ρ Probability for someone sex k activity l that a partner is in group m

ς Recovery rate from primary disease

τ, τ′ Rate of starting or stopping viral suppression

ς Proportion recruited into sexual activity groups

ψ Proportion of those infected developing primary disease

a Proportion developing asymptomatic infection and shedding virus

b Proportion developing asymptomatic infection and shedding virus

c Rate of sex partner change/year

g Fraction suffering recurrences after primary disease or on initial asymptomatic infection

n Number of sex acts per partnership between people in activity groups l and m

q Postprimary infection stage

s Proportion of sex acts remaining with disease

F Proportion shedding

N Number of people of sex k′ in activity group m

X State variables

Y Numbers with chronic infection Cited Here...

Table. No caption av...
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Appendix B:

Rates of Transition Through Model Stages

Duration of each stage was defined assuming 20 postinitial infection stages and a linear decrease by stage in the rate of transition between stages, with stages 3 to 6 inclusive corresponding to the first year of infection (mean stage duration was defined as 1/[transition rate] years). This allowed the proportion shedding in each stage to be calculated by adjusting the initial proportion shedding p0 so that the mean proportion shedding during the first year of infection, pyear1, was 84 days/365 days 22,24 in the following expression:

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where the rate of decay in shedding with time, r = 0.223,24 and with t being time since infection, and τs the time in stage s.

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Appendix C: Calculation of Risk of Transmission per Sex Act During Shedding

The data from the transmission clinical trial, along with assumptions about the frequency of viral shedding within the trial and number of sexual contacts, were used to estimate the transmission probability per sexual contact during viral shedding used in the epidemic model as follows. First, based upon the cumulative risk of infection within the partnerships (β) and the reported number of sex acts (a) we derived an estimate of the transmission probability per unprotected sex act (φ) without suppressive therapy. Since the cumulative risk is given by the binomial probability:

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per sex act transmission probability is given by

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On the basis of an average of 54 sexual contacts per partnership16 over the duration of follow up, the transmission probability per act without suppressive therapy was estimated to be 0.068%.

These per sex act transmission probabilities are independent of whether virus is being shed (i.e., they are averaged over all sex acts). However, assuming that virus is shed for a given fraction of time in control partnerships (s) it is possible to calculate a transmission probability per sex act when virus is being shed and similarly the reduction in shedding that would generate the observed reduction in hazard for the partners on suppressive therapy. In this case we defined a likelihood of transmission (φ′) per unprotected sex act when virus is being shed, and a fraction of time (s) the virus is being shed in the initially infected partner:

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If we assume that suppressive therapy reduced the fraction of time that virus is shed to a new residual fraction (Δ) of its original value, then we can revise this equation for the transmission probability per sexual partnership when suppressive therapy is being used:

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An alternative interpretation would be that the transmission risk per act when virus is being shed is altered to a residual fraction δ. In this case the equation would be

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This generates almost identical results for parameter values similar to those observed.

Assuming that time since diagnosis corresponds to time since infection for the people in the control group in the trial and an exponential decay in viral shedding with time since infection as described in the main text, we estimated that virus was being shed during 9.18% of sexual contacts for those not on suppressive therapy. Suppressive therapy was assumed to reduce the percent of sexual contacts during which viral shedding occurs to 4.31%. An average transmission probability when virus is shed of 0.74% of sex acts is consistent with these figures. Based on earlier analyses it was assumed that the transmission probability from men to women was four times that from women to men.22,26 Cited Here...

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