Herpes simplex virus type-2 (HSV-2) infection is highly prevalent in sub-Saharan Africa^{1–10} and across the globe.^{11–13} The broad spread of HSV-2 is further complicated by the common mode of transmission and the synergistic epidemiologic pattern that it shares with human immunodeficiency virus (HIV). HSV-2 positive and HSV-2/HIV coinfected persons have a higher risk of contracting HIV infection,^{14–16} and of transmitting HIV,^{17,18} respectively. The estimated proportion of HIV infections attributable to HSV-2 in areas with a high HSV-2 prevalence, such as sub-Saharan Africa, is approximately 25%.^{19} Therefore, controlling HSV-2 could have a substantial population-level effect on HIV incidence in sub-Saharan Africa.

HSV-2 vaccines have gained focus after the recent failure of HSV-2 suppression therapy to limit HIV spread in 3 randomized controlled trials.^{20–22} An ideal HSV-2 prophylactic vaccine would induce sterilizing immunity and prevent HSV-2 acquisition in susceptible populations. Meanwhile, imperfect^{23} prophylactic HSV-2 vaccines could partially reduce HSV-2 acquisition in vaccinees, and/or partially reduce infectivity of those who get infected after vaccination, by either reducing their shedding frequency or viral load during shedding episodes. Because the effectiveness of a licensed vaccine is not known, mathematical modeling can determine the population-level effect of various combinations of protection regarding 3 biologic aspects of disease: susceptibility, shedding frequency, and infectivity while shedding.

Two prophylactic recombinant vaccines have completed phase III clinical trials and achieved limited success in protecting against HSV-2 acquisition.^{24–26} A third vaccine that uses the full-length of gD with bupivacaine recently underwent successful testing in a safety and immunogenicity trial.^{27}

Because the current HSV-2 strategies target reduction in shedding as a primary outcome along with the classic target of susceptibility reduction,^{26,28} the results of future clinical trials of vaccines will provide vaccine efficacies in terms of reduction in susceptibility and shedding frequency. These efficacies are obtained for individuals during the short period of the clinical trial. Therefore, the criteria for a favorable vaccine at the population level will not be directly obtained from these trials.

Our goal in this study was to estimate the population-level effects of prophylactic HSV-2 vaccines using mathematical modeling. We introduced a model for HSV-2 in which the different aspects of prophylactic HSV-2 vaccines were parameterized to study their effects. Although previous HSV-2 models^{29,30} studied population-level impact of HSV-2 vaccines in the United States, we estimated the effect of vaccination at the population level in a representative setting of hyperendemic HIV and HSV-2 epidemic in sub-Saharan Africa (Kisumu, Kenya). The effect of vaccination was estimated in terms of impact on prevalence, incidence, and infections averted per vaccination procedure.

#### MATERIALS AND METHODS

We constructed a deterministic compartmental model calibrated to describe HSV-2 transmission in presence of vaccination in different populations but focused most of our analyses on a representative sub-Saharan African population (Kisumu, Kenya). The Supplementary Information Appendix (online only, Supplemental Digital Content 1, http://links.lww.com/OLQ/A7), contains the details of the model and its parameterization. The model stratifies the population into compartments according to vaccination status (vaccinated or unvaccinated), sexual risk group, and stage of HSV-2 infection using 8 coupled nonlinear ordinary differential equations for each risk group of the 4 risk groups in the model. HSV-2 pathogenesis is represented by 3 stages: primary, latent (no shedding), and reactivated (shedding) stages. HSV-2 is of a chronic nature; therefore, the latent and reactivated stages cycle through the entire life of the infected. The shedding frequency is assumed to be at 14% of each cycle.^{31} The baseline transition rates of progression from primary to latent, latent to reactivated, and reactivated to latent are derived from the duration of each stage and the shedding frequency, and they are 18.3, 4.7, and 28.6 per year, respectively. Baseline transmission probabilities per coital act per HSV-2 primary, latent, and reactivated stages are 0.01, 0.00, and 0.01, respectively.^{19} We considered 3 possible efficacies for a prophylactic HSV-2 vaccine^{23}: reducing susceptibility to infection (VE_{S}), and for those who get infected after the time of vaccination, reducing infectivity during shedding episodes (*VEI*), and reducing frequency of viral shedding (*VEP*) (Table 1 and Supplementary Information Appendix, online only, Supplemental Digital Content 1, http://links.lww.com/OLQ/A7).

We quantified the effect that variability in *VES, VEI*, or *VEP* would have on 3 summary measures (Appendix, Supplemental Digital Content 1, http://links.lww.com/OLQ/A7): basic reproduction number in a partially vaccinated population (*R*_{0V}), vaccine utility (φ), and vaccinee infection fitness (ψ). Summary measure *R*_{0V} quantifies the disease transmission sustainability in the partially vaccinated population such that when *R*_{0V} <1 the vaccine would diminish HSV-2 chains of transmission in the general population. Summary measure φ quantifies the utility of the vaccine through relative reduction in the basic reproduction number because of vaccination and reductions in prevalence and incidence^{32,33} such that when φ >0 equilibrium values of prevalence, incidence (absolute number of incident infections per year), and incidence rate (number of incident infections per susceptible individual per year) are reduced from their respective values without vaccination. Finally, vaccinee infection fitness (ψ) is a measure of the heterogeneity in transmission introduced by vaccination^{33} such that when ψ is considerably below 1 (ψ <1), many fewer secondary infections are caused by the infected and vaccinated compared with infected and unvaccinated populations.

Our summary measures are appropriate tools for estimating the long-term effect of a partially efficacious vaccine. To derive each summary measure analytically, we simplified our mathematical model for a population with uniform risk behavior. In the quantitative predictions presented later, for each vaccine efficacy scenario, we assumed universal adolescent vaccination (*f* = 100%). Although it has never been proven that risk behavior compensation could accompany HSV-2 vaccination, for completeness we assumed a moderate risk behavior compensation of *r* = 10% for those vaccinated relative to baseline risk behavior. Other assumptions included a uniform average sexual-risk of 2 partners per year and life-long protection upon vaccination.

To measure the short-term effect of a vaccine in a high prevalence region, we presented a detailed mathematical model that included heterogeneous risk behavior.

This version of the model was fitted to Kisumu's prevalence data. We chose the parameter values of the model according to the best available empirical evidence of the biology and epidemiology of HSV-2 infection. In particular, recently established detailed empirical data about the pattern of HSV-2 reactivation in its clinical and subclinical form,^{34} played a central role in our assumptions. The behavioral parameters in the model are informed by the measurements of the Four City study.^{35–37} The model's assumptions are listed in Table 2 along with their references.

Although there are substantial variations in the rate and pattern of HSV-2 reactivations,^{34,42,43} the critical parameter is the shedding frequency irrespective of whether the pattern is that of short but frequent reactivations or long but less frequent ones^{19}; because by assumption the infectious state is manifested by shedding the virus and irrespective of the pattern of shedding. The assumption that all shedding is associated with possible transmission has not been validated, however. It is possible that only shedding above a certain quantitative threshold (such as 1000 HSV copies DNA/mL) commonly leads to transmission. A vaccine may also decrease infectivity of individual virions irrespective of their number because of increased immune surveillance in the genital tract. Vaccine efficacy of decreasing transmission during shedding *VEI* accounts for both of the aforementioned possibilities.

#### RESULTS

##### Summary Measures of Vaccine Effect at the Population Level

Increasing any of the vaccine efficacies of reducing susceptibility (*VES*), shedding frequency (*VEP*), or infectivity during shedding (*VEI*) from 0% to 100% produces steadily increasing positive vaccine utility (φ), suggesting an increasingly beneficial vaccine at the population-level in terms of prevalence and incidence (Fig. 1). Increasing any of the vaccine efficacies also produces steadily decreasing basic reproduction number with vaccination (*R*_{0V}), suggesting more limited infection transmission and a decreasing fraction of the partially vaccinated population who can sustain the transmission of the disease. The vaccinee infection fitness (ψ) does not depend on the vaccine efficacy of reducing susceptibility (*VES*), but decreases steadily with increasing the vaccine efficacies *VEP* or *VEI*. The steadily decreasing infection fitness manifests an increasing effect on the transmission dynamics of the disease by decreasing the number of secondary infections produced by infected and vaccinated individuals compared with infected and unvaccinated individuals in the partially vaccinated population.

Figure 1A displays that for a vaccine with a limited efficacy of reducing shedding frequency of *VEP* = 10% and no efficacy in reducing infectivity i.e., *VEI* = 0%, the basic reproduction number with vaccination (*R*_{0V}) crosses the threshold of sustainability around a high value of the vaccine efficacy of reducing susceptibility of *VES* = 75%. The vaccinee infection fitness remains flat at ψ = 0.99 for all values of the vaccine efficacy of reducing susceptibility to HSV-2. These scenarios show that for a desirable population-level impact, an HSV-2 vaccine must reduce susceptibility by 75% if its effects on reducing shedding and infectivity during shedding in a vaccinated and infected host are limited.

However, as shown in Figure 1B, if *VEI* = 0% as in Figure 1A, an increase in *VEP* to 75% renders the vaccine more beneficial at smaller values of *VES*. The vaccinee fitness drops to 0.28 due to the higher *VEP* and the basic reproduction number with vaccination drops below sustainability threshold for all values of *VES*. These results suggest that one way to accomplish desirable population-level effect is to have a vaccine that reduces shedding frequency beyond 75% in addition to its protective effects against acquisition. The long-term benefits of such a vaccine are substantial even at low values of the vaccine efficacy of reducing susceptibility.

In contrast to Figures 1A and B, Figures 1C and D show how ψ decreases steadily by increasing *VEP* at 2 different values of *VES* of 10% and 30%, respectively. The more optimistic scenario shown in Figure 1D with *VES* = 30% and at *VEP* = 75% predicts that the vaccine will be 8% more beneficial in terms of φ than if the vaccine has only 10% efficacy of reducing susceptibility as in Figure 1C (φ increases from 0.74 to 0.80). Also *R*_{0V} drops from 0.89 to 0.70 suggesting less sustainable disease in the population. The population-level effects at *VES* = 10% and *VEP* = 10%, and *VES* = 30% and *VEP* = 75%, can increase further if the vaccine also has non-negligible protection against infectivity (*VEI*) as shown in Figures 1E and F, respectively. It is notable that *VEI* must be very high (>70%) if *VES* = 10% and *VEP* = 10% in order for the sustainability threshold to be crossed.

However, our predictions show that a vaccine with efficacy of reducing shedding frequency as high as 75% combined with efficacy of reducing susceptibility as low as 30% would be definitely and substantially beneficial in a population with an average of 2 sexual partners per year. Even though such an imperfect vaccine would not stop new HSV-2 infections among the vaccinated because of its low efficacy of reducing susceptibility, it still would effectively effect the dynamics of disease transmission. Moreover, it would render the number of secondary infections produced by infected and vaccinated individuals to one-quarter of the number produced by those infected and unvaccinated. The moderate risk compensation assumed here at 10% will not undermine the utility of such vaccine.

##### Simulated Intervention

We next considered the epidemiology of intervention using vaccines in Kisumu, Kenya, over a period of 10 years starting in 2010. We explored 2 schedules of vaccination: universal vaccination of adolescents as they enter sexual activity and mass vaccination of the sexually active population achieved within a year. We assumed vaccination using a vaccine with efficacy of reducing susceptibility to HSV-2 of *VES* = 30%, efficacy of reducing HSV-2 shedding of *VEP* = 75%, and no protection against infectivity i.e., *VEI* = 0%. Furthermore, we assumed no risk compensation (*r* = 0) as perception of risk to HSV-2 infection is probably not a strong determinant of risk behavior compared with HIV in sub-Saharan Africa. By the year 2020, the adolescent vaccination would reduce HSV-2 prevalence by 3%, HSV-2 incidence and incidence rate would decrease by 21% and 23%, respectively. A total of 3842 HSV-2 infections would be averted by 2020 in Kisumu (an adult population size of 200,000) using universal adolescent vaccination.

In contrast, mass vaccination of all susceptible persons aged 15 to 49 by the year 2020 would reduce HSV-2 prevalence, incidence, and incidence rate by 7%, 30%, and 35%, respectively. A total of 8430 HSV-2 infections would be averted by 2020 in Kisumu. Figures 2A and B display how the effect of adolescent vaccination on prevalence and incidence rate would be less than mass vaccination and would take longer to accrue due to the delay time in achieving higher vaccination coverage. As shown in Figure 2A, although the impact of either schedule of vaccination on prevalence increases over time, the effect is initially moderate. Equilibrium values of prevalence, incidence, and incidence rate would be achieved beyond year 2050 and would represent a percentage decrease of 69%, 69%, and 82%, about baseline values, respectively. This delay is due to the lifelong nature of HSV-2 infection where the effect on prevalence will not be substantial until the already infected population ages and leaves the sexually active population. An additional cause of the delay is that the beneficial effects of *VEP* and *VEI* take longer to disseminate in a population compared to that of *VES*.

Furthermore, we investigated the 10-year effect of mass vaccination intervention in 2010 on HSV-2 excess prevalence (prevalence postintervention subtracted from prevalence preintervention), and computed the number of vaccinated per infection averted in populations at various levels of total HSV-2 prevalence preserving the hierarchy of sexual risk of Kisumu's settings (Fig. 3). The excess prevalence is large when baseline prevalence in the absence of vaccination is high; the number of vaccinated per infection averted increases when HSV-2 prevalence in the absence of vaccination is lower. Eighteen vaccination procedures are needed per infection averted at high HSV-2 prevalence of 52%, projected for Kisumu, Kenya, in 2010 which is representative of a large part of sub-Saharan Africa. This is compared to 64 vaccination procedures per infection averted for the United States at HSV-2 prevalence of 17%.

We investigated the synergy between the vaccine efficacies of reducing shedding frequency and reducing susceptibility over time. The definition of synergy is delineated in the Supplementary Information Appendix (online only, Supplemental Digital Content 1, http://links.lww.com/OLQ/A7). We found that (not shown) the effects of the 2 efficacies *VES* and *VEP* to be generally synergistic particularly in the long term. Larger value for either parameter leads to enhanced synergy. However in the short term, a slight redundancy between the 2 interventions is present while the transmission effects of *VEP* accrue in the population. The effect of *VEP* in a population is substantial only after substantial number of people are vaccinated and subsequently infected with HSV-2.

Finally, we performed sensitivity and uncertainty analyses to assess the robustness and sensitivity of our short- and long-term predictions to uncertainty in the vaccine efficacies, sexual behavior parameters and risk group structure, HSV-2 progression parameters, and risk compensation behaviors (Supplementary Information Appendix, online only, Supplemental Digital Content 1, http://links.lww.com/OLQ/A7). We found that our short-term predictions for the effect of vaccine intervention by 2020 in terms of excess prevalence, relative reduction in incidence, and excess incidence rate are largely invariable to the assumed variations in the vaccine efficacies of reducing infectivity and shedding frequency, or behavioral and HSV-2 progression parameters. However, the predicted excess prevalence and incidence rate as well as the reduction in incidence show substantial variability in the short-term to the assumed variation in the vaccine efficacy of reducing susceptibility. This is expected as in the short term it is mainly *VES* that is driving the effect of the vaccine.

Over the long term, substantial sensitivity in our predictions are observed about the assumed variations in the vaccine efficacy of reducing shedding frequency and in the shedding frequency itself, respectively. The long-term sensitivity results attest to the role of *VEP* and shedding frequency in determining the course of HSV-2 transmission in the presence of vaccination over a time horizon of few decades.

#### DISCUSSION

Our approach enables prediction of the potential population effect of vaccines immediately after clinical trial results are available. In the case of HSV-2, a vaccine candidate's efficacy measures are likely to become available after a clinical trial: vaccine efficacy of reducing susceptibility (*VES*) is often the primary outcome measure of most vaccine trials; but because current HSV-2 strategies also target reduction in shedding,^{26,28} it is now standard practice to measure the effect of all HSV-2 interventions on shedding frequency, and therefore, a detailed assessment of vaccine efficacy of reducing shedding frequency (*VEP*) will be available as well; any effect on transmissibility during shedding as measured by *VEI* will be difficult to obtain because a quantitative virologic threshold for HSV-2 transmission is not currently known. Nevertheless, if it is assumed that *VEI* is low as in our Kisumu simulations, then the other 2 measures can represent a worse case scenario for a vaccine's effect in a population.

Our results underscore the relative effect of each of the vaccine efficacies at the population level, which is an important aspect of studying any imperfect vaccine. Although the effect of *VES* at the population-level is immediate, the effects of *VEP* and *VEI* accrue over time. When *VES* is large, a small number of infections occur among vaccinees in the short term leaving little room for *VEP* to effect HSV-2 infectious spread. However, in the long term there is a synergy between the effects of the 2 efficacies and they compliment each other.

Our study has several limitations. First, it does not address heterogeneity in shedding frequency in the general population. Ranges of shedding frequency among HSV-2 infected persons are from 0% to 78%.^{44} In addition, there is evidence that frequent shedders may serve as “super spreaders” irrespective of sexual risk behavior.^{45} Therefore, the effect of high *VEP* in this group would decrease the absolute amount of shedding more substantially than in infrequent shedding groups. Future mathematical models of vaccine efficacy would benefit from independent stratification of sexual risk behavior and shedding frequency into subgroups. In addition, a true quantitative surrogate measure for transmission risk has not been identified as of yet. We account for the possibility that low-copy shedding may not be associated with transmission risk in our sensitivity analysis where we decrease shedding frequency, and also by incorporating *VEI*, which is a measure of vaccine efficacy regarding infectivity during shedding only.

Finally our model does not incorporate age-dependent targeting of interventions nor does it allow for differences by sex in transmission probability per coital act.

In summary, if HSV-2 vaccines that are currently under development have limited efficacy against HSV-2 acquisition, but have substantial efficacy of reducing shedding frequency or infectivity, then such vaccines are likely to have a high effect on HSV-2 incidence and prevalence over several decades, and will have a more immediate strong effect on HSV-2 incidence, particularly in high prevalence populations. Conversely, a vaccine that has a moderate effect on acquisition but no effect on viral shedding is unlikely to be as effective. It is therefore imperative, that all future vaccine studies evaluate the effect that a vaccine has on genital viral shedding.