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
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 eight coupled nonlinear ordinary differential equations for each risk group of the four risk groups in the model. HSV-2 pathogenesis is represented by three 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 three possible efficacies for a prophylactic HSV-2 vaccine [23
]: reducing susceptibility to infection (VES
), and for those who get infected after the time of vaccination, reducing infectivity during shedding
) and reducing frequency of viral shedding (VEP
) ( and Supplementary Information Appendix
Prophylactic-vaccine efficacies expected to be an output of vaccine randomized controlled trials [1, 2].
We quantified the effect that variability in VES
, or VEP
would have on three summary measures (Appendix
): basic reproduction number in a partially vaccinated population (R0V
), vaccine utility (Φ), and vaccinee infection fitness (Ψ). Summary measure R0V
quantifies the disease transmission sustainability in the partially vaccinated population such that when R0V
<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 due to vaccination and reductions in prevalence and incidence [32
] 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 one (Ψ < 1), many fewer secondary infections are caused by the infected and vaccinated compared to 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 below, 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 modest risk behavior compensation of r =10% for those vaccinated relative to baseline risk behavior. Other assumptions included a uniform average sexual-risk of two partners per year, and life-long protection upon vaccination.
To measure the short-term impact of a vaccine in a high prevalence region, we next presented a more 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
]. The model’s assumptions are listed in along with their references.
Summary of the parameters used in the model.
Although there are substantial variations in the rate and pattern of HSV-2 reactivations [34
], 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 due to increased immune surveillance in the genital tract. Vaccine efficacy of decreasing transmission during shedding VEI
accounts for both of the above possibilities.