1. Epidemiology and Global Health
  2. Microbiology and Infectious Disease
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Integrating between-host transmission and within-host immunity to analyze the impact of varicella vaccination on zoster

  1. Benson Ogunjimi Is a corresponding author
  2. Lander Willem
  3. Philippe Beutels
  4. Niel Hens
  1. University of Antwerp, Belgium
  2. Hasselt University, Belgium
  3. University of New South Wales, Australia
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Cite as: eLife 2015;4:e07116 doi: 10.7554/eLife.07116

Abstract

Varicella-zoster virus (VZV) causes chickenpox and reactivation of latent VZV causes herpes zoster (HZ). VZV reactivation is subject to the opposing mechanisms of declining and boosted VZV-specific cellular mediated immunity (CMI). A reduction in exogenous re-exposure ‘opportunities’ through universal chickenpox vaccination could therefore lead to an increase in HZ incidence. We present the first individual-based model that integrates within-host data on VZV-CMI and between-host transmission data to simulate HZ incidence. This model allows estimating currently unknown pivotal biomedical parameters, including the duration of exogenous boosting at 2 years, with a peak threefold to fourfold increase of VZV-CMI; the VZV weekly reactivation probability at 5% and VZV subclinical reactivation having no effect on VZV-CMI. A 100% effective chickenpox vaccine given to 1 year olds would cause a 1.75 times peak increase in HZ 31 years after implementation. This increase is predicted to occur mainly in younger age groups than is currently assumed.

https://doi.org/10.7554/eLife.07116.001

eLife digest

The itchy-scratchy misery of a chickenpox was until recently a rite of passage for children around the world. The varicella-zoster virus causes chickenpox infections. This virus persists in small numbers in nerve cells for many years after infection, and can reactivate from these cells. Often this reactivation causes no symptoms, but sometimes it results in a painful skin condition called shingles (or herpes zoster), especially in older adults.

Some countries—including the United States, Australia, Taiwan and Greece—have virtually wiped out childhood cases of chickenpox by requiring that children be vaccinated against the varicella-zoster virus. But some countries have hesitated. One reason for this hesitation is that exposure to individuals with a chickenpox infection helps boost the immunity of individuals who have previously been infected. This may help reduce the likelihood of these people developing shingles later in life. So, some countries have worried that chickenpox vaccinations might inadvertently increase the number of shingles cases. To assess this risk, many scientists have created computer models, but the models have some limitations.

Now, Ogunjimi et al. report a new individual-based model to assess the effect of childhood varicella vaccination on shingles cases that factors in the immune responses to varicella infection. The model suggests that re-exposure to the varicella virus through contact with infected people would only provide extra protection for about two years; this is much shorter than previous predictions that suggested it might last 20 years. The model also predicts that implementing a varicella vaccination program for children would almost double the number of shingles cases 31 years later. But this increase would be temporary.

The predicted increase in shingles cases is likely to disproportionately occur among 31- to 40-year-olds. This is unexpected because most previous models predict that older age groups would bear the brunt of a rise in shingles, but this younger population would be less likely to develop lasting complications of shingles. Together, these findings may allay some fears about implementing childhood varicella vaccination programs by showing that the benefits of re-exposure are limited.

https://doi.org/10.7554/eLife.07116.002

Introduction

Varicella-zoster virus (VZV) causes the itching, erythematous vesicular disease called varicella or chickenpox, mainly during childhood, and remains latent in neural ganglia afterwards. Latency can then be interrupted by episodes of (primarily subclinical) reactivation of VZV as shown by the detection of VZV in saliva or blood from otherwise healthy individuals (Schünemann et al., 1998; Nagel et al., 2011). VZV reactivations may also cause herpes zoster (HZ), which presents clinically as a painful dermatomal rash. HZ occurs most frequently in individuals with a drastically declined cellular immune status (Dolin et al., 1978), but ageing itself is often assumed to substantially reduce resilience of the VZV-specific immune response (Miller, 1980; Berger et al., 1981; Levin et al., 2003, 2008). Recent research supports the hypothesis that waning of VZV cellular mediated immunity (CMI) by age is also influenced by cytomegalovirus (CMV) infection (Ogunjimi et al., 2014).

Effective and safe pediatric vaccines against varicella exist and have been universally implemented in some countries including the US, Australia, Greece, Germany, Japan and Taiwan (Marin et al., 2008). However, in many other countries policy makers have been hesitant to introduce childhood VZV vaccination due to the general population's perception of varicella as a relatively mild disease, as well as the so-called exogenous boosting hypothesis (Hope-Simpson, 1965; Ogunjimi et al., 2013). This hypothesis is based on the concept of the secondary immune response and assumes that boosting of VZV-CMI occurs upon re-exposure to varicella. Boosted VZV-specific cellular immunity would subsequently reduce the risk of VZV reactivation and thence HZ. The introduction of widespread childhood VZV vaccination would reduce opportunities for varicella re-exposure and could therefore increase HZ incidence, as shown in model-based projections (Schuette and Hethcote, 1999; Brisson et al., 2000; Bilcke et al., 2013). Although current data on HZ-incidence post introduction of childhood VZV vaccination has caused controversy, a systematic review rating the quality of the evidence, concluded that exogenous boosting exists, but that its population-wide effect after widespread childhood VZV vaccination remains highly uncertain (Ogunjimi et al., 2013). One of the main points of criticism on current predictions by deterministic VZV simulation models is the entanglement of exogenous boosting, waning of immunity, immunosenescence and reactivation undermining the possibility of estimating the magnitude and duration of exogenous boosting accurately. A concern is that these entangled parameters can be chosen to fit these models well to observed HZ incidence data, but that they are too artificial to allow real and verifiable biological interpretations. This leads to currently unverifiable and potentially poor predictions of VZV dynamics beyond the fitted equilibrium states. An additional, hitherto ignored uncertainty, is the potential occurrence of endogenous boosting by subclinical VZV reactivation. Indeed, some studies have shown VZV to reactivate subclinically both in healthy individuals, immunocompromised and stressed individuals (Schünemann et al., 1997; Mehta et al., 2003; Nagel et al., 2011). However, the effect on VZV-CMI has not yet been quantified.

In the current paper, we describe the first individual-based VZV model, explicitly combining within and between-host dynamics. This model is based on experimental viro-immunological data and allows an accurate estimation of the exogenous boosting characteristics and explicit insertion or validation of experimental data.

Results

VZV IBM parameter prediction

Using a step-wise algorithm we initially found eight unique parameter sets leading to a reasonable fit of Belgian HZ incidence data (see Table 1 and Figure 1). All best-fitting parameter sets were based on boosting scenario 3 (predefined exponential loss of boosted VZV-CMI). Seven of these models include exogenous boosting (defined as an exponential decay) with a peak value of 1.3, a boosting duration ranging between 2 and 15 years, no endogenous boosting, a weekly VZV reactivation probability and an annual VZV-CMI loss (= waning) estimated to be 1–1.5% and 1–2%, respectively. We note that although the fits are excellent for the most relevant age groups, 25 years and older, they are less suited to predict HZ incidence for younger ages. One model predicted a peak boosting value of 2.5, a boosting duration of only 1 year and no endogenous boosting. Although this model was less suited to fit to HZ data for older age groups, it fitted much better to HZ data for younger age groups. In additional analyses relaxing on some parameter constraints, we obtained final parameter sets that led to excellent predictions across all age groups (see Table 1 and Figure 2). The two best fitting parameter sets predicted peak boosting values between 2.8 and 4 (maximum allowable value), a duration of boosting limited to 1 or 2 years and, as before, no endogenous boosting. Averaged VZV-specific CMI levels are shown in Figure 3.

Table 1

Best fitting parameter sets

https://doi.org/10.7554/eLife.07116.003
Parameter setDeviance*Annual waning rate (%)Boosting scenarioDuration of boosting (years)Peak fold increase following exogenous boostingVZV weekly reactivation probability (%)Distribution threshold VZV-CMI for HZPeak fold increase following endogenous boosting
Original Search (obtained after Step 2 in Table 1)
 19262.03101.31.541
 29391.5331.31.541
 39492.0371.31.541
 49512.03121.31.541
 59682.0371.31.041
 69701.0321.31.041
 79692.03151.31.541
 89341.0312.55.041
Border search
 97511.0312.85.041
 107991.0313.15.041
 119651.5323.45.041
 128041.5323.75.041
 137221.5324.05.041
  1. *

    Results shown are averaged results per parameter set.

  2. VZV, varicella-zoster virus; HZ, herpes zoster.

Observed (open circles) and simulated (continuous lines) Belgian herpes zoster (HZ) incidence data by age.
https://doi.org/10.7554/eLife.07116.004
Figure 2 with 1 supplement see all
Observed (open circles) and simulated (continuous lines) Belgian HZ incidence data by age.
https://doi.org/10.7554/eLife.07116.006
Normalized varicella-zoster virus (VZV)-specific CMI averaged over 80 simulation years and over all individuals for the two best parameter sets.

Caption: note that this figure shows average dynamics although some individuals will have VZV-specific CMI values below 1 (making them susceptible to HZ).

https://doi.org/10.7554/eLife.07116.008

Childhood varicella vaccination and its implications for HZ incidence

Using our best fitting parameter sets (set 9 and 13 from Table 1) we simulated the effects of a 100% permanently effective varicella vaccine given to all children aged 1 year (100% coverage). Our predictions (averaged per parameter set) showed a net increase in HZ incidence during approximately 50 years (see Figure 4). The peak increase in HZ incidence was reached approximately 31 years after programme initiation and was 1.75 (1.64–1.87) (100% CI) times higher than the HZ incidence prior to varicella vaccination. The CI is constructed by using three runs per parameter set and normalizing each run by means of the run-specific averaged equilibrium HZ incidence between 100 and 300 years since the beginning of the simulation. This means that per 1,000,000 person-years the total number of HZ cases would increase on average from 3219 to 5313 (set 9) or from 3209 to 5955 (set 13). Figure 5 shows that the relative contribution of different age groups to HZ incidence changes in the time period after introduction of varicella vaccination. Noteworthy is the relative dominance of the 31–40 year old age group between 10–50 years after introduction of varicella vaccination.

Predicted HZ incidence (aggregated for all ages) over time with a CP vaccine for 1 year olds using the best-fitting parameter sets.

The red line indicates the moment of CP vaccine introduction, which is assumed to be 100% effective.

https://doi.org/10.7554/eLife.07116.009
Time-evolution of the relative contribution to HZ incidence per age group before and after introduction of 100% effective varicella vaccination for 1 year olds.
https://doi.org/10.7554/eLife.07116.010

Discussion

It is hypothesized that exogenous re-exposure to varicella increases VZV-specific cellular immunity (VZV-CMI). This natural consequence of the secondary immune response will reduce an individual's risk for HZ. When the probability of contact per unit-time between currently infectious and previously recovered varicella patients reduces, through a reduction in varicella incidence, it can be expected that HZ incidence temporarily increases due to a lack of exogenous boosting (Hope-Simpson, 1965; Ogunjimi et al., 2013).

To our knowledge, this study is the first to use an individual-based dynamic transmission model for VZV. This model allowed us to combine immunological and virological data to estimate key parameters in VZV population dynamics, such as the peak CMI response following re-exposure, duration of boosting and VZV subclinical reactivation characteristics. This means that in contrast to the deterministic models where abstract and ad hoc compartments are created to define the transition between different epidemiological states (for example the transition of a varicella recovered state to a zoster susceptible state), we can actually work with true biological, and verifiable, concepts such as VZV-CMI. Our best fitting parameter sets for Belgium suggest the effective duration of exogenous boosting to last only between 1 and 2 years. These predictions are significantly lower than those from the highly cited deterministic VZV model by Brisson et al., in which the average duration was predicted to be 20 years ([7–41 years] 95%CI) (Brisson et al., 2002). Our peak immunological response was estimated to be 2.8–4.0 times larger than the pre-re-exposure value. These predictions are consistent with those experimentally found in adults re-exposed to VZV by varicella contacts in the household (Arvin et al., 1983; Vossen et al., 2004) or by vaccination (Levin et al., 2008). A possible limitation of our study was that all close contacts with varicella patients were assumed to exert an equal ‘average’ boosting effect on the exposed individual. Future studies could assess how important it would be to incorporate variability in the impact of an exposure through direct contact with a varicella case, based on characteristics of both the exposed and the infectious person (e.g., age, comorbidity).

The VZV reactivation probability was estimated to be 5% per week. Observed data on VZV reactivation probability are rather sparse and highly divergent regarding study design, sampling site (saliva, blood, cerebrospinal fluid) and results (Schünemann et al., 1997; Mehta et al., 2003; Engelmann et al., 2008; Birlea et al., 2011; Nagel et al., 2011; van Velzen et al., 2013). The observed weekly VZV reactivation probability is a topic of discussion in the literature and varies between 0 and 71%. As such it is difficult to compare our estimates with the range of observed values. We also note that VZV reactivation in our model might only be detectable at the neural ganglia at not (always) necessarily in peripheral tissues. In order for HZ to occur, we assumed that VZV-CMI should be below a relative threshold (following a specific distribution) during VZV reactivation. None of our best fitting parameter sets predicted a significant effect of VZV reactivation on VZV-CMI, implying that endogenous boosting most likely does not have an impact on the occurrence of HZ. This finding is important since the existence of endogenous boosting has been proposed to have an effect in reducing the negative effects of varicella vaccination on HZ incidence. Future experimental studies should focus on confirming our predicted VZV reactivation probability and the lack of endogenous boosting.

The annual decline of VZV-CMI was predicted to be between 1 and 1.5%. This result is lower than the 2.7–3.9% experimentally observed by Levin et al. for individuals older than 60 years (Levin et al., 2008). The twofold difference in waning rate can be explained by the explicit disentanglement of waning and boosting (with younger age groups having—on average—higher probabilities of being boosted recently thereby actually increasing the observed waning rate). A limitation in our study is the use of a fixed waning rate for all ages. Our results might be interpreted as an averaged result of lower waning rates for younger age groups and higher waning rates for older age groups (as documented by Levin et al. (2008)). A higher waning rate in older age groups could for example be caused by chronic CMV infection (Ogunjimi et al., 2014). Although different types of waning (both in model specification and age dependency) can be used in this kind of simulation models, we believe that further experimental data documenting VZV specific cellular memory as a function of age is needed so that new waning models can be appropriately formulated. One future avenue of research could be the fitting of our predicted VZV-CMI to observed VZV-CMI data, as this will be a mixture of waning, immunosenescence and boosting. Better VZV-CMI datasets than those currently available are needed to be able to do this. These datasets could and should contain immune responses against different VZV peptides and could differentiate between the different cellular immunity compartments (CD4 vs CD8 and central vs effector memory cells). The use of our VZV IBM could help us identify which VZV-CMI compartment is of importance in controlling HZ.

We used our best fitting models to analyze the effects of a 100% effective varicella vaccine implemented for all 1-year-old children. We predicted a net increase in HZ incidence during 50 years and a 1.75 peak fold increase 31 years after introduction of the vaccination program. This delay in the HZ peak incidence is caused by cohorts born close to the time varicella vaccination was introduced experiencing less repeated boosting instances during their childhood than previously born cohorts (a mechanism that is similar to the progressive immunity model proposed in the deterministic VZV model by Guzzetta et al. (2013)). Although increases in HZ incidences following universal childhood varicella vaccination have been noticed, some authors have attributed these increases to a background evolution that was already present prior to CP vaccination (see discussion in Ogunjimi et al. (2013)). However, our analysis shows that proper documentation of significant increases in HZ incidence might not be possible during the first 10 years, even if a 100% effective vaccine would be used. For instance, during the first 10 years of the US program, both uptake and efficacy with the initial single dose vaccination programme were far below 100%. Although our model predicts a much lower duration of boosting than used hitherto in compartmental models (Ogunjimi et al., 2013), some of our overall HZ projections are qualitatively similar. However, in contrast to earlier model estimates our VZV IBM predicts that 31–40 year olds contribute the most to the peak in HZ incidence following varicella vaccination. Some observational studies found no effect of varicella vaccination on HZ incidence for those aged 60 years and older (Hales et al., 2013). This could be compatible with an overall HZ incidence increase due to rising HZ incidence among 31–40 year olds. Importantly, younger adults have been shown to be less likely to develop post-herpetic neuralgia (Opstelten et al., 2002; Drolet et al., 2010). Thus although our aggregated predictions regarding the increase in HZ incidence following varicella vaccination may appear similar to those published using deterministic models, cost-effectiveness analyses using our VZV IBM would be more in favor of universal childhood varicella vaccination.

A major benefit of our modeling approach is the possibility to verify our best–fit parameter values via experimental studies, or vice versa, to adapt parameter values when empiricism delivers new insights. For example, if a new experimental study would prove the existence of endogenous boosting, this could be readily implemented in our VZV IBM so that parameter sets could be estimated, conditional on the existence of endogenous boosting. Although our IBM has given us valuable insights into between-host and within-host VZV dynamics, other influential factors could be introduced in future versions. These factors could relate to CMV-immunosenescence (Ogunjimi et al., 2014), maternal antibodies, reduced VZV-CMI induction if infected during the first year of life as this might improve the prediction of the teenage group (Terada et al., 1994), co-infection with other viruses (Ogunjimi et al., 2015), risk groups (for e.g., immunosuppressed individuals) and HLA types (Meysman et al., 2015). Although current deterministic compartmental models should be able to partially account for these effects, a VZV IBM seems better suited to directly model the influence of these immunity-perturbing factors. Future VZV IBM should also explore more realistic vaccination scenarios as well as inter-country variability (Poletti et al., 2013).

We conclude that our VZV individual-based model has explicitly estimated the duration of exogenous boosting to be limited to only 1 or 2 years and that there was no significant effect from endogenous boosting.

Materials and methods

Model overview

We present an individual-based model in which the individual's risk of HZ is determined by the individual's VZV-CMI vs the so defined ‘Force of Reactivation (FoR)’ that represents the strength of VZV reactivation (as detailed in the Modeling VZV reactivation paragraph). In contrast to classical deterministic epidemiological models, our model is not explicitly compartmentalized by means of ad hoc defined epidemiological groups. Instead the main ‘flow diagram’ represents the evolution of VZV-CMI with time and under several events (for more details see the next paragraphs). Briefly, Figure 6 illustrates that individuals are born susceptible and that VZV-CMI is equal to zero during this time period. After exposure to chickenpox or HZ, VZV-CMI receives an initial value. Next, VZV-CMI is expected to undergo waning and several events can occur. The first event depicted (but the reader should realize that the timing of the events are interchangeable) is exogenous boosting after re-exposure to either chickenpox or HZ. Exogenous boosting is assumed to increase VZV-CMI temporary, after which decay towards ‘the original trajectory of VZV-CMI’ is assumed to occur. Next, we depicted unsuccessful reactivation of VZV that is assumed to cause endogenous boosting of VZV-CMI (again followed by a decay). However, if the FoR is relatively higher than VZV-CMI, VZV reactivation will be successful and will cause HZ (followed by a reinstatement of VZV-CMI).

Simplified dynamics of VZV-CMI, VZV reactivation and boosting events as modeled.

The sequence of exogenous boosting and VZV reactivation can be switched.

https://doi.org/10.7554/eLife.07116.011

Demographics

The dynamics of the synthetic population of the individual-based model are based on Belgian population and mortality data normalized to a fixed total population of 998,400 individuals (Eurostat, 2012). The chosen population size is the result of a trade-off between ensuring sufficient heterogeneity and a manageable computational burden. Natural deaths are selected based on the age-dependent mortality rate. Per time step, the number of newborns equals the number of deaths to obtain a constant population size. To conduct predictions over many years, a stationary demographic structure is required throughout the simulated period. The Belgian population from 2012 has an overrepresentation of people from age 40 to 60 years (see Figure 7). Applying a fixed age-dependent mortality rate in combination with the replacement by newborns would results in an oscillating population distribution over time with respect to age. Therefore, the initial age distribution is not based on the Belgian population count from 2012 but on the survivor function estimated from data on the number of deaths per capita. The survivor function by age is estimated from data on the number of deaths per capita by m(a)=exp(0aμ(t)dt) with age-dependent mortality rate μ using a thin plate regression spline model with the gam-function in the R-package mgvc (Wood, 2011; Hens, 2012). Figure 7 illustrates the survivor function by age together with the Belgian population and mortality rates in 2012.

The model runs in time steps of 1 week and people with week-age 53 move to the next age class. To obtain homogeneous age transitions throughout the simulated period, initial week-ages are randomly assigned between 1 and 52. People from the last age class with 53 weeks are removed from the population so that the demographic structure remains stable throughout the simulated period.

Modeling dynamics of primary VZV infection

At the start of the simulation, 30 individuals between ages 1 and 3 are randomly infected with CP. The weekly probability λi,t for a susceptible individual to become infected with VZV (after contact with at least one infectious individual) is calculated by λi,t=1n=180(1w(i,n))CPIn·(1m·w(i,n))HZIn with w(i,n) the weekly effective contact probability for an individual from group i with a random individual from group n, m the relative HZ infectiousness (empirically estimated to be 0.17 [cf. paragraph ‘Modeling VZV endogenous reactivation’]) and CPIn and HZIn the total number of infectious individuals per age class for CP and HZ, respectively. This formula is thus constructed by the complement of the probability that an individual did not have a successful contact with any of the chickenpox or HZ patients. The VZV infection probability, w(i, n), is based on empirical social contact data as described elsewhere (Ogunjimi et al., 2009). Here w(i, n) equals the number of close contacts per week lasting longer than 15 min between two random individuals in age classes i and n multiplied by the best fitting proportionality parameter q = 0.181 based on Belgian social contact and VZV seroprevalence data (Ogunjimi et al., 2009).

Individuals infected for the first time with VZV are infectious for 1 week after an incubation period of 2 weeks. Next, they are CP recovered and receive a normalized CMI value of 1 ± a randomly distributed factor (normal distribution with variance 0.1 as suggested by Terada et al. (1994)).

Modeling waning of VZV-CMI

Once arrived in the CP recovered state, VZV-CMI starts waning at a weekly rate via the multiplication with (1—waning-rate). The waning-rate (see Table 2) is informed by the annual decline of 2.7–3.9% per age-year as noted by baseline VZV-CMI values by Levin et al. (2008). In all model steps, waning is applied to all variables. Note that in our model waning and ageing are indistinguishable.

Table 2

Initial parameter sets

https://doi.org/10.7554/eLife.07116.013
ParametersStep 1Step 2
Annual waning rate (%)2.00.5
3.01.0
4.01.5
2.0
2.5
Boosting scenario13
2
3
Duration of boosting (years)11
22
43
74
125
7
10
12
15
Peak fold increase following exogenous boosting11.3
1.61.6
2.21.9
2.2
2.5
VZV weekly reactivation probability (%)0.010.001
0.10.05
0.30.01
0.50.015
0.1
0.2
0.3
0.4
Distribution threshold VZV-CMI for HZ11
22
34
4
Peak fold increase following endogenous boosting11
1.41.2
1.8
2.2

Modeling exogenous re-exposure to VZV

At each weekly update, the CP recovered individuals have a probability λi, t to receive a boost of VZV-specific immunity. Although HZ is less infectious than CP, we assume that if boosting has occurred, the magnitude of VZV-CMI boosting will be similar for both CP and HZ. To analyze the effect of boosting, we retain a CMI value for each individual with and without boosting.

In the first 6 weeks after exogenous boosting, VZV-CMI is assumed to increase linearly up to ‘Peak fold increase’ times the pre-boosting value (Levin et al., 2008), but is limited to a maximum of 4 times the VZV-CMI value without re-exposure. The 6 week duration between the boosting event and the peak has been influenced by the Levin et al. (2008) data. Limiting the effect of boosting to a factor 4 is based on the recent finding that pediatricians, highly exposed to CP, have T-cell values that are on average 3–4 times higher than controls, but not higher (Ogunjimi et al., 2014).

Next, VZV-CMI will decrease following one of three different boosting scenarios (as shown in Figure 8) until it reaches the pre-boosting value again (after a ‘duration of boosting’):

  1. Exponential decrease from peak to pre-boosting value based on VZV ELISPOT CMI data after Zostavax vaccination as published by Levin et al. (2008). Levin et al. (2008) presented ELISPOT data on Zostavax vs placebo-vaccinated individuals and the relative increases were (visual reference to figure in the Levin et al. paper): 120% (6 weeks), 60% (1 year), 50% (2 years) and 40% (3 years). Using these average values we performed a regression analysis to estimate the VZV-CMI exponential decay rate per week.

  2. Exponential decrease from peak to 60% of pre-boosting value ([Levin et al., 2008], based on simulation from peak to year 1, cf. supra), followed by a constant value for x years with x defined by the parameter set, but ≥3 years. After x years, VZV-CMI returns to the pre-boosting value. This scenario is compatible with the assumption that memory cells have a predefined and fixed lifespan as implied by Westera et al. (2013).

  3. Exponential decrease from peak to pre-boosting value based on the boosting period of x years as defined by the parameter set. The exponential decay is defined by the peak and duration of boosting: Y(t)=PY0eln(P)xt with Y(t) = VZV-CMI (disregarding age), P = peak fold increase, Y0 = VZV-CMI prior to entering boosting sequence (= ‘original VZV-CMI’) and x = duration of boosting. This function is constructed by the boundary conditions that Y(t = x) = Y0 and Y(t = 0) = P*Y0.

Three different boosting scenarios.

(A) Illustrates the exponential decline parameterized by a peak (+120%) at 6 weeks, (+60%) 1 year later, (50%) 2 years later and (+40%) 3 years later as presented by the Zostavax vaccine trial by Levin et al. (B) Illustrates the exponential decline from peak (+120%) to (+60%) 1 year later and constant for x years (as defined by the parameter set) after wards, as a modified interpretation of the results of the Zostavax vaccine trial by Levin et al. (C) Illustrates the increase to a peak value as defined by the parameter set that is followed by an exponential decline so that the pre-boosting value is reached after x years.

https://doi.org/10.7554/eLife.07116.014

It is important to clarify that if a new boosting event occurs during an ongoing boosting sequence, the VZV-CMI value attained right before the new boosting event occurs, is assumed to be the baseline ‘pre-boosting’ reference for the new boosting sequence. This means that for scenario 3 in case of a new boosting event 6 weeks (and mutatis mutandis for the other situations) after the first boost VZV-CMI evolves as

Y(t)=PY1eln(P)x(tt1)=PPY0eln(P)xt1Y1eln(P)x(tt1)=P2Y0eln(P)xt,

with the subscript 1 referring to the situation when the second boosting event occurs.

This shows that boosting during an ongoing boosting episode prolongs the time before the ‘original VZV-CMI (Y(t) = Y0)’ is reached again.

Modeling VZV reactivation

After primary infection, VZV is assumed to remain latent, but capable of reactivation. The frequencies of VZV reactivation used in the parameter sets were informed by observed VZV reactivation frequencies in random samples from healthy individuals (2% in blood [Schünemann et al., 1997]; 0 out of 112 saliva samples [Mehta et al., 2003]; 2.5% in saliva [Nagel et al., 2011]), immunosuppressed patients (8.1% from various sites [Engelmann et al., 2008]), individuals with malignancies (7.5% in blood [Malavige et al., 2010]) and HIV patients (9% in saliva [van Velzen et al., 2013]; 16% in cerebrospinal fluid [Birlea et al., 2011]). The consequence of reactivation can either be endogenous boosting or clinical reactivation (HZ) and this is defined by the difference between VZV-CMI and the FoR.

The FoR defines the VZV-CMI needed to resist clinical reactivation and if VZV-CMI < FoR, reactivation will lead to HZ. The reader should imagine the FoR to represent independent reactivation behavior of VZV and whether this reactivation will lead to HZ or endogenous boosting will depend on the value of VZV-CMI. The FoR deviates per time step and individual by means of a gamma probability density function. This gamma function is chosen as it represents the summation of unknown biological phenomena that are assumed to have an exponential distribution. The parameter set includes four different gamma distributions (see Table 2 and Figure 9). HZ individuals are assumed to be infectious for 1 week and receive a VZV-CMI reset to 1 ± random factor (normally distributed, cf. primary infection). There exists no data on the relative infectiousness of HZ patients nor is it likely that this can be estimated through experiments. We chose to approximate the relative infectiousness of HZ patients by the relative infectiousness of breakthrough CP patients (Bernstein et al., 1993). This has previously been estimated at 0.17 (Brisson et al., 2002). Although HZ infectiousness was needed to maintain circulation of VZV in our model, the relative effects on overall VZV transmission are—compared to CP—marginal. Figure 2—figure supplement 1 shows the results of a sensitivity analysis in which we varied HZ infectiousness from 0.03 to 0.45 for the 13 best fitting parameter. As can be seen in Figure 2—figure supplement 1 our results are quite robust. Reinstallation of VZV-specific immunity after HZ is based on experimental data showing that a second case of HZ only occurs in about 5% of individuals (Yawn et al., 2011) and that VZV-CMI is higher in recovered HZ patients than in age-matched controls (Weinberg et al., 2009).

Different cumulative distribution functions (CDF) for Force of Reactivation (FoR).
https://doi.org/10.7554/eLife.07116.015

If VZV-CMI ≥ FoR, endogenous boosting occurs followed by an exponential decrease according to one of the scenarios described in the previous section. The peak following endogenous boosting, however, is restricted to be at most equal to the peak following exogenous boosting. In addition, we assume that an endogenous boosting sequence will always be overruled by a new successful exogenous re-exposure boosting episode.

Statistical and computational details

Simulations were performed using Matlab 2012b on the Flemish VSC supercomputer. Simulations ran for 320 years and model output was obtained by averaging the age-specific results over the last 80 years. The main outputs were CP incidence, HZ incidence, VZV serology and VZV-CMI. In order to optimize the fitting procedure, we performed a two-step parameter set analysis. The following 7 parameters were estimated by means of the fitting procedure: VZV-CMI waning rate, type of boosting scenario, duration of exogenous boosting, peak fold increase following exogenous boosting, VZV reactivation probability, FoR distribution and the peak fold increase following endogenous boosting.

In the first step we ran each parameter set three times. We calculated per set the Binomial likelihood by fitting the HZ age-specific output data to Belgian HZ incidence data (Bilcke et al., 2012). Next, we selected the parameter set leading to the lowest mean deviance (= −2*loglikelihood) based on the three repetitions with different stochastic seed and all other parameter sets with deviance +5% at most in order to account for model selection uncertainty (Castro Sanchez et al., 2013). In order to broaden the parameter selection, we also selected the most prevalent (marginal) parameter values in the lowest mean deviance 2.5% percentile (see Table 3).

Table 3

Step 2 parameter set selection

https://doi.org/10.7554/eLife.07116.016
ParametersBest parameter sets + deviance +5%Most prevalent parameters in Q2.5
Annual waning rate (%)2.02.0
Boosting scenario33
Duration of exogenous boosting (years)11
42
4
7
12
Peak fold increase following exogenous boosting1.61.6
2.2
VZV weekly reactivation probability (%)0.010.01
0.10.3
Distribution threshold VZV-CMI for HZ21
42
Peak fold increase following endogenous boosting11

In the second step we adapted our parameter ranges and intervals according to the best fitting values to obtain new parameter combinations (see Table 3). Again, we ran each parameter set three times and calculated the mean deviance. The best parameter sets were defined by those parameter sets that had at least one run with a deviance within the 5% range of the deviance of the best fitting parameter set.

Given the fact that some selected parameter values were on an unexplored border of the parameter grid, we studied whether more extreme values for the border parameters led to better results (and continuing if deviance was within the second step best deviance +5%). Doing this, we allowed the other parameters to vary for one unit in both parameter directions.

Predicting the effects of CP vaccination on Belgian HZ incidence

We used our best parameter sets and introduced a simplistic hypothetical single dose 100% effective CP vaccine (without waning of vaccine-induced immunity) for all children ageing between 1 and 2 years. Vaccinated individuals were assumed not to be susceptible to HZ.

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Decision letter

  1. Mark Jit
    Reviewing Editor; London School of Hygiene & Tropical Medicine, and Public Health England, United Kingdom

eLife posts the editorial decision letter and author response on a selection of the published articles (subject to the approval of the authors). An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent (see review process). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.

[Editors’ note: this article was originally rejected after discussions between the reviewers, but the submission was accepted after an appeal against the decision.]

Thank you for choosing to send your work entitled “Integrating between-host transmission and within-host immunity to analyze the impact of varicella vaccination on zoster” for consideration at eLife. Your full submission has been evaluated by Prabhat Jha (Senior editor) and three peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the decision was reached after discussions between the reviewers. Based on our discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in eLife.

The following individuals responsible for the peer review of your submission have agreed to reveal their identity: Mark Jit (Reviewing editor); Alessia Melegaro (reviewer #3). Another reviewer chose to remain anonymous.

All of us agreed that it is innovative and addresses an important issue which is being explicitly modelled for the first time, i.e. the role of the dynamics of cell-mediated infection and endogenous boosting in VZV reactivation. Given that this concern has had a large influence on vaccine decision making in Europe and elsewhere, the topic is of considerable public health importance. However, we had a number of major concerns with the paper which would require substantial changes to the methodology to address.

Below are the most substantive concerns; however we would encourage the authors to look at the more detailed comments from each reviewer as well.

1) The model is itself is hard to understand and therefore to assess what it adds to the existing literature. The Methods section plunges straight into a discussion of the estimation of the various parameters. It is not clear whether the follows the traditional Brisson/Edmunds/van Hoek approach, the Guzzetta progressive immunity one (AJE 2013) or a different approach entirely. It would be helpful to start with an overview of the model structure (with a written description and/or compartmental flow diagram), as well as the main ways it differs from previous models.

2) It is not clear what the conclusions add to existing modelling work on the same topic. The manuscript criticises existing deterministic models used in current research in the field. However, the main conclusions of the paper (e.g. with regards to vaccine impact) are in line with those of available deterministic models. Although the rise in herpes zoster is predicted to occur earlier in life, it is unclear whether the magnitude of the HZ rise would be smaller, the same or larger than in previous models, and hence the overall significance of this age shift. The fact that a perfect vaccine is used makes the comparison particularly difficult, although it is understandable why this was done in order to show effects more clearly. Hence it would be important to explain clearly what the gains achieved by an individual-based framework taking into account cell-mediated infection explicitly are.

3) In addition, the manuscript points out that a variety of models are able to fit age-specific incidence or prevalence data so conclusions may be a function of model structure rather than biological fact. However, the model as it stands has at least 6 free parameters (i.e. more than in currently used deterministic models), which appear to be fitted to a single output, a zoster age-specific incidence profile. This should worse over-fitting problems, thereby increasing rather than reducing the lack of identifiability. There needs to be some way to address this problem, or at least more extensive sensitivity analyses to show that the conclusions are robust to the range of possible parameter values.

4) Furthermore, like previous models, the conclusions are not completely independent of subjective model choices, since the form and sometimes the parameter values of functions representing cell-mediated immunity and boosting have to be pre-determined (albeit with reference to empirical work). In particular, in the three exogenous boosting scenarios, a number of parameters are simply assumed and no explanations on their values are provided. For example the force of boosting (subsection “Modeling exogenous re-exposure to VZV”) is assumed to occur at the same rate as the force of infection. This assumption (which contrasts with the earlier remark that the actual magnitude of the boosting effects is unknown) should be emphasized, as it might be a main responsible of the fact that seven of the best models “include exogenous boosting” (see Results). Better justification for all the assumptions and assumed parameter values is required; at present it is not clear that this is the “final answer” to the exogenous boosting question.

Reviewer #1:

This paper deals with an important issue, i.e. the extent to which childhood varicella vaccination may cause an increase in HZ in adults due to reduction in exogenous boosting. The observational and ecological evidence about boosting are hard to interpret precisely. As the authors point out, a variety of mathematical models are able to fit age-specific incidence or prevalence data so conclusions may be a function of model structure rather than biological fact. This paper offers a number of improvements that may enhance the believability of conclusions, particularly an individual-based structure which allows tracking of within-host immune dynamics, allowing the duration of exogenous boosting to be fitted rather than largely assumed.

The main difficulty is that the model itself is hard to understand and therefore to assess what it adds to the existing literature. The Methods section plunges straight into a discussion of the estimation of the various parameters. It would be helpful to start with an overview of the model (with a written description and/or compartmental flow diagram), as well as the main ways it differs from previous models.

The comparison with previous models (which have been influential to vaccine policy in much of Europe) needs to be a bit sharper. In particular, it is not clear whether the magnitude of the HZ rise is smaller, the same or larger than previous models (e.g. Brisson). The fact that a perfect vaccine is used makes the comparison particularly difficult, although it is understandable why this was done in order to show effects more clearly. Hence even though the rise in HZ occurs earlier in life, it is not clear what the impact on cost-effectiveness will be.

Also it should be noted that the conclusions are not completely independent of subjective model choices, since the form and sometimes the parameter values of functions representing cell-mediated immunity and boosting have to be pre-determined (albeit with reference to empirical work), as is inevitable. Hence it is not clear that this is the “final answer” to the exogenous boosting question.

However, the model clearly adds a great deal of additional insight to the existing debate, including the use of data that was not previously used in this fashion.

Reviewer #2:

The paper has some innovative aspects, as it represents a first attempt (to my knowledge) to explicitly include into a single model for VZV transmission dynamics and reactivation (and vaccination), the trend in cell mediated immunity (CMI) and endogenous boosting. As trends in CMI and the role of boosting are thought to be the primary determinants of VZV reactivation, explicit consideration of such effects (instead than e.g. implicitly as in available models) is worthwhile.

I have however some major points that should be carefully tackled. Authors criticize deterministic models used in current research in the field (Introduction, “One of the main points of criticism ... equilibrium states.”) Since however some of the main conclusions of this paper are in line with those of available deterministic models (e.g. in regards of the impact of vaccination) authors should explain clearly which are the possible gains allowed by IBMs, particularly in what respects the present approach should be superior to the deterministic models used in the literature. My main point here deals with identifiability of model parameters. The current model has at least 6 free parameters (i.e. more than in the currently used deterministic models), which as I understand are fitted to a single output, a zoster age-specific incidence profile. This should worse over-fitting problems, thereby emphasizing rather than reducing, the aforementioned criticism.

I am not entirely clear about the three hypotheses about CMI decrease after a boosting event (subsection “Modeling exogenous re-exposure to VZV”). In subsection “Modeling waning of VZV-CMI” a hypothesis has been made about CMI decline after primary CP infection. I believe one should take this – for reasons of both modeling parsimony and simplicity – as a baseline holding also for CMI decline after a boosting event, especially given that the data by Levin et al. used by the authors to parametrize the model did not seem to refer to CMI decline after primary chickenpox only. Other hypotheses could then naturally be grounded against this baseline. In particular I am not clear about the meaning of HP1, in subsection “Modeling exogenous re-exposure to VZV”, “Exponential decrease from peak to pre-boosting value based”. Why do you want to prevent that decline continues beyond the pre-boosting situation? The Hp3 formula is incomprehensible and needs careful explanation.

The force of boosting (subsection “Modeling exogenous re-exposure to VZV”) is assumed to occur at the same rate as the FOI. This assumption (which contrasts the authors' remark that the actual magnitude of the boosting effects is unknown) should be emphasized, as it might be a main responsible of the fact that seven of the best models “include exogenous boosting” (see Results).

About the modeling of the Force of reactivation (subsection “Modeling VZV endogenous reactivation”), recent papers have modeled it as an increasing function of age (=senescence), and of time elapsed since last boosting episode. In the paper this is modeled as a purely random factor “The FoR deviates per time step and individual by means of a gamma function.” Am I understanding correctly? In my opinion that should be taken as a (useful) baseline against which, however, to ground alternative, possibly more realistic hypotheses. Therefore this point should be motivated more carefully. How was this gamma (density?) parametrized? This is important because one of the main results on the impact of vaccination i.e. the young age of zoster cases in the post-vaccination period (“Noteworthy is the relative dominance of the 31–40 year...”) might strongly follow from this hypothesis.

Reviewer #3:

This work aims at answering some relevant questions about VZV infection and in particular estimating parameters that describe the exogenous and endogenous boosting effect, a key aspect when considering the introduction of varicella vaccination. For this reason I believe that the paper, in principle, is very relevant and of interest for the research community that is involved in VZV modeling and policy decision making.

However, also considering the standard of the eLife journal, I believe the paper cannot be accepted in its current form. Some major improvements and changes are required to make it fit for publication. In particular, specific modeling assumptions and fitting procedures need to be carefully re-addressed and properly clarified before consideration for publication. See the list below for the required amendments:

1) The analysis is based on an Agent-Based Modeling framework. These models require a very thorough validation procedure, especially when considering a realistic demographic population. The authors do not show any model output that convinces us that the demographic component is suitable to model VZV in Belgium. I believe that these validations outputs should be presented.

2) Details of the model structure used are missing. Is the structure following the traditional Brisson/Edmunds/van Hoek approach or the Guzzetta progressive immunity one (AJE 2013)? Details on this should be available to the reader.

3) The three exogenous boosting scenarios: a number of parameters are simply assumed and no explanations on their values are provided. In particular, why six weeks to reach the peak after exogenous boosting? Also, in scenario 2, 60% of pre-boosting value (why?), steady state for x years (?) and why >= 3 years? A better explanation on these parameter values is required. Also what is the biological explanation for the return to pre-boosting values after x years? Finally, in scenario 3 there's a little bit of confusion between delta t and x. The authors should check the formula of Y(t).

4) The lines “HZ individuals are assumed to be infectious for 1 week and receive a VZV-CMI reset to 1 +/− random factor (normally distributed, cf. primo infection) and “HZ only occurs in about 5% of individuals [Yawn 2011] and that VZV-CMI is higher in recovered HZ patients than in age-matched controls” seem contradicting. What is the post HZ value of VZV CMI? As after primary infection or higher?

5) The sentence “Although HZ infectiousness was needed to maintain circulation of VZV in our model, the relative effects on overall VZV transmission are – compared to CP – marginal”: it is not clear here why you need HZ infectiousness to maintain circulation of VZV infection. If it is post-vaccination we don't care to maintain VZV circulation. If it is pre-vaccination, then there is something wrong if the model need HZ to keep VZV infection.

6) The approximation of HZ infectiousness to varicella breakthrough is a strong assumption. at the least we need to check the sensitivity of model results to variations of this parameter value.

7) The fitting procedure needs to be rethought. It seems that the authors explore in a two-step approach a grid of values and parameter sets. First of all, where is the decision to run the simulation three times coming from? And how is the grid of parametric space explored? And also how are the values in the grid selected? What is the criteria? From Table 2 I notice some very weird combinations of parameters going from step 1 to step 2. It does not seem we are considering the whole parametric space in step 1 and then narrowing the ranges as a function of the results obtained in step 1. A much more comprehensive sensitivity analysis should be performed to evaluate more thoroughly the entire parametric space.

8) The best parameter sets are chosen based on a fit of the HZ incidence data, considered to be binomially distributed. Wouldn't it be better to consider a Poisson distribution for the HZ incidence data (Guzzetta et al., 2013), considering that incidence refers to count of HZ episodes per age group?

9) The authors built an IBM that accounts for both between and within host dynamics, namely, taking into consideration both exogenous and endogenous boosting. The best parameter sets to inform the mathematical model are chosen based on repeated fitting of the HZ age-specific incidence estimates from the model to observed HZ incidence data from Belgium. As regards the fit of the best sets of parameters to the observed HZ data, as shown in Figure 1 and 2, the fit is very poor for the younger age groups, even for the two best parameter sets (9 and 13), as it is duly noted by the authors. Is there any way to improve the fit in this age group, considering that in the deterministic model by Guzzetta et al. (2013) it can be observed a better fit of HZ in young age groups? Maybe the authors should aggregate the incidence into age classes as otherwise the stochastic nature of the data might prevail over the goodness of fit.

10) It seems, from parameters sets 8, 9, and 13, that a higher peak fold increase following exogenous boosting is associated with a better fit of HZ incidence data in the first ten years of age. What about the age group between 10 and 20 years of age, the one suffering the poorest fit?

11) The authors claim that their model can easily accommodate new parameter value coming from experimental studies. However, when it comes to consider the effect of an hypothetic vaccination program, they choose a very simplistic and unrealistic one. Wouldn't it be better if they considered more realistic scenarios, such as those taken into consideration by Poletti et al. (2013) and other works, or some actual vaccination program, as the one in the US or in other countries with an effective varicella vaccination program? Also, the amount and timing of zoster reactivation may be country-specific as shown in Poletti (2013). This should be mentioned in the Discussion, especially considering the current debate on whether or not to introduce universal VZV vaccination in several countries.

12) Figures 4 and 5 should be redone considering maybe an aggregation over time, to avoid all the stochasticity of the model output. In Figure 4 the authors plot the pre-steady state and pre-vaccination incidence which is not of interest. And there is also a part of the plot without any line (right hand side). The interesting bit is the post vaccination part to which the authors only dedicate a small portion of the graph. Also, why are there different colors?

https://doi.org/10.7554/eLife.07116.017

Author response

We believe that the individual comments by the reviewers do not point to major shortcomings of our methodology but mainly request clarifications of methods and results. Moreover, we believe some of the reviewers' comments are based on misconceptions, probably due to the paradigm shifting nature of our paper. We hope that eLife is willing to reconsider its position.

Reviewer #1:

The main difficulty is that the model itself is hard to understand and therefore to assess what it adds to the existing literature. The Methods section plunges straight into a discussion of the estimation of the various parameters. It would be helpful to start with an overview of the model (with a written description and/or compartmental flow diagram), as well as the main ways it differs from previous models.

We understand the demand for a better structuring and more elaboration. We have added a new figure detailing an important part of the model, we have majorly restructured the Methods section and we have added a new paragraph called “Model overview”.

The comparison with previous models (which have been influential to vaccine policy in much of Europe) needs to be a bit sharper. In particular, it is not clear whether the magnitude of the HZ rise is smaller, the same or larger than previous models (e.g. Brisson). The fact that a perfect vaccine is used makes the comparison particularly difficult, although it is understandable why this was done in order to show effects more clearly. Hence even though the rise in HZ occurs earlier in life, it is not clear what the impact on cost-effectiveness will be.

We would like to emphasize that our paper is not intended to be a new cost-effectiveness analysis, but instead to present a whole new framework allowing new cost-effectiveness studies to be performed. This is indeed the reason why we discussed the scenario of a perfect vaccine and why we have minimized the direct comparison of results with those resulting from using the other framework. However, we do clearly state that the total peak increase in HZ incidence is similar compared to the results from the other framework, but that a shift to younger age groups could have an important effect on morbidity.

Also it should be noted that the conclusions are not completely independent of subjective model choices, since the form and sometimes the parameter values of functions representing cell-mediated immunity and boosting have to be pre-determined (albeit with reference to empirical work), as is inevitable. Hence it is not clear that this is the “final answer” to the exogenous boosting question.

However, the model clearly adds a great deal of additional insight to the existing debate, including the use of data that was not previously used in this fashion.

We agree with the reviewer that subjective model choices could be the reason of bias. However, the fact that our model is based on experimentally observed data, in contrast to the ad hoc compartmentalization of the deterministic models, helps us in model selection.

Reviewer #2:

[…] I have however some major points that should be carefully tackled. Authors criticize deterministic models used in current research in the field (Introduction, “One of the main points of criticism ... equilibrium states.”) Since however some of the main conclusions of this paper are in line with those of available deterministic models (e.g. in regards of the impact of vaccination) authors should explain clearly which are the possible gains allowed by IBMs, particularly in what respects the present approach should be superior to the deterministic models used in the literature. My main point here deals with identifiability of model parameters. The current model has at least 6 free parameters (i.e. more than in the currently used deterministic models), which as I understand are fitted to a single output, a zoster age-specific incidence profile. This should worse over-fitting problems, thereby emphasizing rather than reducing, the aforementioned criticism.

We would like to note that the 2002 Brisson paper, that lies at the base of all Brisson-alike papers, clearly states in the Appendix that 11 parameters were estimated. However, we do acknowledge that Guzzetta and colleagues only use four parameters to estimate their reactivation rate. An important distinction however is the fact that they do not explicitly account for endogenous boosting for which we have reserved two parameters.

HZ incidence is not a scalar variable but a vectorized variable meaning that – in our case – 80 data points are taken into account for the goodness-of-fit (sufficient to estimate the seven parameters as also shown by our analyses). We do agree that future research should try and account for other fit possibilities and we suggest in our Discussion that new studies should try and obtain better VZV-CMI data as a function of age.

We have added the following text to the Discussion: “This means that in contrast to the deterministic models where abstract and ad hoc compartments are created to define the transition between different epidemiological states (for example the transition of a varicella recovered state to a zoster susceptible state), we can actually work with true biological, and verifiable, concepts such as VZV-CMI.” We also note that the following text was already present in the Discussion: “A major benefit of our modeling approach is the possibility to verify our best–fit parameter values via experimental studies, or vice versa, to adapt parameter values when empiricism delivers new insights. For example, if a new experimental study would prove the existence of endogenous boosting, this could be readily implemented in our VZV IBM so that parameter sets could be estimated, conditional on the existence of endogenous boosting. Although our IBM has given us valuable insights into between-host and within-host VZV dynamics, other influential factors could be introduced in future versions.”

I am not entirely clear about the three hypotheses about CMI decrease after a boosting event (subsection “Modeling exogenous re-exposure to VZV”). In subsection “Modeling waning of VZV-CMI” a hypothesis has been made about CMI decline after primary CP infection. I believe one should take this – for reasons of both modeling parsimony and simplicity – as a baseline holding also for CMI decline after a boosting event, especially given that the data by Levin et al. used by the authors to parametrize the model did not seem to refer to CMI decline after primary chickenpox only. Other hypotheses could then naturally be grounded against this baseline.

Levin et al. presented two types of data: (1) the decline of baseline (thus prior to vaccination) VZV-CMI as a function of age and (2) the decay of VZV-CMI after vaccination. The first is used as a starting value for the waning of VZV-CMI, whereas the second is used as a starting value for the decay of VZV-CMI after vaccination. Our model is thus based on these experimental findings. In order to avoid confusion we have added the notion in the Methods section that the waning of VZV-CMI is informed by the baseline evolution of VZV-CMI as a function of age.

In particular I am not clear about the meaning of HP1, in subsection “Modeling exogenous re-exposure to VZV”, “Exponential decrease from peak to pre-boosting value based”. Why do you want to prevent that decline continues beyond the pre-boosting situation?

We assume that boosting causes a temporary increase of VZV-CMI, so that when VZV-CMI has reached the “pre-boosting” value we can assume that the system has returned to its equilibrium state meaning that waning of VZV-CMI can continue. Figure 6 illustrates this concept. This is indeed an assumption and we hope that future VZV-CMI data will provide disclosure.

The Hp3 formula is incomprehensible and needs careful explanation.

We have changed delta_t to x and we have added “This function is constructed by the boundary conditions that Y(t = x) = Y0 and Y(t = 0) = P* Y0” to the explanation. This clarifies the equation (given the prior explanation that the formula represents an exponential decay).

The force of boosting (subsection “Modeling exogenous re-exposure to VZV”) is assumed to occur at the same rate as the FOI. This assumption (which contrasts the authors' remark that the actual magnitude of the boosting effects is unknown) should be emphasized, as it might be a main responsible of the fact that seven of the best models “include exogenous boosting” (see Results).

The statement in the subsection “Modeling exogenous re-exposure to VZV” refers to a probability and not to a rate. We intentionally did not use the wording “force of infection” as this is a typical deterministic phrasing that is not applicable in this individual-based modeling setting. We followed the example of the progressive immunity model of Guzzetta et al. and assumed that all re-exposures to varicella resulted in effective boosting. Furthermore, the parameter values allow situations in which infectious contact occurs, without being boosted. These models, however, did not fit well to the data as none of these models were retained after our selection procedure.

About the modeling of the Force of reactivation (subsection “Modeling VZV endogenous reactivation”), recent papers have modeled it as an increasing function of age (=senescence), and of time elapsed since last boosting episode. In the paper this is modeled as a purely random factor “The FoR deviates per time step and individual by means of a gamma function.” Am I understanding correctly? In my opinion that should be taken as a (useful) baseline against which, however, to ground alternative, possibly more realistic hypotheses. Therefore this point should be motivated more carefully. How was this gamma (density?) parametrized? This is important because one of the main results on the impact of vaccination i.e. the young age of zoster cases in the post-vaccination period (“Noteworthy is the relative dominance of the 31–40 year...”) might strongly follow from this hypothesis.

First of all it is important to emphasize that the deterministic models use an epidemiological compartmentalization in which the force of reactivation represents the transition rate between two groups. In case of the deterministic models, this force of reactivation integrates the concepts of waning of immunity, VZV reactivation and endogenous boosting. And depending of the type of model, exogenous boosting might also be found in the equation for the reactivation rate (Brisson: No; Guzzetta: Yes). We use the force of reactivation as an explicit and independent characteristic of the behavior of VZV. It simply represents VZV reactivation. Whether it will evolve into zoster or endogenous boosting will depend on the value of VZV-CMI. This kind of modeling is not possible when using a deterministic framework. We have added “The reader should imagine the FoR to represent independent reactivation behavior of VZV and whether this reactivation will lead to HZ or endogenous boosting will depend on the value of VZV-CMI.” and “The FoR deviates per time step and individual by means of a gamma probability density function. This gamma function is chosen as it represents the summation of unknown biological phenomena that are assumed to have an exponential distribution.” to the paragraph concerning VZV reactivation. Furthermore, we have changed the title from “Modeling VZV endogenous reactivation” to “Modeling VZV reactivation”. In our VZV-IBM we have tested four different gamma distributions and these were included into the parameter set selection procedures. We reckon that our choice for a gamma distribution might be considered to be arbitrary, but we would like to emphasize that even in deterministic models arbitrary choices are made given the fact the exponential distribution is implicitly assumed for all these models (although often not explicitly mentioned).

Reviewer #3:

[…] However, also considering the standard of the eLife journal, I believe the paper cannot be accepted in its current form. Some major improvements and changes are required to make it fit for publication. In particular, specific modeling assumptions and fitting procedures need to be carefully re-addressed and properly clarified before consideration for publication. See the list below for the required amendments:

We believe we have made the necessary changes that allow our innovative paper to be suitable for publication in eLife.

1) The analysis is based on an Agent-Based Modeling framework. These models require a very thorough validation procedure, especially when considering a realistic demographic population. The authors do not show any model output that convinces us that the demographic component is suitable to model VZV in Belgium. I believe that these validations outputs should be presented.

We have completely reformatted our description of demography to “The dynamics of the synthetic population of the individual-based model are based on Belgian population and mortality data normalized to a fixed total population of 998,400 individuals [Eurostat, 2012]. The chosen population size is the result of a trade-off between ensuring sufficient heterogeneity and a manageable computational burden. Natural deaths are selected based on the age-dependent mortality rate. Per time step, the number of newborns equals the number of deaths to obtain a constant population size. To conduct predictions over many years, a stationary demographic structure is required throughout the simulated period. The Belgian population from 2012 has an overrepresentation of people from age 40 to 60 years (see Figure 7). Applying a fixed age-dependent mortality rate in combination with the replacement by newborns would results in an oscillating population distribution over time with respect to age. Therefore, the initial age distribution is not based on the Belgian population count from 2012 but on the survivor function estimated from data on the number of deaths per capita. The survivor function by age is estimated from data on the number of deaths per capita by m(a)=exp(0aμ(t)dt) with age-dependent mortality rate μ using a thin plate regression spline model with the gam-function in the R-package mgvc (Hens 2012, Wood 2011). Figure 7 illustrates the survivor function by age together with the Belgian population and mortality rates in 2012.

The model runs in time steps of one week and people with week-age 53 move to the next age class. To obtain homogeneous age transitions throughout the simulated period, initial week-ages are randomly assigned between 1 and 52. People from the last age class with 53 weeks are removed from the population so that the demographic structure remains stable throughout the simulated period.”

2) Details of the model structure used are missing. Is the structure following the traditional Brisson/Edmunds/van Hoek approach or the Guzzetta progressive immunity one (AJE 2013)? Details on this should be available to the reader.

We understand the demand for a better structuring and more elaboration. We have added a new figure detailing an important part of the model, we have majorly restructured the Methods section and we have added a new paragraph called “Model overview”.

3) The three exogenous boosting scenarios: a number of parameters are simply assumed and no explanations on their values are provided. In particular, why six weeks to reach the peak after exogenous boosting?

Our model is informed by experimentally observed data and most of the information is based on the 2008 Levin et al paper where the time point of six weeks was used as the time point to assess VZV-CMI. We agree that the time point of boosting could also be placed at four weeks after re-exposure, but on a larger scale this will have no effect on our results. We have added “The six week duration between the boosting event and the peak has been influenced by the Levin et al. data (Levin 2008)” to the “Modeling exogenous re-exposure to VZV” paragraph.

Also, in scenario 2, 60% of pre-boosting value (why?), steady state for x years (?) and why >= 3 years? A better explanation on these parameter values is required.

Again, these numbers come from the Levin et al. paper. In order to further clarify this we have expanded our citation to that reference to “(cf. Figure 3 in the Levin et al. paper)”.

Also what is the biological explanation for the return to pre-boosting values after x years?

All vaccine studies show the tendency for cellular immunity after boosting to decay (in many studies after some time) to the base line values. Speculations in the experimental studies where this has been observed and in the biomedical literature in general, to try and explain this goes beyond VZV and certainly beyond the purpose of our paper. From a biological perspective this means that the original infection creates an equilibrium value (set-point) for VZV-CMI. From a clinical perspective this could also be illustrated by the decline of Zostavax vaccine efficacy with time after vaccination. However, we note that our parameter sets allow the “x” to be very large so that the duration of boosting could even go up to 20 years.

Finally, in scenario 3 there's a little bit of confusion between delta t and x. The authors should check the formula of Y(t).

The reviewer is correct. We have changed all delta t’s to x.

4) The lines “HZ individuals are assumed to be infectious for 1 week and receive a VZV-CMI reset to 1 +/− random factor (normally distributed, cf. primo infection) and “HZ only occurs in about 5% of individuals [Yawn 2011] and that VZV-CMI is higher in recovered HZ patients than in age-matched controls” seem contradicting. What is the post HZ value of VZV CMI? As after primary infection or higher?

In our model successful VZV reactivation is assumed to cause an equal increase of VZV-CMI as compared to chickenpox. However, due to waning of VZV-CMI in individuals not having HZ the actual VZV-CMI could be higher in those after HZ.

5) The sentence “Although HZ infectiousness was needed to maintain circulation of VZV in our model, the relative effects on overall VZV transmission are – compared to CP – marginal”: it is not clear here why you need HZ infectiousness to maintain circulation of VZV infection. If it is post-vaccination we don't care to maintain VZV circulation. If it is pre-vaccination, then there is something wrong if the model need HZ to keep VZV infection.

Deterministic models do not need HZ infectiousness to maintain VZV transmission, but IBM do need HZ infectiousness (or multiple re-introductions from outside our populations, but that is beyond the scope of this paper) to reach endemic equilibrium (we realize that our model might be the only model so far to endemically model a viral infection by means of a IBM).

6) The approximation of HZ infectiousness to varicella breakthrough is a strong assumption. at the least we need to check the sensitivity of model results to variations of this parameter value.

We understand the hesitance of the reviewer regarding this approximation. We note that Brisson et al. (2000) used the same approximation. We added a sensitivity analysis to verify the robustness for our 13 best fitting parameter sets. This is shown as Figure 2–figure supplement 2. The reader can verify that for a range of parameter values of the HZ infectiousness (from 0.03 to 0.45) the predicted HZ incidence does not vary that much. We have also added “Figure 2–figure supplement 2 shows the results of a sensitivity analysis in which we varied HZ infectiousness from 0.03 to 0.45 for the thirteen best fitting parameter. As can be seen in Figure 2–figure supplement 2 our results are quite robust” to the respective Methods paragraph.

7) The fitting procedure needs to be rethought. It seems that the authors explore in a two-step approach a grid of values and parameter sets. First of all, where is the decision to run the simulation three times coming from? And how is the grid of parametric space explored? And also how are the values in the grid selected? What is the criteria? From Table 2 I notice some very weird combinations of parameters going from step 1 to step 2. It does not seem we are considering the whole parametric space in step 1 and then narrowing the ranges as a function of the results obtained in step 1. A much more comprehensive sensitivity analysis should be performed to evaluate more thoroughly the entire parametric space.

Our results showed that the stochasticity of the simulations did not have a major influence on the predicted HZ incidences per parameter set as illustrated by the fact that the median relative variance of the deviance of the top 13 parameter sets for the three runs is only 1.9% (also see Figure 2–figure supplement 2). As such, we decided to use three runs per parameter set to account for a reasonable amount of stochasticity.

All parameter values are combined in the first parameter sets meaning that the entire parameter grid (informed by existing experimental data) is explored in the first step. In the second step we explore in more detail the most significant regions (as detailed in the Methods section). It is also important to realize that 1 simulation (thus one run for one parameter set) costs about 6-7 hours of computing time for one core meaning that it is not feasible to explore the entire parameter space with equal detail. Our presented results include data from more the 24,000 runs thus representing approximately 150,000 CPU hours (not including preparatory work).

8) The best parameter sets are chosen based on a fit of the HZ incidence data, considered to be binomially distributed. Wouldn't it be better to consider a Poisson distribution for the HZ incidence data (Guzzetta et al. 2013), considering that incidence refers to count of HZ episodes per age group?

Published data by Yawn et al. showed that HZ recurrence rate within two years is 2% (even not significantly different from 1 when only looking at immunocompetent individuals). As such we assumed that individuals had either HZ or not during a year and this is best modeled by a binomial distribution.

9) The authors built an IBM that accounts for both between and within host dynamics, namely, taking into consideration both exogenous and endogenous boosting. The best parameter sets to inform the mathematical model are chosen based on repeated fitting of the HZ age-specific incidence estimates from the model to observed HZ incidence data from Belgium. As regards the fit of the best sets of parameters to the observed HZ data, as shown in Figure 1 and 2, the fit is very poor for the younger age groups, even for the two best parameter sets (9 and 13), as it is duly noted by the authors. Is there any way to improve the fit in this age group, considering that in the deterministic model by Guzzetta et al. (2013) it can be observed a better fit of HZ in young age groups? Maybe the authors should aggregate the incidence into age classes as otherwise the stochastic nature of the data might prevail over the goodness of fit.

We disagree with the strong statement that our model fits “very poor” for younger age groups. We also note that Figure 3 in Guzzetta et al. shows a poorer fit for the teenagers (although the size and scale of Figure 3 in Guzetta et al. hampers full appreciation of the fit). We do agree that our fit for the younger age groups is not as good as our excellent fits for the older – and more relevant – age groups and this finding might be due to a lack of relevant biological data for these age groups. We believe that future models and experimental studies should look into the effect of having chickenpox as an infant as it has been observed (as mentioned in our Discussion) that these individuals have lower VZV-CMI compared to others. We have expanded our sentence in the Discussion to “reduced VZV-CMI induction if infected during the first year of life as this might improve the prediction of the teenage group (Terada 1994)”.

10) It seems, from parameters sets 8, 9, and 13, that a higher peak fold increase following exogenous boosting is associated with a better fit of HZ incidence data in the first ten years of age. What about the age group between 10 and 20 years of age, the one suffering the poorest fit?

Parameter sets 8, 9 and 13 also have other different parameters (including a higher VZV reactivation rate). As stated in the previous response, we believe that it is rather the observed HZ incidence in the teenage group that is higher than would be expected and we think that future versions of our model (in the same way that the Brisson models improved over the years) should try to account for this.

11) The authors claim that their model can easily accommodate new parameter value coming from experimental studies. However, when it comes to consider the effect of an hypothetic vaccination program, they choose a very simplistic and unrealistic one. Wouldn't it be better if they considered more realistic scenarios, such as those taken into consideration by Poletti et al. (2013) and other works, or some actual vaccination program, as the one in the US or in other countries with an effective varicella vaccination program? Also, the amount and timing of zoster reactivation may be country-specific as shown in Poletti (2013). This should be mentioned in the Discussion, especially considering the current debate on whether or not to introduce universal VZV vaccination in several countries.

Our paper presents the first VZV IBM to date and presents a whole new method for dealing with the VZV “problem”, and estimates hitherto poorly documented immunological parameters. We agree with the comment by the reviewer that future more applied analyses should account for a broader (and more realistic) range of vaccination scenarios than the illustrative example from this conceptual paradigm shifting paper. We have added “If future VZV IBM are applied to project the impact of interventions, they should of course explore more realistic vaccination scenarios and assess inter-country variability in these explorations (Poletti 2013)” to the Discussion with reference to the Poletti et al. paper.

12) Figures 4 and 5 should be redone considering maybe an aggregation over time, to avoid all the stochasticity of the model output. In Figure 4 the authors plot the pre-steady state and pre-vaccination incidence which is not of interest. And there is also a part of the plot without any line (right hand side). The interesting bit is the post vaccination part to which the authors only dedicate a small portion of the graph. Also, why are there different colors?

Aggregation can be understood as presmoothing and it has been shown in the statistical literature that presmoothing is often not appropriate to handle stochasticity (see e.g. [Aerts 2010]). In order to present our results as transparent as possible we prefer to present the results “as they are”, meaning with the inclusion of full stochasticity. Otherwise the reader might be confused with the traditional output from deterministic models. We strongly disagree that the “interesting bit is post vaccination”. We have fitted this model to data pre-vaccination, and verify simultaneously some poorly understood biomedical parameters using a highly novel individual-based approach. The concept of the model is the primary interest in this paper, not the projections that can be made with it. We thus prefer to show all data including the pre-steady and pre-vaccination data. We only analyzed the post-vaccination data up to 80 years after vaccination.

https://doi.org/10.7554/eLife.07116.018

Article and author information

Author details

  1. Benson Ogunjimi

    1. Centre for Health Economics Research and Modeling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
    2. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Hasselt, Belgium
    Contribution
    BO, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article
    For correspondence
    1. benson.ogunjimi@uantwerp.be
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon 0000-0002-0831-2063
  2. Lander Willem

    1. Centre for Health Economics Research and Modeling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
    2. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Hasselt, Belgium
    3. Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium
    Contribution
    LW, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article
    Competing interests
    The authors declare that no competing interests exist.
  3. Philippe Beutels

    1. Centre for Health Economics Research and Modeling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
    2. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Hasselt, Belgium
    3. School of Public Health and Community Medicine, University of New South Wales, Sydney, Australia
    Contribution
    PB, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article
    Competing interests
    The authors declare that no competing interests exist.
  4. Niel Hens

    1. Centre for Health Economics Research and Modeling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
    2. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Hasselt, Belgium
    Contribution
    NH, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article
    Competing interests
    The authors declare that no competing interests exist.

Funding

Fonds Wetenschappelijk Onderzoek (G040912N)

  • Benson Ogunjimi

University of Antwerp (Special Research Fund predoctoral fellowship)

  • Lander Willem

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Hercules Foundation and the Flemish Government—department EWI. In particular, we thank Drs Bex, Becuwe and Backeljauw for their support in using the Supercomputers.

Reviewing Editor

  1. Mark Jit, Reviewing Editor, London School of Hygiene & Tropical Medicine, and Public Health England, United Kingdom

Publication history

  1. Received: February 21, 2015
  2. Accepted: July 17, 2015
  3. Version of Record published: July 11, 2015 (version 1)

Copyright

© 2015, Ogunjimi et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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