Pre-vaccination age-specific VZV seroprevalence data for Finland, Italy and the UK were made available from the European Seroepidemiological Network 2 [1], which is the largest available population-based study on VZV seroprevalence in Europe. The method of sera collection adopted (residual sera) is the same in the three countries considered in this paper. The results from the assays adopted in the ESEN2 study are standardized which make international comparisons possible. The total sample sizes were in the range (about 2000) considered optimal for these types of studies, and all studies were designed to be representative by age. These data describe the natural history of infection and are critical for estimating the force of infection (FOI) of varicella. Age-specific HZ case notification data were obtained from published studies for Finland [28], Italy [3] and United Kingdom [23]. Country-specific routine socio-demographic data for the three different countries were obtained from the Eurostat databases [31], for estimation of contact distributions.

The mathematical model for VZV transmission dynamics and HZ development extends earlier compartmental models [12], [25], [27], [32] by incorporating different country-specific levels of boosting (flow diagram in Fig. 1). Full technical details are given in Text S1. Briefly, newborn individuals are assumed to be protected by maternal antibodies for six months on average [33], after which they become susceptible to varicella and are exposed to an age-specific FOI . In the absence of vaccination, the FOI is defined as follows: where as we consider a population subdivided in 100 1- year age classes, q is an age-independent transmission coefficient, according to the so-called social contact hypothesis [34]; is an age-specific contact matrix whose entries describe the average numbers of different persons in age group j encountered by an individual belonging to age group a per unit of time (so that the product defines the number of adequate contacts for having infection transmission); and are, respectively, the fractions of varicella and HZ cases of age j in the population and is the relative VZV infectiousness associated with HZ; latency and infectious periods are assumed to last, respectively, 14 and 7 days on average [33], [35], [36]. After recovery, individuals become permanently immune to varicella. VZV immune individuals become susceptible to HZ due to the decline in CMI, which occurs at constant rate . HZ susceptibles have two possibilities, either boosting their CMI by exposure to infectious individuals, thus reacquiring the protection against the development of HZ, or progressing to HZ disease, at a rate which is higher in children and the elderly and lower in adults [25]–[27]. HZ cases contribute to the varicella force of infection for 7 days on average [36]; afterwards, they become permanently immune to HZ disease. The CMI of HZ susceptible individuals is boosted according to a force of boosting (FOB) , which is assumed to be proportional to the varicella FOI.

The incomplete protection supplied by the licensed varicella vaccine against varicella and HZ [15], [17], [18], [20], [37]–[43] makes the post-vaccination model articulated in several cases. A proportion P of vaccinated individuals suffer an initial vaccine failure and remain susceptible, while the complementary fraction of vaccinated individuals (1-P) have a fixed take probability T to acquire temporary protection against VZV infection and a lifelong partial protection against HZ. For the sake of simplicity in model simulation, we assume that vaccine coverage accounts also for primary failure. This means that e.g. when we consider a coverage of 90%, we assume that a possibly higher proportion of individuals is vaccinated, but only 90% are vaccinated without experiencing the primary vaccine failure. As a consequence, when the coverage is set to 100%, primary failure probability is assumed to be zero. Vaccine protected individuals lose immunity against varicella at a waning rate W.

Vaccinated individuals who suffer a secondary failure (a fraction (1–T)(1-P)) and vaccine protected individuals whose immunity against varicella has waned are exposed to the natural FOI, but are assumed to acquire a milder infection commonly referred as breakthrough varicella which will be less infectious than natural varicella (i.e., varicella occurring among unvaccinated individuals). Vaccinees can develop HZ after breakthrough varicella or directly from the vaccine strain [6]. In the latter case, HZ is caused by vaccine virus instead of wild type. The mechanism of varicella and HZ development among vaccinees is the same as the one described for individuals who experience natural varicella infection. However the rate at which vaccinated HZ susceptibles develop HZ is lower [44] (instead of where ). The post-vaccination varicella FOI becomes: where is the fraction of breakthrough varicella cases of age j and is their relative VZV infectiousness; is the fraction of HZ cases of age j. A full listing of model parameters and literature sources is given in Table 1.

Model parameterization involved several steps. First, age-specific contact matrices for each country considered were taken from [45]. These contact matrices were computed by an approach similar to the one introduced in [46] but further developed to derive social contact structures for several European countries. Briefly, a synthetic population of agents, each one corresponding to an individual in the real population, is generated by using highly detailed routine socio-demographic data [31], such as household distributions by type, size and age of members, school sizes for the various school levels, workplace sizes and employment rates by age, and the age distribution of the general population. From this synthetic population, age-specific contact matrices for each country considered were computed. These synthetic matrices are possibly more harmonized compared to Polymod matrices and less prone to observational biases. Nonetheless, they share several common features with the Polymod matrices, e.g. strong assortativeness and the presence of similar secondary diagonal contact pattern, and as shown in [45], most statistical variation between Polymod-type and synthetic matrices can be captured by a single scale factor.

Second, age-specific FOI estimates for varicella in the three selected countries were estimated by fitting an age-structured SIR model at endemic equilibrium to age-specific varicella serological data (Fig. 2abc) and estimating the three country-specific transmission coefficients q (as in [34], [46]–[49]) which, together with the synthetic contact matrices, maximized the likelihood of the varicella seroprofiles observed in each country by assuming a negligible contribution of HZ to the pre-vaccination varicella FOI (details in Text S1).Third, parameters describing progression to HZ disease () were estimated by fitting the whole pre-vaccination model to HZ age-specific incidence data conditionally on the estimates found for varicella transmission and by minimizing the mean squared error between observed and predicted HZ incidence (Fig. 2def) in the different countries.

Considering the difficulties related to HZ susceptibility status being non observable, we favored a novel approach to parameter fitting which we call simultaneous, whereby HZ parameters were estimated using age-specific zoster incidence data from all the three countries together assuming that parameters describing strictly biological processes (such as the average duration of CMI and the VZV reactivation rates) were the same in all countries, while parameters reflecting social interactions might be different. This approach was preferred to the traditional one, based on separate parallel fitting for each country, as the latter might yield inconsistent inter-country estimates of biologically based HZ parameters (see further details in Text S1). On the other hand, we allowed the scaling factor z of CMI boosting to be country-specific. Indeed, this parameter is not a purely biological parameter but may depend also on social factors, e.g. contacts of the elderly, and as such may account for the large uncertainty in the FOI, and therefore in the FOB, at higher ages.

Unlike previous modeling work [12], [23]–[26], where some vaccine related parameters were estimated from vaccine trials data using simple dynamic models and making a-priori assumptions on the duration of CMI, we decided to rely on literature estimates. Our simulations include the reduction factor in the reactivation rate for vaccinated individuals documented in [44], where it is shown that individuals with a history of varicella vaccination have a 4 to 12 times lower risk of developing HZ compared to individuals with a history of natural infection (further uncertainty on is investigated in Text S1). However, we preferred to explore a wide range of possible values for the waning rate W and the take probability T in order to account for the large uncertainty characterizing these parameters [7], [50]–[52].

The impact of VZV vaccination on HZ incidence is investigated under different scenarios of coverage and schedule. The program consisting in one single dose provided to 1 year old children is analyzed by assuming coverage levels ranging from 70% to 100%. Moreover, a two-dose program has been suggested to be more effective and appropriate [15], [17], [18], [20] and the Advisory Committee on Immunization Practices (ACIP) in the US modified its recommendations to a routine 2-dose program in 2006 [18]. As a matter of fact, given the reported number of breakthrough cases in countries where vaccination is in place, a two-dose program seems to be unavoidable [15], [38], [39]. Thus, a two dose program was also considered with the first dose administered to 1 year old children and the second one to 5 years old children. Coverage of 90% and 80% have been assumed for the first and the second dose respectively. To sum up, we consider the following immunization scenarios: a single dose program, with the vaccine administered to 1 year old children with 70%, 80%, 90% and 100% coverage, and the two-dose program described above.

Uncertainty in model outputs depends on the uncertainty in three classes of input parameters, i.e. those related to (a) varicella transmission, (b) HZ development, (c) vaccine-related parameters. Specifically, for vaccine-related parameters, uniform distributions were assumed over the ranges reported in Table 1. For the structural uncertainty characterizing all HZ parameters, which implies that there are many parameter configuration which best fit HZ incidence data, we decided to take into account all these best fitting configurations. Bootstrap techniques were used to evaluate uncertainties about VZV transmission (i.e. q) and parameters related to HZ development (see Text S1). Moreover, sampling from the various uncertainty distributions of parameters was performed by Latin-Hypercube-Sampling (LHS) method [53].

The observed varicella seroprofiles for Italy, Finland and the UK are remarkably different (see Fig. 2a,b,c). In Finland, the fraction of population aged 10–19 immune to varicella is, on average, 6% larger than in the UK and 13% larger than in Italy, indicating a relatively higher FOI in Finland. In agreement with this and based on contact matrices described in the methods, we obtained values of the basic reproductive number (i.e. the average number of secondary infections resulting from a single infectious individual in a fully susceptible population [54]) also remarkably different across countries: 3.36 (95% CI 3.26,3.48) in Italy, 6.86 (95% CI 6.40,7.17) in Finland and 4.67 (95% CI 4.51,4.90) in the UK (distributions can be found in Text S1). Values of R0 obtained here are compliant with previous estimates provided by using different contact matrices [49]. However, it is worth noting that the obtained ranking in the transmissibility potential among countries, cannot be extended in general for other childhood disease (e.g. pertussis [55]), given the different natural and epidemiological history of each single disease.

Age-specific HZ incidences in the three countries show similar profiles (low and constant rates among young individuals, then a rapid increase in adults, though the pattern is less clear in the very old, e.g. in Italy there seems to be a decline), but also remarkable differences in scale, with the UK rates being twice as high as the ones from Finland (see Fig. 2d,e,f).

By ascribing these differences to varicella transmissibility and HZ susceptibility, while keeping biological HZ related parameters constant across countries, we were able to well reproduce both serological varicella data (Fig. 2abc) as well as the observed HZ incidence (Fig. 2d,e,f).

More specifically, given that CMI duration and the reactivation rate were simultaneously fitted on the three country-specific datasets, the major between-country difference was the predicted role of boosting, which resulted stronger in Finland compared to Italy and the UK. This role is well illustrated (Fig. 2g,h,i) by the differences in the predicted age profile of HZ susceptibility among individuals, which is remarkably lower in Finland compared to Italy and the UK. This result is consistent with the observed scale of HZ incidence, which is about twice as large in the UK as in Finland (Fig. 2d,e,f). The somewhat counterintuitive interpretation is that though Finland suffers a higher varicella FOI, i.e. more (and occurring earlier) varicella infection, thereby creating more space for HZ, this higher transmissibility also yields a stronger boosting effect, and therefore ultimately a fewer overall number of HZ cases in the population. Given the remarkable inter-country epidemiological differences in terms of both age specific HZ incidence and VZV transmissibility potential, the impact of varicella vaccination on HZ epidemiology is expected to be strongly country-specific.

The predicted age distribution of boosting episodes is similar among countries (see Text S1) and it is characterized by two peaks, the first one at ages 5–10, the second one at ages 20–50, probably determined by contacts of infected children with siblings and/or schoolmates in the first case and with parents in the second. Moreover, the reactivation rate is predicted to decline from birth to about age 30 and starting to increase thereafter (see Text S1). This is consistent with the idea that immune competence is not completely developed in young children and that it decreases with age. The average duration of CMI is estimated to be in the range of 60–100 years, which is surprisingly different from the one estimated in previous studies (i.e. 20 years in Brisson et al. [12] and following papers). Though seemingly different from previous estimates, these values are fully compatible with the obtained 30% HZ lifetime risk [12]. For example, for years, given the exponential decline in CMI levels after varicella immunity, 39% of those who had varicella are - in absence of boosting - already susceptible to zoster 40 years after varicella infection (i.e. essentially at ages 40–49). Even if boosting is considered, the risk of HZ is higher than the FOB at high ages, which implies that a substantial proportion of adult HZ susceptible will get HZ prior to being boosted.

We investigated carefully the case of perfect boosting (z = 1 for all countries i.e., FOB equal to country-specific FOIs) and our conclusions are that the model fails to reproduce the country specific HZ incidences unless we relax our principal hypothesis that the duration of CMI and the reactivation rate are the same in all countries. Indeed, following the traditional approach, based on separate parallel fitting, the model is able to well reproduce the HZ incidences, though yielding strongly inconsistent inter-country estimates of CMI duration i.e., in the range of 20–80 for the UK and in the range of 120–160 for Finland (see Text S1 for more details).Therefore, all results presented hereafter are based on the simultaneous fitting approach whereas the parallel fit is considered only for sensitivity analyses.

Under all programs considered, a remarkable decrease in varicella incidence after vaccination is predicted, on average, in the medium and long term in all countries considered (main scenarios reported in Fig. 3, alternative scenarios reported in Text S1). However, a large uncertainty surrounds the average predictions, which is essentially the consequence of the uncertainty surrounding vaccine related parameters. Cases of natural varicella are predicted to decrease as the mass immunization program progresses. However, in general, even with 100% coverage, varicella cannot be eliminated with a single dose administered to 1 year-old infants (See Fig. 3a,b,c), unless vaccine protection wanes remarkably slowly and the probability of vaccine failure is sufficiently small. As expected, vaccination is predicted to be less effective in reducing varicella incidence in countries where the VZV transmissibility potential (R0) is large, as in Finland. As a rule, there is an initial phase after the introduction of the vaccine where virus circulation is sustained by older unvaccinated individuals. However, due to vaccine failure and waning immunity, in less than 10 years (on average) breakthrough varicella becomes the main source of VZV transmission. This is supported by the analysis of empirical data [19] and also found in other modeling studies [12], [23]–[27]. Specifically, when 100% coverage is considered, most varicella infections in the medium and long term are breakthrough cases while for lower coverage levels, the fraction of natural varicella infections remains large. Indeed, in the 70% coverage scenario (Fig. 3def), the long term (after about 50 years) fraction of total predicted cases due to natural varicella is 53.3% (95% CI 34.4,73.1) for Finland, 52.9% (95% CI 35.5,75.2) in Italy, and 54.0% (95% CI 34.8,74.9) in the UK. Under the two-dose program (90% +80% coverages), the predicted impact of vaccination on varicella in the three different countries is similar to the one predicted for a single dose with 100% coverage (see Fig. 3a,b,c and Fig. 3g,h,i).

Model simulations suggest the possibility that incidence of breakthrough varicella might be very relevant in the long term. For instance, a scenario where breakthrough varicella may be as high as 10 per 1000 individuals per year in Finland i.e., very close to the pre-vaccination varicella incidence (about 12 per 1000 individuals per year) cannot be excluded.

Moreover, model predictions show that the age at varicella infection increases in all considered scenarios (See Fig. 4 and Text S1). Specifically, in Finland, before the introduction of vaccination, less than 5% of varicella cases are predicted to occur among individuals older than 20. If a single-dose program with 100% coverage is considered, after 20 years of vaccination, the proportion of cases occurring in Finland among individuals older than 20 is predicted to increase to 20% and to more than 50% after 50 years of VZV vaccination. Similar results have been obtained for Italy and the UK. The effect is milder when considering lower vaccine uptake. However, in the medium-long term, the fraction of cases occurring in individuals older than 20 is predicted to increase from 5% to at least 25% for all coverages and countries (details in the Text S1).

To sum up, in the long term we expect essentially all breakthrough infections mostly occurring in adults and the elderly. Finally, as expected, VZV mass vaccination results in a dramatic decline of yearly boosting incidence (details in Text S1), namely 78% in Finland, 97% in Italy and 94% in UK when 100% coverage is considered.

There is a striking difference between model predictions on HZ compared to varicella: short and medium-term predictions on HZ are surprisingly robust, unlike the ones on varicella, because these predictions mainly concern individuals who acquired varicella before the start of vaccination. Consequently these predictions are not affected by the large uncertainty characterizing vaccine-related parameters (i.e., the corresponding prediction intervals are surprisingly narrow).

The predicted impact of VZV vaccination on HZ incidence is strongly country-specific (main scenarios reported in Fig.5, alternative scenarios reported in the Text S1). In Finland, HZ incidence is predicted to increase by 17–32% (depending on coverage and number of doses) for about 40–60 year after the start of immunization (Fig5 a,d,g), whereas in Italy, where the observed HZ incidence in absence of immunization is larger and the force of infection of varicella is lower, the increase is much smaller (+2.5–3%, Fig 5 b,e,h). Finally, in the UK (Fig. 5 c,f,i), HZ results remarkably mitigated by vaccination. More specifically, in Finland HZ incidence is expected to increase from 2.69 (95% CI 2.50,2.84) to 3.54 (95% CI 3.13,3.75) per 1000 individuals per year at 30 years post vaccination, when the 1-dose program with 100% coverage is considered (Fig. 5a) and up to 3.15–3.45 per 1000 when lower coverages (70%) are considered (Fig. 5d). Similarly, in the two-doses program, the HZ incidence is expected to increase to 3.53 (95% CI 3.14,3.74) per 1000 (Fig. 5g). In Italy (Fig. 5beh), HZ incidence is instead predicted to increase only slightly from about 3.79 to about 3.88–3.90 per 1000 individuals per year while, in the UK (Fig. 5cfi), HZ incidence is predicted to continuously decrease together with the progress of mass immunization.

Medium-term predictions indicate that an increase of HZ incidence is not a certain fact, but rather seems to depend on the presence or absence of factors which promote a strong boosting intensity (and, as a consequence, a lower HZ susceptibility) and thus may or may not be heavily affected by changes in varicella circulation due to mass immunization. Indeed an increase in HZ incidence occurs in countries where the incidence rate was lower prior to vaccination, possibly due to a higher force of boosting (e.g. Finland), whereas the increase in HZ incidence is minor or absent where the force of boosting was milder (e.g. the UK).

A general remark about the impact of VZV immunization on HZ is that whatever the country specific initial conditions in terms of HZ incidence and VZV force of infection, and despite different assumptions about the degree of success of immunization in the various countries, HZ incidence remain steadily above around 3 per 1000 cases per year and lands on the level of 3 per 1000 after about 60 years of vaccination programs. This surprising convergence result is quantitatively accurate at high immunization levels (as exemplified either by the one dose-100% program, or by the two-doses programs, respectively in the top and bottom rows of Fig. 5). The explanation is that at high levels of immunization the force of boosting, which is the only factor differentiating the HZ epidemiology among the three countries considered, rapidly becomes negligible and the three countries remain exposed only to the equalizing role jointly played by vaccination (generating an identical flow of HZ cases from the vaccine strain the three countries) and by the action of biological HZ parameters, which by hypotheses are identical in the different countries. At lower immunization levels (as exemplified by the middle row in Fig. 5) convergence is only slightly less quantitatively accurate due to the fact that the lower coverage allows some differences in the force of boosting among countries to persist over time.

Our results about the impact of VZV immunization on HZ incidence, e.g. in the UK, are remarkably different from those obtained in previous modeling studies which were dealing with a single country 12,23–28,32. Indeed, by removing the constraint that the duration of CMI and the reactivation rate are the same in all countries (as in our parallel fit approach) the HZ incidence is predicted to increase in all countries considered, as illustrated in the two-dose scenario of Fig. 6). When the 70% program is considered instead of the 100% program, the predicted increase in HZ incidence is smaller (e.g. for Finland, see Fig. 5d) due to the smaller impact of vaccination on boosting, but the burden of natural varicella obviously remains larger (Fig. 3d).

For at least 50 years after the introduction of the vaccine, the dynamics of HZ incidence are driven by natural HZ, i.e. by HZ cases occurring among unvaccinated individuals that have experienced natural varicella (Fig. 5). This is the consequence of the decline of protective effect of boosting against HZ for unvaccinated individuals as a consequence of the reduction of varicella infected individuals caused by mass VZV immunization. This phenomenon is well illustrated by the ideal scenario of a 100% coverage program, implemented with a perfect vaccine with probability of failure equal to zero and conferring permanent immunity against varicella (details in Text S1). For instance, in Finland, HZ incidence is predicted to increase in the short-medium term due to the removal of the protective effect of boosting, and to vanish in the long term due to the gradual removal of all VZV and HZ susceptibles through the perfect protection provided by vaccination. However, this process requires at least the removal, by natural causes, of an entire generation, i.e. more than 70–80 years.

On the other hand, once the population becomes mostly composed of vaccinated individuals and the fraction exposed to natural varicella declines, which occurs after 5–6 decades after the introduction of the immunization program, HZ is strongly reduced by vaccination and attains levels well below those before vaccination, reaching in all countries levels around 2 per 1000 per year. Nonetheless, as already shown in [23], [28], HZ is far from being eliminated, given that the vaccine protects only partially against varicella and HZ. In the long term, HZ incidence is mainly caused by the vaccine strain. For instance, if a coverage of 100% is considered, the latter is expected to slowly increase from the beginning of the immunization program up to around 0.9 per 1000 individuals per year after 100 years of vaccination. The large uncertainty surrounding long term predictions on HZ from the vaccine strain compared to natural HZ is again the consequence of the large uncertainty about vaccine-related parameters.

Predictions of the age distribution of HZ cases for all considered scenarios show that both before and after the introduction of vaccination most of HZ cases occur in the elderly (see Fig. 7 and Text S1). For instance, in Finland, in the absence of immunization, 61% of HZ cases are predicted to occur among 60+ old individuals (59% in Italy and 54% in the UK) while 21% occur among those aged 40–59 (21% in Italy and 25% in the UK). Under the single dose 100% coverage program, the proportion of cases occurring in Finland among individuals older than 60 is predicted to slightly decline initially (first 15 years after the start of immunization) due to the sudden decline in the FOB and consequent increase in zoster across all age groups, and then to sharply increase, up to a maximum of 85%, 55 years after the initiation of the program. Finally, after 100 years of vaccination the age distribution of HZ cases is surprisingly almost restored to the pre-vaccination level (see Fig. 7, top row) although the overall number of cases is considerably reduced. This peculiar post-vaccination dynamics is explained in Fig.7 (bottom) which reports the absolute HZ incidence by age at various time points following the introduction of the vaccine. For instance in Finland, in all age groups which are not vaccinated, the absolute incidence of HZ increases due to the sudden decline in the FOB caused by the introduction of the vaccine, which increases the speed at which all initial HZ susceptibles acquire zoster at subsequent times. On the other hand, HZ cases decrease among individuals who have been vaccinated, due to the highly effective role of the vaccine in preventing natural varicella infections (and subsequent HZ development from the wild strain) and dramatically slowing VZV reactivation for vaccinees. The interplay of these two factors yields an increase in the weight of the elderly in the medium term.

Similar results have been obtained for Italy and the UK and for other coverages and schedules considered (see Text S1).

Unlike previous single-country modeling studies [12], [23]–[28], [32], the proposed multi-country perspective shows, under different vaccination scenarios, that an increase in HZ incidence is not a certain fact, but rather seems to depend on the presence or absence of factors promoting a strong boosting intensity and that may, or may not, be heavily affected by changes in varicella circulation due to the introduction of mass immunization programs.

These findings might provide an explanation for the ambiguous empirical evidences about the increases of HZ in those sites where mass varicella vaccination is ongoing [30]. In particular, they suggest which are the sites where such increases in HZ incidence are more likely to occur: those where pre-vaccination HZ incidence was low due to a high pre-vaccination force of boosting. Therefore, these findings supply potentially useful strategies for the selection of HZ sentinel sites aimed at detecting possible symptoms of HZ upsurge as a consequence of mass immunization.

Moreover, though following VZV immunization HZ is predicted to increase in Finland and to decline in the UK, the overall HZ incidence in Finland always remains below the corresponding UK figure, and overlaps to it in the medium-long term. This finding suggests an equalizing role of vaccination which is important to consider from an international, e.g. European, policy making viewpoint.