The epidemiology of varicella-zoster virus infections: a mathematical model

The health and economic impact of switching vaccines in universal varicella vaccination programs using a dynamic transmission model: An Israel case study

Currently available health economic models for varicella infection are designed to inform the cost-effectiveness of universal varicella vaccination (UVV) compared with no vaccination. However, in countries with an existing UVV program, these models cannot be used to evaluate whether to continue with the current varicella vaccine or to switch to an alternative vaccine. We developed a dynamic transmission model that incorporates the historical vaccination program to project the health and economic impact of changing vaccination strategies. We applied the model to Israel, which initiated UVV in 2008 with a quadrivalent vaccine, MMRV-GSK, and switched to MMRV-MSD in 2016. The model was calibrated to pre-vaccination incidence data before projecting the impact of the historical and future alternative vaccination strategies on the clinical burden of varicella. Total costs and QALYs lost due to varicella infections were projected to compare continuing with MMRV-MSD versus switching to MMRV-GSK in 2022. Over a 50-year time horizon, continuing with MMRV-MSD reduced varicella incidence further by 64%, reaching 35 cases per 100,000 population by 2072, versus a 136% increase in incidence with MMRV-GSK. Continuing with MMRV-MSD reduced cumulative hospitalization and outpatient cases by 48% and 58% (vs. increase of 137% and 91% with MMRV-GSK), respectively. Continuing with MMRV-MSD resulted in 139 fewer QALYs lost with total cost savings of 3% compared with switching to MMRV-GSK, from the societal perspective. In Israel, maintaining the UVV strategy with MMRV-MSD versus switching to MMRV-GSK is projected to further reduce the burden of varicella and cost less from the societal perspective.

Characterizing and Discovering Spatiotemporal Social Contact Patterns for Healthcare

During an epidemic, the spatial, temporal and demographic patterns of disease transmission are determined by multiple factors. In addition to the physiological properties of the pathogens and hosts, the social contact of the host population, which characterizes the reciprocal exposures of individuals to infection according to their demographic structure and various social activities, are also pivotal to understanding and predicting the prevalence of infectious diseases. How social contact is measured will affect the extent to which we can forecast the dynamics of infections in the real world. Most current work focuses on modeling the spatial patterns of static social contact. In this work, we use a novel perspective to address the problem of how to characterize and measure dynamic social contact during an epidemic. We propose an epidemic-model-based tensor deconvolution framework in which the spatiotemporal patterns of social contact are represented by the factors of the tensors. These factors can be discovered using a tensor deconvolution procedure with the integration of epidemic models based on rich types of data, mainly heterogeneous outbreak surveillance data, socio-demographic census data and physiological data from medical reports. Using reproduction models that include SIR/SIS/SEIR/SEIS models as case studies, the efficacy and applications of the proposed framework are theoretically analyzed, empirically validated and demonstrated through a set of rigorous experiments using both synthetic and real-world data.

Viral Dynamics and Mathematical Models

Mathematical tools have been widely applied in understanding the dynamics and control of viral infections. Here we present some fundamental aspects of infection dynamics, starting with acute immunising infections as a case study for herd immunity and other important factors in the spread and control of infection. We then discuss the dynamics of infections with more complex life histories, including chronic infections, and those showing evolution for immune escape. We conclude with a discussion of important gaps in our current understanding of viral dynamics, along with future research needs.

Does monastic life predispose to the risk of Saint Anthony's fire (herpes zoster)?

BACKGROUND

The consequences of the epidemiology of varicella for zoster epidemiology are still debated. We therefore compared the frequency of herpes zoster in an adult population with virtually no varicella zoster virus (VZV) exposure with that in the general population (GP).

METHODS

We performed a national, multicenter, observational, exposed versus nonexposed, comparative study. The nonexposed population consisted of members of contemplative monastic orders (CMO) of the Roman Catholic Church living in 40 isolated monasteries in France. The exposed population consisted of a sample of the GP representative of the French population in terms of age group, sex, socio-occupational categories, and regions.

RESULTS

The primary analysis population comprised 920 members of CMO (41.5% nuns; mean age, 64.2 years) and 1533 members of the GP (51.9% women; mean age, 64.6 years). The reported frequency of zoster was 16.2% among CMO and 15.1% in the GP (P = .27, adjusted for sex and age). The reported mean age of onset of zoster was 54.8 and 48.6 years, respectively (P = .06).

CONCLUSIONS

This study failed to demonstrate an increased risk or earlier onset of zoster in members of CMO not exposed to VZV, compared with that in the GP. Although adults highly exposed to VZV could have a reduced risk of zoster, compared with the GP, our results suggest that the opposite is not true: adults not exposed to VZV are not at increased risk of zoster when compared with the GP, challenging the relevance of the assumptions and forecasts of current epidemiological models.

The incidence of varicella and herpes zoster in Taiwan during a period of increasing varicella vaccine coverage, 2000-2008

The introduction and the widespread use of the varicella vaccine in Taiwan has led to a 75-80% decrease in the incidence of varicella in children. However the vaccine's long-term impact on the incidence of herpes zoster (HZ) has attracted attention. By controlling gender, underlying diseases, and age effects, a Poisson regression was applied on the 2000-2008 chart records of 240 000 randomly selected residents who enrolled in the Universal National Health Insurance. The results show that, as the vaccine coverage in children increases, the incidence of varicella decreases. However, the incidence of HZ increased even before the implementation of the free varicella vaccination programme in 2004, particularly in females. The increase in the incidence of HZ cannot be entirely and directly attributed to the widespread vaccination of children. Continuous monitoring is needed to understand the secular trends in HZ before and after varicella vaccination in Taiwan and in other countries.

Modelling the effects of population structure on childhood disease: the case of varicella

Realistic, individual-based models based on detailed census data are increasingly used to study disease transmission. Whether the rich structure of such models improves predictions is debated. This is studied here for the spread of varicella, a childhood disease, in a realistic population of children where infection occurs in the household, at school, or in the community at large. A methodology is first presented for simulating households with births and aging. Transmission probabilities were fitted for schools and community, which reproduced the overall cumulative incidence of varicella over the age range of 0-11 years old.Moreover, the individual-based model structure allowed us to reproduce several observed features of VZV epidemiology which were not included as hypotheses in the model: the age at varicella in first-born children was older than in other children, in accordance with observation; the same was true for children residing in rural areas. Model predicted incidence was comparable to observed incidence over time. These results show that models based on detailed census data on a small scale provide valid small scale prediction. By simulating several scenarios, we evaluate how varicella epidemiology is shaped by policies, such as age at first school enrolment, and school eviction. This supports the use of such models for investigating outcomes of public health measures.

Assessment of varicella vaccine effectiveness in Germany: a time-series approach

A multivariate time-series regression model was developed in order to describe the 2005-2008 age-specific time-course of varicella sentinel surveillance data following the introduction of a varicella childhood vaccination programme in Germany. This ecological approach allows the assessment of vaccine effectiveness under field conditions by relating vaccine coverage in cohorts of 24-month-old children to the mean number of cases per reporting unit in the sentinel network. For the 1-2 years age group, which is directly affected by the vaccination programme, a one-dose vaccine effectiveness of 83·2% (95% CI 80·2-85·7) was estimated which corresponds to previous approaches assessing varicella vaccine effectiveness in the field in the USA.

Using empirical social contact data to model person to person infectious disease transmission: an illustration for varicella

With the aim to improve dynamic models for infections transmitted predominantly through non-sexual social contacts, we compared three popular model estimation methods in how well they fitted seroprevalence data and produced estimates for the basic reproduction number R(0) and the effective vaccination level required for elimination of varicella. For two of these methods, interactions between age groups were parameterized using empirical social contact data whereas for the third method we used the current standard approach of imposing a simplifying structure on the 'Who Acquires Infection From Whom' (WAIFW) matrix. The first method was based on solving a set of differential equations to obtain an equilibrium value of the proportion of susceptibles. The second method was based on finding a solution for the age-specific force of infection using the formula of the mass action principle by means of iteration. Both solutions were contrasted with observed age-specific seroprevalence data. The best fit of the WAIFW matrix was obtained with contacts involving touching, and lasting longer than 15min per day. Plausible values for R(0) for varicella in Belgium ranged from 7.66 to 13.44. Both approaches based on empirical social contact data provided a better fit to seroprevalence data than the current standard approach.

Deterministic SIR (Susceptible-Infected-Removed) models applied to varicella outbreaks

Deterministic SIR models were applied to simulate Susceptible-Infected-Removed and to estimate the threshold condition for varicella outbreaks in children, reported in Medellín, Colombia. The expected numbers of susceptible, infected and removed individuals were compared with observed cases from notification of varicella outbreaks to the local Board of Health and from survey data. The threshold condition was estimated by the basic reproductive ratio and by the relative removal rate, through which measures for preventing and curtailing the outbreaks were identified. The model demonstrated a reasonable fit to the observations, except in two of the six outbreaks which probably reflected under-registration of cases. In order to have prevented these outbreaks, between 4.4% and 52.9% of the susceptible population should have been vaccinated assuming an 85% vaccine effectiveness. Similarly, isolation of affected children should have been increased to between 4.3% and 44.8% per week.

A dynamic model for induced reactivation of latent virus

We develop a deterministic mathematical model to describe reactivation of latent virus by chemical inducers. This model is applied to the reactivation of latent KSHV in BCBL-1 cell cultures with butyrate as the inducing agent. Parameters for the model are first estimated from known properties of the exponentially growing, uninduced cell cultures. Additional parameters that are necessary to describe induction are determined from fits to experimental data from the literature. Our initial model provides good agreement with two independent sets of experimental data, but also points to the need for a new class of experiments which are required for further understanding of the underlying mechanisms.

Infections with Varying Contact Rates: Application to Varicella

We develop methods for the analysis of infectious disease data when age-specific contact rates vary over time. Our methods are valid when contact rates vary slowly on the time scale of the infection process, and are applicable to a variety of data types including serial seroprevalence surveys and case reports. The methods exploit approximate endemic equilibria, and require numerical solution of an associated integral equation in age and time. We also estimate summary statistics such as time-dependent analogs of the basic reproduction number and critical immunization threshold. We illustrate the methods with data on varicella (chickenpox) in the United Kingdom.

Immunogenicity of a two-dose regime of varicella vaccine in children with cancers

OBJECTIVE

Live-attenuated varicella vaccine is effective and safe in immunocompetent children. In this study, we assess the immunogenicity and adverse events following varicella vaccination in immunosuppressed cancer children.

METHODS

Varicella-zoster virus (VZV)-seronegative cancer children received two doses of live-attenuated VZV vaccine (Varilrix) in a span of 3 months. Patients with acute lymphoblastic leukaemia (ALL) were in the maintenance phase of chemotherapy, whereas those with solid tumours joined the study around 3-6 months from treatment discontinuation. VZV-specific cellular and humoral immune responses were measured before and after VZV vaccination.

RESULTS

The median (range) age of the 17 patients was 4.4 yr (2.0-14.5). Thirteen had ALL, one had myelodysplastic syndrome and three had solid tumours. Following vaccination, the VZV-specific stimulation index (SI) increased from 1.7 (0.9-2.9) to 17.9 (5.9-36.0) (P < 0.001). Similarly, SI to phytohaemagglutinin mitogen increased from 1136 (499-1930) to 1714 (848-2518) (P = 0.028). There were also significant increases in CD4+ cells and CD4:CD8 ratio as well as a reduction in CD16/56+ cells in peripheral blood lymphocytes. Seroconversion rate to VZV was 19% after one dose and increased to 94% after the second dose of VZV vaccine. Serum VZV-specific IgG concentrations also increased significantly following two doses when compared with one dose of VZV vaccine (P = 0.0004). One subject developed possibly vaccine-related chickenpox with self-limiting hepatitis at 5 wk following vaccination. None of the patients developed herpes-zoster at a median (range) follow-up of 27.5 months (24.0-30.0).

CONCLUSIONS

Non-immune cancer children can be effectively vaccinated against chickenpox at the defined period. However, the safety of chickenpox vaccine in these immunosuppressed children needs to be further studied.

A qualitative analysis of a model for the transmission of varicella-zoster virus

Varicella-zoster virus (VZV) is a herpesvirus which is the known agent for causing varicella (chickenpox) in its initial manifestation and zoster (shingles) in a reactivated state. The standard SEIR compartmental model is modified to include the cycle of shingles acquisition, recovery, and possible reacquisition. The basic reproduction number R(0) shows the influence of the zoster cycle and how shingles can be important in maintaining VZV in populations. The model has the typical threshold behavior in the sense that when R(0)</=1, the VZV disappears from the population, and when R(0)>1, the virus persists over time and so chickenpox and shingles remain endemic.

The effect of vaccination on the epidemiology of varicella zoster virus

Varicella zoster virus (VZV) causes chickenpox (varicella) on primary exposure and can reactivate later in life to cause shingles (zoster). As primary infection is more serious in adults than children, and exposure to the virus might boost the immune response to both chickenpox and shingles, there are two main concerns regarding infant VZV vaccination: that it could lead to an increase in adult disease; and/or that it could lead to a temporary increase in the incidence of shingles. This paper reviews the evidence for such outcomes. The consensus view of mathematical modelling studies is that the overall varicella associated burden is likely to decrease in the long term, regardless of the level of vaccine coverage. On the other hand, recent evidence suggests that an increase in zoster incidence appears likely, and the more effective vaccination is at preventing varicella, the larger the increase in zoster incidence. Targeted vaccination of susceptible adolescents and/or the contacts of high-risk individuals can be effective at preventing disease in these individuals with minimal risk to the community. However, targeted strategies would not prevent most disease (including most severe disease), and will not lead to a long-term reduction in the incidence of zoster. Understanding the mechanisms for maintaining immunity against varicella and zoster is critical for predicting the long-term effects of vaccination. Meanwhile sensitive surveillance of both chickenpox and shingles is essential in countries that have implemented, or are about to implement, varicella vaccination.

The cost-effectiveness of varicella vaccination in Canada

A deterministic realistic age-structured model was used to predict the impact of vaccination on the incidence of varicella and zoster. Unit costs, estimated from literature, were applied to the predicted health outcomes. Various vaccination programs were investigated and a sensitivity analysis was performed. Assuming no impact of vaccination on zoster, varicella vaccination is estimated to cost 45,000 dollars, 51,000 dollars and 18,000 dollars per life-year gained from the health payer's perspective for infant, infant with catch-up campaign, and preteen programs, respectively. From the societal perspective, mass infant varicella vaccination was estimated to be highly cost saving in Canada. Importantly, infant varicella vaccination could result in a short- to medium-term increase of zoster incidence and thus cause vaccination to be highly cost-ineffective (118,000 dollars per life-year gained) under the health payer's perspective. From a health payer's perspective the preteen vaccination is the only strategy that is deemed cost-effective. The cost-effectiveness of infant vaccination rests heavily on the unknown relationship between varicella and zoster.

Vaccination to prevent varicella and shingles

Vaccination of healthy children against varicella using the live attenuated Oka vaccine has been available in Japan and south Korea for several years. In 1996, a programme of universal vaccination of children to prevent varicella was introduced in the USA and other countries, including Canada, Germany, and Sweden, have licensed the vaccine for use in healthy children. This article reviews the origin of the Oka vaccine and the evidence for vaccine safety and efficacy in children and adults. Universal vaccination of children and targeted vaccination of groups at risk of severe varicella are discussed. The possible use of the Oka vaccine to prevent zoster is reviewed, and initiatives to develop new varicella zoster virus vaccines are outlined.

Impact on immunization of seasonal cycle of chickenpox

The objective of this work was to study the effect of incorporating a seasonal term in a compartmental age-structured theoretical transmission model, on the performance of vaccination strategies for chickenpox. The epidemiologic parameters are taken from data or are based on a review of literature. We used a realistic age-structure model (RAS): It is a model that incorporate both age and seasonal structure. The seasonality was introduced in the model with the addition of sinusoidal forcing term. This seasonal term varies between 0 and 1. From a susceptible/exposed/infectious/removed (SEIR) model with or without age-structure, the pattern of time series is dramatically modified after introducing a seasonal term. This dynamic ends to the transition to chaos. Regarding the evaluation of vaccination strategies, the results of the model without seasonality may be disturbed when the seasonality is introduced, especially during the first 30 years of simulations.

A discrete-event computer model of feline herpes virus within cat populations

The purpose of this work was to study the epidemiology of feline herpes virus (FHV), which causes a respiratory disease within natural populations of domestic cats. A stochastic model was constructed using discrete-events simulation. Two habitats (rural vs. urban) were simulated, featuring different demographic, spatial and social patterns. The evolution of immunity in individuals was reproduced, allowing for the random recrudescence of latent infections (influenced by environment and reproduction). Hypotheses concerning the circulation of FHV were examined regarding the role of host density and the possibility of reinfection of host. Uncertainty analyses were performed on the basis of replicated Monte Carlo sampling. The results were in good agreement with serologic data from a long-term study conducted on five populations in France. The model satisfactorily reproduced the variability of natural immunity, and the epidemic features observed. The simulations have shown that FHV can persist in small populations (because of its capacity of reactivation leading to epidemics). However, the impact on demography was not dramatic. The most important parameters in determining change in epidemiology of FHV were: transmission rate corresponding to 'friendly' contacts, and the recrudescence rate of FHV. However, an interaction between these two parameters did not allow estimation of their values.

Estimation of the contact rate in a seasonal SEIR model: application to chickenpox incidence in France

This work was an attempt at analysing the seasonal pattern of varicella epidemics in France by fitting a susceptibles-exposed-infectives-recovered (SEIR) model with a periodic contact rate function to weekly chickenpox incidence data collected over the period 1991 to 1996. The contact rate was assumed to be either a continuous, or a piecewise constant, periodic function. Both assumptions gave a reasonable fit to the data and yielded estimates of the incubation and infectious periods that were consistent with values derived on clinical or serological grounds. Seasonal fluctuation of the estimated contact rate function was likely to reflect the impact of school holidays on chickenpox diffusion among schoolchildren.

Environmental chemical exposures and risk of herpes zoster

This study investigated whether residence in Aberdeen, North Carolina, the location of the Aberdeen pesticides dumps site (a national priority list Superfund site containing organochlorine pesticides, volatile organic compounds, and metals), is associated with immune suppression as indicated by a higher incidence of herpes zoster and recent occurrences of other common infectious diseases. Study participants included 1,642 residents, 18-64 years of age, who responded to a telephone survey concerning potential occupational and recreational exposures to pesticides and other chemicals, lifetime history of herpes zoster (shingles), and the recent occurrence of other common infectious diseases. Stratified and logistic regression analyses were used to compare the cumulative incidence of herpes zoster among Aberdeen residents and residents of nearby communities. There was little evidence of an overall increased risk of herpes zoster among Aberdeen residents during the period 1951-1994 [relative risk (RR), 1.3; 95% confidence interval (CI), 0.8-2.1]. However, an elevated risk of herpes zoster was noted consistently among Aberdeen residents of younger ages as compared to residents of the nearby communities. The RR was 2.0 (CI, 1.0-4.0) among those 18-40 years of age and was not affected by controlling for potential confounders. The RR of herpes zoster was also consistently elevated in all age groups for the period before 1985. No differences were noted between residents of Aberdeen and those of the nearby communities with respect to the recent occurrence of other common infectious diseases. These results support the plausibility of an association between exposure to the Aberdeen pesticides dumps site and immune suppression and the potential use of herpes zoster as a marker of immune suppression in studies of environmental chemical exposures.

Epidemiologic effects of varicella vaccination

For a plausible range of values for the different efficacy characteristics of the live varicella (Oka) vaccine at different levels of coverage, modeling results suggest that routine immunization of preschool children would greatly reduce the number of primary varicella cases, whereas the shift in age distribution of cases would not result in increased overall morbidity as measured by number of hospitalizations. Although information about some of the vaccine assumptions is scanty, the combinations of assumptions leading to an increase in morbidity seem unlikely. A catch-up program in older children who have not yet had chickenpox will be important. The number and age distribution of the cases in vaccinees are sensitive to assumptions about the vaccine, especially the degree and distribution of partial protection against infection, relative residual infectiousness, and waning of immunity. Responsiveness to boosting by wild-type VZV infection was especially important in reducing the number of older cases. The advantage conferred by responsiveness to boosting depends on the level of transmission. The direct and indirect effects of vaccines and vaccination programs interact. Understanding how a vaccine works at the individual level is important for the vaccinated individual, but it also influences the overall public health benefits of an immunization programs. Lieu et al based a cost-effectiveness analysis of varicella vaccines on this model of varicella dynamics and assumptions about how the vaccines work. Models cannot replace biologic understanding. The purpose of such models is not to predict the number of cases of varicella, but to examine some possible consequences of introducing a vaccine into the routine immunization schedule of preschool children in the United States, effects of different vaccination strategies, and the benefits of a temporary catch-up program for older children. Modeling exercises of this sort force us to formalize our thinking, for instance about the vaccine mechanisms, and to admit our uncertainties, such as about the vaccine efficacy assumptions. Such models also show where more data need to be collected, for example, on boosting and waning of immunity and relative residual infectiousness. Improvements in the design of vaccine efficacy studies are necessary to provide the input to these models for looking at the long-term effects of vaccination programs. Frailty models can be used to analyze the data in the presence of heterogeneities in susceptibility. Waning can also be estimated using appropriate methods. Relative infectiousness of vaccinees with breakthrough cases can be measured by comparing the relative secondary attack rates when the index infected person is vaccinated and when the index infected person is unvaccinated. More studies are needed to understand how to evaluate responsiveness to boosting. Vaccine efficacy studies in the field should be designed to obtain better estimates of residual susceptibility, residual infectiousness, duration of protection, and the effects of boosting by reinfection with wild-type VZV.

Mass vaccination to control chickenpox: the influence of zoster

The impact of transmission events from patients with shingles (zoster) on the epidemiology of varicella is examined before and after the introduction of mass immunization by using a stochastic mathematical model of transmission dynamics. Reactivation of the virus is shown to damp stochastic fluctuations and move the dynamics toward simple annual oscillations. The force of infection due to zoster cases is estimated by comparison of simulated and observed incidence time series. The presence of infectious zoster cases reduces the tendency for mass immunization to increase varicella incidence at older ages when disease severity is typically greater.

Epidemiologic effects of vaccines with complex direct effects in an age-structured population

Vaccines can alter the dynamic interaction of an infectious agent with a host in complex ways. The effect of routine childhood immunization on age-specific cases was studied in an age-structured population, assuming different vaccine effects at the individual level. Assumptions about vaccine efficacy include partial protection to infection and disease, reduction in infectiousness, waning of protection, and boosting of the level and duration of protection by natural infection. The concept of relative pathogenicity is introduced to describe the effect of a vaccine on the development of disease conditional on being infected. The concepts of the immunologically naive susceptible, naive susceptible equivalent, and relative residual infection potential are introduced in the context of defining the reproduction number of a population vaccinated with a partially protective vaccine. Sensitivity to boosting has a particularly pronounced effect in reducing the number of older vaccinated cases. Near the threshold for eliminating transmission, the dynamic behavior and number as well as age distribution of cases is very sensitive to the degree of protection and relative residual infectiousness. The number of unvaccinated cases is more sensitive to the level of coverage than to the type of vaccine, while the number of vaccinated cases is very sensitive to assumptions about vaccine efficacy.

The age of infection with varicella-zoster virus in St Lucia, West Indies

Sera from an age-stratified sample of 1810 people from the Caribbean island of St Lucia were tested for antibodies against varicella-zoster virus. The results indicate that very few infections occur in childhood, which agrees with clinical survey data from other tropical countries, but contrasts with the observed high case rate in children in temperate countries. The alternative hypotheses which may explain these results are discussed, and it is suggested that high ambient temperatures interfere with the transmission of the virus. Irrespective of the cause, the pattern of varicella incidence observed has important implications for any vaccination policy adopted in tropical countries.

The epidemiology of varicella-zoster virus infections: the influence of varicella on the prevalence of herpes zoster

This paper uses mathematical models and data analysis to examine the epidemiological implications of possible immunologically mediated links between patterns of varicella and herpes-zoster incidence in human communities. A review of previously published reports does not clarify whether or not there is a relationship between the incidence of varicella and the incidence of zoster. However, new analysis of data collected by the Royal College of General Practitioners provides indirect evidence for the hypothesis that a high intensity of varicella transmission suppresses viral reactivation. The significance of this finding for proposed varicella vaccination campaigns is explored by a review of published data on the use of the vaccine. No significant difference is shown to exist between the risk of zoster caused by the vaccine and the wild virus. A mathematical model is then developed to take into consideration the influence of the prevalence of varicella on viral reactivation and the impact of vaccination with attenuated virus, which may be able to recrudesce. Under some conditions, mass application of such vaccines may have the impact of increasing zoster incidence. The results presented here indicate that, before starting any vaccination programme against varicella, its consequences need to be assessed in much more depth.