Multiple pandemic waves vs multi-period/multi-phasic epidemics: Global shape of the COVID-19 pandemic.

The overall course of the COVID-19 pandemic in Western countries has been characterized by complex sequences of phases. In the period before the arrival of vaccines, these phases were mainly due to the alternation between the strengthening/lifting of social distancing measures, with the aim to balance the protection of health and that of the society as a whole. After the arrival of vaccines, this multi-phasic character was further emphasized by the complicated deployment of vaccination campaigns and the onset of virus' variants. To cope with this multi-phasic character, we propose a theoretical approach to the modeling of overall pandemic courses, that we term multi-period/multi-phasic, based on a specific definition of phase. This allows a unified and parsimonious representation of complex epidemic courses even when vaccination and virus' variants are considered, through sequences of weak ergodic renewal equations that become fully ergodic when appropriate conditions are met. Specific hypotheses on epidemiological and intervention parameters allow reduction to simple models. The framework suggest a simple, theory driven, approach to data explanation that allows an accurate reproduction of the overall course of the COVID-19 epidemic in Italy since its beginning (February 2020) up to omicron onset, confirming the validity of the concept.

Multiple epidemic waves as the outcome of stochastic SIR epidemics with behavioral responses: a hybrid modeling approach.

In the behavioral epidemiology (BE) of infectious diseases, little theoretical effort seems to have been devoted to understand the possible effects of individuals' behavioral responses during an epidemic outbreak in small populations. To fill this gap, here we first build general, behavior implicit, SIR epidemic models including behavioral responses and set them within the framework of nonlinear feedback control theory. Second, we provide a thorough investigation of the effects of different types of agents' behavioral responses for the dynamics of hybrid stochastic SIR outbreak models. In the proposed model, the stochastic discrete dynamics of infection spread is combined with a continuous model describing the agents' delayed behavioral response. The delay reflects the memory mechanisms with which individuals enact protective behavior based on past data on the epidemic course. This results in a stochastic hybrid system with time-varying transition probabilities. To simulate such system, we extend Gillespie's classic stochastic simulation algorithm by developing analytical formulas valid for our classes of models. The algorithm is used to simulate a number of stochastic behavioral models and to classify the effects of different types of agents' behavioral responses. In particular this work focuses on the effects of the structure of the response function and of the form of the temporal distribution of such response. Among the various results, we stress the appearance of multiple, stochastic epidemic waves triggered by the delayed behavioral response of individuals.

General methods for measuring and comparing medical interventions in childbirth: a framework.

BACKGROUND: The continue increase of interventions during labour in low risk population is a controversial issue of the current obstetric literature, given the lack of evidence demonstrating the benefits of unnecessary interventions for women or infants' health. This makes it important to have approaches to assess the burden of all medical interventions performed. METHODS: Exploiting the nature of childbirth intervention as a staged process, we proposed graphic representations allowing to generate alternative formulas for the simplest measures of the intervention intensity namely, the overall and type-specific treatment ratios. We applied the approach to quantify the change in interventions following a protocol termed Comprehensive Management (CM), using data from Robson classification, collected in a prospective longitudinal cohort study carried out at the Obstetric Unit of the Cà Granda Niguarda Hospital in Milan, Italy. RESULTS: Following CM a substantial reduction was observed in the Overall Treatment Ratio, as well as in the ratios for augmentation (amniotomy and synthetic oxytocin use) and for caesarean section ratio, without any increase in neonatal and maternal adverse outcomes. The key component of this reduction was the dramatic decline in the proportion of women progressing to augmentation, which resulted not only the most practiced intervention, but also the main door towards further treatments. CONCLUSIONS: The proposed framework, once combined with Robson Classification, provides useful tools to make medical interventions performed during childbirth quantitatively measurable and comparable. The framework allowed to identifying the key components of interventions reduction following CM. In its turn, CM proved useful to reduce the number of medical interventions carried out during childbirth, without worsening neonatal and maternal outcomes.

Optimal time-profiles of public health intervention to shape voluntary vaccination for childhood diseases.

In order to seek the optimal time-profiles of public health systems (PHS) Intervention to favor vaccine propensity, we apply optimal control (OC) to a SIR model with voluntary vaccination and PHS intervention. We focus on short-term horizons, and on both continuous control strategies resulting from the forward-backward sweep deterministic algorithm, and piecewise-constant strategies (which are closer to the PHS way of working) investigated by the simulated annealing (SA) stochastic algorithm. For childhood diseases, where disease costs are much larger than vaccination costs, the OC solution sets at its maximum for most of the policy horizon, meaning that the PHS cannot further improve perceptions about the net benefit of immunization. Thus, the subsequent dynamics of vaccine uptake stems entirely from the declining perceived risk of infection (due to declining prevalence) which is communicated by direct contacts among parents, and unavoidably yields a future decline in vaccine uptake. We find that for relatively low communication costs, the piecewise control is close to the continuous control. For large communication costs the SA algorithm converges towards a non-monotone OC that can have oscillations.

The potential impact of the demographic transition in the Senegal-Gambia region of sub-Saharan Africa on the burden of infectious disease and its potential synergies with control programmes: the case of hepatitis B.

BACKGROUND: Sub-Saharan Africa (SSA) continues to suffer high communicable disease burdens as its demographic transition (DT) proceeds. Although the consequent changes in population structures influence age-specific contact patterns relevant for transmission, the age distribution of immunity, and the disease burden, investigation of the potential of DT to affect infectious disease epidemiology in regions of SSA has hitherto been overlooked. With a substantial disease burden and complex epidemiology, hepatitis B virus (HBV) represents a prime example of an infection whose epidemiology may be significantly influenced by the DT. METHODS: An age-structured mathematical model for HBV in the Senegal and Gambia (SG) region was set within a demographic framework with varying vital rates mirroring the entire course of the DT there over 1850-2100, to investigate the effects of the DT on HBV epidemiology, with and without the combined action of vaccination. The model was run from its reconstructed ancien régime (old order) demo-epidemiologic equilibrium and calibrated against SG 1950 age-distribution estimates and Gambian pre-vaccination HBV age-prevalence data. RESULTS: The model, which reproduced well demographic and HBV age-prevalence data, predicted a complex transition of HBV epidemiology over the course of the DT. This included a prolonged epoch of expansion alongside population growth and rejuvenation until 1990-2000, followed by a dramatic retreat, mainly reflecting projected fertility decline during the twenty-first century. This transitional pattern was mostly explained by the underlying demographically driven changes in horizontal transmission resulting from the changes in the age structure of the population. During 2000-2150 the HBV burden is predicted to decline by more than 70% even in the absence of vaccination. CONCLUSIONS: Demographic change alone may strongly affect HBV disease burden and shape HBV endemicity. The onset of the demographically driven decline in HBV prevalence, aligned with the expansion of HBV vaccination, forms a synergy potentially boosting effectiveness of control. Such a synergy currently appears to be presenting a "window of opportunity" facilitating HBV elimination which it would be important to exploit and which underlines the importance of taking demographic change into account when assessing the potential longer term impact of vaccination and other control measures.

The Epidemiology of Herpes Zoster After Varicella Immunization Under Different Biological Hypotheses: Perspectives From Mathematical Modeling.

The impact of varicella vaccination on the epidemiology of herpes zoster (HZ) critically depends on the mechanism of immunological boosting, through which reexposures to varicella-zoster virus are thought to reduce the individual risk of HZ development. However, the qualitative and quantitative dynamics of this process are largely unknown. Consequently, mathematical models evaluating immunization strategies need to rely on theoretical assumptions. Available varicella-zoster virus models can be classified in 3 main families according to the postulated effect of exogenous boosting: 1) progressive accumulation of immunity following repeated reexposures; 2) partial protection that wanes over time; or 3) full but temporary immunity against HZ. In this work, we review and compare quantitative predictions from the 3 modeling approaches regarding the effect of varicella immunization on HZ. All models predict a qualitatively similar, but quantitatively heterogeneous, transient increase of HZ incidence. In particular, novel estimates from the progressive immunity model predict the largest increase in natural HZ and the largest incidence of HZ cases from reactivation of the vaccine strain, which in the long term will likely outnumber prevaccination numbers. Our results reinforce the idea that a better understanding of HZ pathogenesis is required before further mass varicella immunization programs are set out.

Perspectives on optimal control of varicella and herpes zoster by mass routine varicella vaccination.

Herpes zoster arises from reactivation of the varicella-zoster virus (VZV), causing varicella in children. As reactivation occurs when cell-mediated immunity (CMI) declines, and there is evidence that re-exposure to VZV boosts CMI, mass varicella immunization might increase the zoster burden, at least for some decades. Fear of this natural zoster boom is the main reason for the paralysis of varicella immunization in Europe. We apply optimal control to a realistically parametrized age-structured model for VZV transmission and reactivation to investigate whether feasible varicella immunization paths that are optimal in controlling both varicella and zoster exist. We analyse the optimality system numerically focusing on the role of the cost functional, of the relative zoster-varicella cost and of the planning horizon length. We show that optimal programmes will mostly be unfeasible for public health owing to their complex temporal profiles. This complexity is the consequence of the intrinsically antagonistic nature of varicella immunization programmes when aiming to control both varicella and zoster. However, we show that gradually increasing-hence feasible-vaccination schedules can perform better than routine programmes with constant vaccine uptake. Finally, we show the optimal profiles of feasible programmes targeting mitigation of the post-immunization natural zoster boom with priority.

The relative importance of frequency of contacts and duration of exposure for the spread of directly transmitted infections.

The recent availability of survey data on social contact patterns has made possible important advances in the understanding of the social determinants of the spread of close-contact infections, and of the importance of long-lasting contacts for effective transmission to occur. Still, little is known about the relationship between two of the most critical identified factors (frequency of contacts and duration of exposure) and how this relationship applies to different types of infections. By integrating data from two independently collected social surveys (Polymod and time use), we propose a model that combines these two transmission determinants into a new epidemiologically relevant measure of contacts: the number of "suitable" contacts, which is the number of contacts that involve a sufficiently long exposure time to allow for transmission. The validity of this new epidemiological measure is tested against Italian serological data for varicella and parvovirus-B19, with uncertainty evaluated using the Bayesian melding technique. The model performs quite well, indicating that the interplay between time of exposure and contacts is critical for varicella transmission, while for B19 it is the duration of exposure that matters for transmission.

Evaluating vaccination strategies for reducing infant respiratory syncytial virus infection in low-income settings.

BACKGROUND: Respiratory syncytial virus (RSV) is a leading cause of lower respiratory tract disease and related hospitalization of young children in least developed countries. Individuals are repeatedly infected, but it is the first exposure, often in early infancy, that results in the vast majority of severe RSV disease. Unfortunately, due to immunological immaturity, infants are a problematic RSV vaccine target. Several trials are ongoing to identify a suitable candidate vaccine and target group, but no immunization program is yet in place. METHODS: In this work, an individual-based model that explicitly accounts for the socio-demographic population structure is developed to investigate RSV transmission patterns in a rural setting of Kenya and to evaluate the potential effectiveness of alternative population targets in reducing RSV infant infection. RESULTS: We find that household transmission is responsible for 39% of infant infections and that school-age children are the main source of infection within the household, causing around 55% of cases. Moreover, assuming a vaccine-induced protection equivalent to that of natural infection, our results show that annual vaccination of students is the only alternative strategy to routine immunization of infants able to trigger a relevant and persistent reduction of infant infection (on average, of 35.6% versus 41.5% in 10 years of vaccination). Interestingly, if vaccination of pregnant women boosts maternal antibody protection in infants by an additional 4 months, RSV infant infection will be reduced by 31.5%. CONCLUSIONS: These preliminary evaluations support the efforts to develop vaccines and related strategies that go beyond targeting vaccines to those at highest risk of severe disease.

The impact of demographic changes on the epidemiology of herpes zoster: Spain as a case study.

Varicella zoster virus (VZV) causes varicella upon first exposure and may reactivate later in life into herpes zoster (HZ), with a risk that is thought to be reduced by re-exposures to VZV. Given the decades-long time scales of reactivation and its dependence on the accumulation of re-exposure episodes, adopting a long-term perspective may be useful to correctly interpret current epidemiological trends of VZV. In this study, we investigate the possible impact of demographic changes on varicella and HZ in Spain, using an age-structured mathematical model informed with historical demographic data and calibrated against age-specific profiles of varicella seroprevalence and HZ incidence data. The model qualitatively reproduces the remarkable growth of HZ incidence observed in Spain between 1997 and 2004, before the introduction of varicella vaccination programmes. We demonstrate that this growth may be partially ascribed to the reduction of varicella circulation that followed the overall decline of the birth rate in the twentieth century. Model predictions further suggest that, even under the most optimistic projections, HZ incidence will continue its rise until at least 2040. Considering the effect of demographic changes can help interpreting variations in epidemiological trends of HZ, contributing to a more accurate evaluation of vaccination programmes against VZV.

Epidemic control by social distancing and vaccination: Optimal strategies and remarks on the COVID-19 Italian response policy.

After the many failures in the control of the COVID-19 pandemic, identifying robust principles of epidemic control will be key in future preparedness. In this work, we propose an optimal control model of an age-of-infection transmission model under a two-phase control regime where social distancing is the only available control tool in the first phase, while the second phase also benefits from the arrival of vaccines. We analyzed the problem by an ad-hoc numerical algorithm under a strong hypothesis implying a high degree of prioritization to the protection of health from the epidemic attack, which we termed the "low attack rate" hypothesis. The outputs of the model were also compared with the data from the Italian COVID-19 experience to provide a crude assessment of the goodness of the enacted interventions prior to the onset of the Omicron variant.

Optimal social distancing in epidemic control: cost prioritization, adherence and insights into preparedness principles.

The COVID-19 pandemic experience has highlighted the importance of developing general control principles to inform future pandemic preparedness based on the tension between the different control options, ranging from elimination to mitigation, and related costs. Similarly, during the COVID-19 pandemic, social distancing has been confirmed to be the critical response tool until vaccines become available. Open-loop optimal control of a transmission model for COVID-19 in one of its most aggressive outbreaks is used to identify the best social distancing policies aimed at balancing the direct epidemiological costs of a threatening epidemic with its indirect (i.e., societal level) costs arising from enduring control measures. In particular, we analyse how optimal social distancing varies according to three key policy factors, namely, the degree of prioritization of indirect costs, the adherence to control measures, and the timeliness of intervention. As the prioritization of indirect costs increases, (i) the corresponding optimal distancing policy suddenly switches from elimination to suppression and, finally, to mitigation; (ii) the "effective" mitigation region-where hospitals' overwhelming is prevented-is dramatically narrow and shows multiple control waves; and (iii) a delicate balance emerges, whereby low adherence and lack of timeliness inevitably force ineffective mitigation as the only accessible policy option. The present results show the importance of open-loop optimal control, which is traditionally absent in public health preparedness, for studying the suppression-mitigation trade-off and supplying robust preparedness guidelines.

Hope-Simpson's progressive immunity hypothesis as a possible explanation for herpes zoster incidence data.

Varicella-zoster virus (VZV) is the causative agent of both varicella (chickenpox) and herpes zoster (HZ) (shingles). After varicella infection, the virus remains dormant in the host's dorsal ganglia and can reactivate due to waning cell-mediated immunity, causing HZ. Exposure of varicella-immune persons to VZV may boost the host's immune response, resulting in a protective effect against HZ. In this study, we used mathematical models of VZV transmission and HZ development to test the biological hypothesis of "progressive immunity," originally proposed by Hope-Simpson (Proc R Soc Med. 1965;58:9-20), that cell-mediated protection against HZ increases after each episode of exposure to VZV. Predictions from a model incorporating such a hypothesis were compared with those of other concurrent models proposed for explaining HZ epidemiology. The progressive immunity model fits significantly better the age profile of HZ incidence for Finland (years 2000-2006), Italy (2003-2005), Spain (1997-2004), and the United Kingdom (1991-1992), suggesting that this mechanism may be critical in shaping HZ patterns. The model thus validated is an alternative to VZV models currently used to evaluate the impact of mass immunization programs for varicella and therefore extends the range of tools available to assist policy-makers with the present decision paralysis on the introduction of vaccination.

Inferring the structure of social contacts from demographic data in the analysis of infectious diseases spread.

Social contact patterns among individuals encode the transmission route of infectious diseases and are a key ingredient in the realistic characterization and modeling of epidemics. Unfortunately, the gathering of high quality experimental data on contact patterns in human populations is a very difficult task even at the coarse level of mixing patterns among age groups. Here we propose an alternative route to the estimation of mixing patterns that relies on the construction of virtual populations parametrized with highly detailed census and demographic data. We present the modeling of the population of 26 European countries and the generation of the corresponding synthetic contact matrices among the population age groups. The method is validated by a detailed comparison with the matrices obtained in six European countries by the most extensive survey study on mixing patterns. The methodology presented here allows a large scale comparison of mixing patterns in Europe, highlighting general common features as well as country-specific differences. We find clear relations between epidemiologically relevant quantities (reproduction number and attack rate) and socio-demographic characteristics of the populations, such as the average age of the population and the duration of primary school cycle. This study provides a numerical approach for the generation of human mixing patterns that can be used to improve the accuracy of mathematical models in the absence of specific experimental data.

Spatiotemporal dynamics of viral hepatitis A in Italy.

Viral hepatitis A is still common in Italy, especially in Southern regions. In this study, a metapopulation model for hepatitis A virus (HAV) transmission is proposed and analyzed. Analytical results on the asymptotic and transient behaviors of the system are carried out. Based on the available Italian movement data, a national spatial contact matrix at the regional level, which could be used for new studies on the transmission dynamics of other infectious diseases, is derived for modeling fluxes of individuals. Despite the small number of fitted parameters, model simulations are in good agreement with the observed average HAV incidence in all regions. Our results suggest that the mass vaccination program introduced in one Italian region only (Puglia, the one with the highest endemicity level) could have played a role in the decline of HAV incidence in the country as a whole. The only notable exception is represented by Campania, a Southern region showing a high endemicity level, which is not substantially affected by HAV dynamics in Puglia. Finally, our results highlight that the continuation of the vaccination campaign in Puglia would have a relevant impact in decreasing long-term HAV prevalence, especially in Southern Italy.

The impact of vaccine side effects on the natural history of immunization programmes: an imitation-game approach.

When the incidence and prevalence of most common vaccine preventable childhood infectious diseases are constantly low, as is the case in many industrialized countries, the incidence of vaccine-associated side effects might become a key determinant in vaccine demand. We study an SIR transmission model with dynamic vaccine demand based on an imitation mechanism where the perceived risk of vaccination is modelled as a function of the incidence of vaccine side effects. The model shows some important differences compared to previous game dynamic models of vaccination, and allows noteworthy inferences as regards both the past and future lifetime of vaccination programmes. In particular it is suggested that a huge disproportion between the perceived risk of disease and vaccination is necessary in order to achieve high coverages. This disproportion is further increased in highly industrialised countries. Such considerations represent serious challenges for future vaccination programmes.

Little Italy: an agent-based approach to the estimation of contact patterns- fitting predicted matrices to serological data.

Knowledge of social contact patterns still represents the most critical step for understanding the spread of directly transmitted infections. Data on social contact patterns are, however, expensive to obtain. A major issue is then whether the simulation of synthetic societies might be helpful to reliably reconstruct such data. In this paper, we compute a variety of synthetic age-specific contact matrices through simulation of a simple individual-based model (IBM). The model is informed by Italian Time Use data and routine socio-demographic data (e.g., school and workplace attendance, household structure, etc.). The model is named "Little Italy" because each artificial agent is a clone of a real person. In other words, each agent's daily diary is the one observed in a corresponding real individual sampled in the Italian Time Use Survey. We also generated contact matrices from the socio-demographic model underlying the Italian IBM for pandemic prediction. These synthetic matrices are then validated against recently collected Italian serological data for Varicella (VZV) and ParvoVirus (B19). Their performance in fitting sero-profiles are compared with other matrices available for Italy, such as the Polymod matrix. Synthetic matrices show the same qualitative features of the ones estimated from sample surveys: for example, strong assortativeness and the presence of super- and sub-diagonal stripes related to contacts between parents and children. Once validated against serological data, Little Italy matrices fit worse than the Polymod one for VZV, but better than concurrent matrices for B19. This is the first occasion where synthetic contact matrices are systematically compared with real ones, and validated against epidemiological data. The results suggest that simple, carefully designed, synthetic matrices can provide a fruitful complementary approach to questionnaire-based matrices. The paper also supports the idea that, depending on the transmissibility level of the infection, either the number of different contacts, or repeated exposure, may be the key factor for transmission.

COVID-19 epidemic and mitigation policies: Positive and normative analyses in a neoclassical growth model.

The COVID-19 pandemic is still ravaging the planet, but its (short-, medium-, and long-term) diverse effects on health, economy, and society are far from being understood. This article investigates the potential impact of a deadly epidemic and its main nonpharmaceutical control interventions (social distancing vs. testing-tracing-isolation, TTI) on capital accumulation and economic development at different time scales. This is done by integrating an epidemiological susceptible-infectious-recovered model with a Solow-type growth model including public expenditure, as a parsimonious setting to offer insights on the trade-off between protecting human lives and the economy and society. The work clarifies (i) the long-term interactions amongst a deadly infection, demography, and capital accumulation, (ii) the lack of viability of persistent social distancing measures also using an analytical characterization, and the threat of policy-enhanced COVID-19 endemicity, (iii) the potentially high return on investments in TTI activities to avoid future lockdowns and related capital disruption. It also quantifies the welfare effects of a range of policies, confirming a counterintuitive role for tax-funded preventive investments aimed at strengthening TTI as more desirable interventions than generalized lockdowns.

Dynamics of partially mitigated multi-phasic epidemics at low susceptible depletion: phases of COVID-19 control in Italy as case study.

To mitigate the harmful effects of the COVID-19 pandemic, world countries have resorted - though with different timing and intensities - to a range of interventions. These interventions and their relaxation have shaped the epidemic into a multi-phase form, namely an early invasion phase often followed by a lockdown phase, whose unlocking triggered a second epidemic wave, and so on. In this article, we provide a kinematic description of an epidemic whose time course is subdivided by mitigation interventions into a sequence of phases, on the assumption that interventions are effective enough to prevent the susceptible proportion to largely depart from 100% (or from any other relevant level). By applying this hypothesis to a general SIR epidemic model with age-since-infection and piece-wise constant contact and recovery rates, we supply a unified treatment of this multi-phase epidemic showing how the different phases unfold over time. Subsequently, by exploiting a wide class of infectiousness and recovery kernels allowing reducibility (either to ordinary or delayed differential equations), we investigate in depth a low-dimensional case allowing a non-trivial full analytical treatment also of the transient dynamics connecting the different phases of the epidemic. Finally, we illustrate our theoretical results by a fit to the overall Italian COVID-19 epidemic since March 2020 till February 2021 i.e., before the mass vaccination campaign. This show the abilities of the proposed model in effectively describing the entire course of an observed multi-phasic epidemic with a minimal set of data and parameters, and in providing useful insight on a number of aspects including e.g., the inertial phenomena surrounding the switch between different phases.

Evidence of disorientation towards immunization on online social media after contrasting political communication on vaccines. Results from an analysis of Twitter data in Italy.

BACKGROUND: In Italy, in recent years, vaccination coverage for key immunizations as MMR has been declining to worryingly low levels, with large measles outbreaks. As a response in 2017, the Italian government expanded the number of mandatory immunizations introducing penalties to unvaccinated children's families. During the 2018 general elections campaign, immunization policy entered the political debate with the government in-charge blaming oppositions for fuelling vaccine scepticism. A new government (formerly in the opposition) established in 2018 temporarily relaxed penalties and announced the introduction of forms of flexibility. OBJECTIVES AND METHODS: First, we supplied a definition of disorientation, as the "lack of well-established and resilient opinions among individuals, therefore causing them to change their positions as a consequence of sufficient external perturbations". Second, procedures for testing for the presence of both short and longer-term collective disorientation in Twitter signals were proposed. Third, a sentiment analysis on tweets posted in Italian during 2018 on immunization topics, and related polarity evaluations, were used to investigate whether the contrasting announcements at the highest political level might have originated disorientation amongst the Italian public. RESULTS: Vaccine-relevant tweeters' interactions peaked in response to main political events. Out of retained tweets, 70.0% resulted favourable to vaccination, 16.4% unfavourable, and 13.6% undecided, respectively. The smoothed time series of polarity proportions exhibit frequent large changes in the favourable proportion, superimposed to a clear up-and-down trend synchronized with the switch between governments in Spring 2018, suggesting evidence of disorientation among the public. CONCLUSIONS: The reported evidence of disorientation for opinions expressed in online social media shows that critical health topics, such as vaccination, should never be used to achieve political consensus. This is worsened by the lack of a strong Italian institutional presence on Twitter, calling for efforts to contrast misinformation and the ensuing spread of hesitancy. It remains to be seen how this disorientation will impact future parents' vaccination decisions.