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Estimation of Household Transmission Rates of Pertussis and the Effect of Cocooning Vaccination Strategies on Infant Pertussis

de Greeff, Sabine C.a; de Melker, Hester E.a; Westerhof, Annekea; Schellekens, Joop F.P.b; Mooi, Frits R.a; van Boven, Michiela

doi: 10.1097/EDE.0b013e31826c2b9e
Infectious diseases

Background: Despite >50 years of universal vaccination, pertussis remains the most prevalent vaccine-preventable infectious disease in developed countries. Pertussis is often mild in adults, but can run a severe course in young infants.

Methods: Data on transmission of pertussis within households were captured in a population-based, nationwide, prospective study performed in the Netherlands between February 2006 and December 2009. We estimated the transmission rates of pertussis with a clinically confirmed infection in 140 households, using stochastic epidemic models. Parameter estimates were used to gauge the effect of vaccinating household members (cocooning) to prevent the infection in young infants.

Results: Overall transmission rates in the household were high. Fathers were less susceptible than other household members (estimated relative susceptibility of fathers = 0.44 [95% confidence interval (CI) = 0.27–0.72]), whereas mothers may be more infectious to their infants than are other household members (estimated relative infectiousness of mothers = 3.9 [95% CI = 0.59–14]). Targeted vaccination of mothers would approximately halve the probability of infants’ infection. Vaccination of siblings is less effective in preventing transmission within the household, but may be as effective overall because siblings more often introduce an infection in the household. Vaccination of fathers is expected to be least effective.

Conclusions: Selective vaccination of persons in households with a young infant may substantially reduce the disease burden of pertussis in infants by reducing transmission within the household.

Supplemental Digital Content is available in the text.

From the aCentre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, The Netherlands; and bLaboratory for Infectious Diseases, Groningen, The Netherlands.

Submitted 19 August 2011; accepted 9 May 2012.

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article ( This content is not peer-reviewed or copy-edited; it is the sole responsibility of the author.

The authors report no conflict of interest.

Correspondence: Michiel van Boven, Centre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, The Netherlands. E-mail:

Large-scale childhood vaccination programs have been very successful in reducing the morbidity and mortality caused by the targeted diseases.1 However, in many countries with high vaccination coverage, the incidence of pertussis has risen sharply in the past decade.2 5 Circulation of the causative organism, Bordetella pertussis, has increased, particularly in adolescents and adults.6,7 The observed increase may be attributable to various factors, including increased awareness, suboptimal vaccines, waning immunity, and pathogen adaptation.8,9 In infants younger than 6 months of age (too young to be completely protected by vaccination), pertussis can run a severe course.10 Most infections in adults, however, are relatively mild. Descriptive epidemiologic studies have demonstrated that mothers and siblings play a pivotal role in the transmission of pertussis to young infants.10–12 One could therefore argue that selective vaccination of household members may help to prevent the transmission of pertussis to newborns. However, there is currently no quantitative estimate of the magnitude of the effect of selective vaccination of household members (“cocooning”) on infant pertussis. Using stochastic epidemic models, we quantify the role of mothers, fathers, and siblings as propagators of pertussis infection in the household, and as infectors of infants too young to be (fully) vaccinated. Armed with quantitative estimates of the household transmission rates, we explore the effectiveness of various cocooning vaccination strategies.

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Study Overview

Data on the transmission of pertussis within households were captured in a nationwide, population-based, prospective study on pertussis in infants which was performed in the Netherlands. An overview of the study setup and diagnostic methods is given in a report by de Greeff and colleagues.10 Two enrollment schemes were used. In the first, households with an infant aged younger than 6 months who was hospitalized between February 2006 and November 2008 with laboratory-confirmed pertussis (n = 164) were visited by a study nurse. All 560 household members were tested for pertussis (by polymerase chain reaction [PCR] and serology) within the first week after diagnosis of the infant and were interviewed using a standard questionnaire that included questions on clinical symptoms in the past 2 months. Four to six weeks after the initial home visit, follow-up data on symptoms were collected by phone for all participants. A household contact was regarded as a confirmed pertussis case if found positive by PCR, culture, or serology. The first day of illness was defined as the onset of coughing or cold symptoms (such as runny nose, otitis, conjunctivitis, and/or fever) that preceded a cough. Cold symptoms occurring >2 weeks before onset of coughing were regarded as a separate episode, not related to pertussis infection. A case was considered typical pertussis if it entailed at least 2 weeks of coughing plus one or more of the following symptoms: paroxysmal coughing, posttussive vomiting, or inspiratory whooping.

Within families, infected persons (household contacts with laboratory-confirmed pertussis and the infected infants) were classified according to the chronology of the onset of symptoms. The person with the earliest date of onset was considered the primary case of the household. Here, we restrict the analyses to households with a clearly defined primary case (ie, we excluded households with one or more asymptomatic infected household members), thus leaving 128 households with 128 infants, 128 mothers, 121 fathers, and 176 other family members. The infected infant was the primary case in 54 of the households.

Our second enrollment scheme was aimed at estimating the absolute risk of infection of the infant. In this scheme, households were selected in a manner similar to that of the original study, but the enrollment criterion was now a confirmed pertussis patient (not an infant) in a household containing an infant younger than 6 months of age. Data using this enrollment scheme were collected from cases with first day of illness between November 2008 and December 2009, resulting in 12 enrolled households. There were no asymptomatic infections, and all 12 households were included. Our final dataset contained 140 households consisting of 140 infants, 140 mothers, 133 fathers, and 188 other family members (Fig. 1, eTables 1 and 2



Vaccination in the Netherlands is given at 2, 3, 4, and 11 months of age, with a booster dose given at age 4 years. Vaccination coverage in the Netherlands has been high in recent decades (ranging from 91% to 97%), and almost all mothers, fathers, and other household members had been vaccinated in childhood. This pattern applies to our data, in which only 7% of the household contacts had not been vaccinated. Vaccine-induced immunity is likely to have waned after 5–10 years.13 Our model describes transmission among mothers, fathers, and other household members—most of whom had been vaccinated—and unvaccinated infants.

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Model Structure and Estimation

The statistical analyses are based on a stochastic susceptible-exposed-infectious-recovered (SEIR) model in which persons are classified as susceptible (S), infected but not yet infectious (E), infected and infectious (I), or recovered and immune (R). We include four types of individuals: infants (labeled I), mothers (M), fathers (F), and other household members, mostly siblings (O).

We focus on the final size of household epidemics, ie, on the state of the individuals in the household after the household outbreak has come to an end. The appeal of final-size analyses lies in the fact that (1) final-size distributions are invariant with respect to the latent-period distribution, ie, the final size is not affected by the (distribution of the) latent period, and (2) different assumptions on the distribution of the infectious period are easily incorporated.14 With respect to the contact process, we may assume frequency-dependent transmission or density-dependent transmission.15 In a frequency-dependent transmission model, each person makes a fixed expected number of contacts per unit of time in the household, whereas in the density-dependent transmission model, each person makes a fixed expected number of contacts per unit of time with each of the other persons in the household. Hence, under the density-dependent transmission assumption, a person makes more contacts per unit of time in a large household than in a small household, whereas the (expected) number of contacts is fixed under the frequency-dependent transmission assumption.

The final-size distributions are specified by triangular equations that can be solved recursively and form the basis for statistical inference.14 If we let a = (a I,a M,a F,a O) denote the initially infected number of infants, mothers and fathers, and other persons in the household, n = (n I,n M,n F,n O) the number of initially uninfected persons, and j = (j I,j M,j F,j O) the number of household infections, then the final size in a household of composition a + n is given by a + j. Using this notation, the infection probabilities

of the frequency-dependent transmission model are implicitly specified by the equations

where j i = 0,…, n i. For a given n i and a i, the final-size distribution is fully specified by the Laplace transform ø[s] of the probability distribution of the infectious period and the transmission parameters βij (see below). Without loss of generality, we measure time in units equal to the mean duration of the infectious period.14 In the following, we consider models with a fixed infectious period and with an exponentially distributed infectious period. In view of the fact that the unit of time is the mean infectious period, we have ø[s] = e −s in the case of a fixed infectious period, and

in the case of an exponentially distributed infectious period.

In the density-dependent transmission model, the above equations need to be adapted slightly. Specifically, by replacing total household size (|a + n|) in the Laplace transform by 1 and by interpreting the transmission rate parameters as rates per infectious period per person, the above equations immediately apply to the density-dependent transmission model.16

Because households were included only if an infected person was present, the final-size distributions need to be conditioned on the presence of an infected person. In the following, we will call the infected person who was the basis of the household’s inclusion in the study the “index case,” and the person(s) with laboratory-confirmed infection who had the earliest date of onset of symptoms the “primary case(s).” If we denote by q(j | a, n) the unconditioned probability of an outbreak of composition a + j in a household of composition a + n, and we assume that an infant is the index case but not the primary case, the conditional probability of observing a + j infections is given by

In our dataset, conditioning was necessary for 74 households in our first enrollment scheme; no conditioning was needed in the second enrollment scheme because the index case was always also a primary case (Fig. 1).

The above preparations enable calculation of the likelihood function, which is given by the product of the likelihood contributions of the individual households. Maximum likelihood estimates of the parameters of interest are obtained by straightforward numerical maximization of the log- transformed likelihood.16–18 Confidence bounds for the parameter estimates are calculated using appropriate chi-square approximations of the profile likelihood. To assess the validity of the confidence intervals calculated by this method and to investigate the robustness of the parameter estimates, we also re-estimated the parameters in a parametric bootstrap (1000 replicate datasets), with numbers of households, sizes of the households, and primary case(s) as in our original dataset (Fig. 1). All analyses were carried out using Mathematica 8.0.

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Model Selection

A saturated model containing a parameter for each transmission route is impractical, and we focus on simpler proportionate-mixing models in which the transmission parameters are decomposed as a product βij = gi fj, where fj and gi are the infectiousness of type j persons and susceptibility of type i persons.19 The proportionate-mixing model contains eight parameters. One of these is made redundant by rescaling the parameters.19 The rescaled proportionate-mixing model contains seven parameters, viz. the overall infant transmission rate β and the infectiousness and susceptibility of the other types of persons relative to infants. The relative infectiousness of mothers, fathers, and siblings are denoted by ƒM, ƒF, and ƒO, respectively, and the corresponding susceptibilities by g M, g F, and g O, respectively.

The full proportionate-mixing model is labeled model D. We also considered simplified proportionate-mixing models in which all types are equally susceptible (g i = 1 for all; i ∈ {M, F, O}; model C), equally infectious (fi = 1 for all i; model B), or equally susceptible and equally infectious (gi = 1 fi = 1 for all i; model A). Based on the analyses of the proportionate-mixing models, we also considered a number of variations on model C by repeated forward and backward selection. These models pose restrictions on the susceptibility parameters, and they contain specific parameters for transmission to infants. The best-fitting models allow for differential susceptibility of fathers but not of mothers and siblings [g M = g O = 1, model C(1)], for differential susceptibility of fathers plus variable infectiousness of the other types for transmission to infants [model C(2)], or for differential susceptibility of fathers plus variable infectiousness of mothers to their infants [model C(3)]. An overview of the model scenarios is given in eTable 3 (

To choose among models of different complexity, we make use of Akaike Information Criteria (AIC). The model with the smallest AIC is denoted by AIC min, and the difference between model i and the model with smallest AIC is given by Δi = AIC iAIC min. The model odds

represents the relative strength of evidence for model i.20

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Vaccination Scenarios

With estimates of the model parameters at hand, we explore the effectiveness of cocooning vaccination strategies by studying the reduction of the infection probability of the infant for various (assumed) efficacies of the vaccine. For various household compositions, we consider vaccination of mothers, of fathers, of additional household members, of mothers and fathers, and of all household members.

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Estimation of Household Transmission Rates

The Table gives an overview of the statistical analyses, assuming models with fixed infectious periods and frequency-dependent transmission. Models with an exponentially distributed infectious period (eTable 4, or assuming density-dependent transmission (eTable 5, give a very poor fit to the data and will not be considered in the sequel.



Within the set of proportionate-mixing models (models A–D), the model that allows for variable susceptibility but does not include differential infectiousness (model C) has by far the highest statistical support (Table). The models that allow for variable infectiousness (models B and D), or the one-parameter model that makes no distinction among types of persons (model A) have low statistical support, and can be discarded from consideration.

The variable-susceptibility model indicates that, within the household, fathers are less susceptible than mothers and other household members. However, the 95% CIs associated with the parameter estimates are wide. Analysis of the pairwise profile likelihoods of the transmission rate parameter and relative susceptibilities shows a strong negative correlation between the transmission rate parameter and the relative susceptibilities (Fig. 2). Whereas the transmission rate parameter and relative susceptibilities cannot be estimated with precision separately, the product of transmissibility and relative susceptibility can be estimated with considerable precision.



We therefore simplified the variable-susceptibility model to incorporate susceptibilities of mothers and other household members into the transmission rate parameter (ie, we take g M = g O = 1). The resulting model C(1) has higher statistical support and allows for more precise estimation of the transmission parameter and relative susceptibility of fathers. Specifically, this model indicates that the susceptibility of fathers is lower than that of mothers and other household members (ĝ F = 0.393 [95% CI = 0.24−0.83]).

To investigate whether the transmission rates from mothers, fathers, and other household members to infants can be estimated separately, we extended the model with variable susceptibility of fathers by allowing for differential transmissibility from mothers, fathers, and other household members to infants. The resulting model C(2) has slightly lower support than the model incorporating only variable susceptibility of fathers, and this model indicates that pertussis is more easily transmitted from mother to infant than from father or other household members to infant.

Finally, we considered a suite of simplified models based on model C(2) with variable susceptibility of fathers and specific transmissibility to infants. Of these, the best-fitting model incorporates a parameter for transmission from mothers to infants, but not from fathers or siblings to infants [model C(3)]. This model has the highest empirical support, with fathers having low overall susceptibility (ĝ F = 0.444 [95% CI = 0.27−0.72]), and mothers being more infectious to their infants than fathers or siblings (ĥ M = 3.89). The 95% CI associated with this parameter estimate, however, remains wide ([95% CI = 0.59−14]; p = 0.10). These results are confirmed by re-estimating the parameters of 1000 resampled datasets using a parametric bootstrap (Fig. 3): fathers are less susceptible to infection in the household than other household members (0.44 [95% CI = 0.26–0.70]), and mothers may be more infectious to their infants than fathers or siblings (4.1 [95% CI = 0.93–99]).



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Predicting the Effect of Household Vaccination

With estimates of the parameters of interest in hand, we evaluate the likely effect of cocooning vaccination strategies. To this end, we take parameter estimates of the model with variable susceptibility of fathers and specific transmission parameters for transmission to the infant [model C(2)]. This model has high support but at the same time takes best estimates for less-certain transmission routes into account (mother to infant, father to infant, and other household members to infant). We focus on the most common household composition: a mother and father, a single infant, and one sibling. The introduction of an infected mother is expected to lead to infection of the infant in 40% of such households (eFigure 1, In households where the father or other person is the primary infected person, the probability that the infant will become infected decreases to 15% and 20%, respectively.

To explore whether vaccination of mothers could be effective, we calculated infant infection probabilities for various cocooning vaccination strategies. We assume that the vaccine does not prevent infection, but reduces infectiousness by 90%. The analyses show that by vaccinating young mothers the probability of infection of the infant can be reduced from 0.40 to 0.05 if the primary case is the mother, from 0.15 to 0.08 if it is the father, and from 0.20 to 0.13 if it is the other household member (eFigure 1, Hence, vaccination of mothers not only has a substantial direct effect in reducing transmission directly from mother to infant but also has an indirect effect by preventing the infection of the infant by the father-to-mother-to-infant and the others-to-mother-to-infant routes.

To gauge the overall effect of vaccination of mothers, we argue as follows. In our main dataset (ie, households 1–128), there are 50 households with an infant, a mother and father, and a single other person (the family composition in the majority of the households with children in the Netherlands). Of these, the infant is the primary case in 16 households. In the remaining 34 households, the mother is the primary case in 9 households, the father in 7 households, and the other person in 18 households. If these figures are indicative for the introduction probabilities, we could argue that, in households in which the infant is not the primary case, the mother is the primary case with probability 9/34 = 0.26, the father with probability 7/34 = 0.21, and the other household member with probability 18/34 = 0.53. Combining these introduction figures with the outbreak compositions computed above yields an overall probability of infection of the infant of 0.24 without vaccination, and 0.10 if mothers are vaccinated—a greater-than-two-fold reduction (Fig. 4).



To investigate the robustness of these results, and to explore whether vaccination of other household members could be effective, we considered vaccination not only of mothers but also of fathers, siblings, mothers and fathers, and all household members (excluding the infant). For all models with high statistical support, vaccination of mothers (or siblings) is substantially more effective than vaccination of fathers (Fig. 5).



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It is known that infants hospitalized for pertussis are most often infected by their mother or by a sibling.10 Here we add that the estimated risk of infection of the infant is approximately 40% if the mother is an infected primary case, and 10%–20% if it is the father or sibling. Based on these estimated transmission probabilities, vaccination of mothers appears to be a particularly promising means of preventing infection of the infant (Figs. 4, 5). In fact, our analyses show that vaccination of mothers with an effective vaccine could potentially prevent half of the household infections in infants. Vaccination of fathers is expected to be less effective (preventing at most 20% of infant infections). Our analyses also suggest that in households with an infant, a mother and father, and a single sibling, the protective effect of vaccination of the sibling is comparable with the protective effect of vaccination of the mother. This is attributable to the fact that siblings are more likely than the mother to introduce the infection into the household (26% vs. 53%).

The high estimated infectiousness of mothers compared with fathers and other household members may be the result of their more intensive contact with the infant as a result of pregnancy leave, which in the Netherlands is currently arranged by law only for mothers. This is in agreement with other household transmission studies, where mothers, in particular, were identified as coughing contacts.11,21 The higher seroprevalence in men compared with women7 implies that fathers are not intrinsically less susceptible than mothers, but suggests that fathers are likely infected in other locations on other occasions.

Our study has a number of limitations and assumptions that need discussion. First, our model applies to infections occurring within the household. Casual contacts outside the household may also play a role in the transmission to young infants,22 and the effect of vaccinating household members may vary depending on the intensity and frequency of such contacts. In our earlier study,10 we could not determine the source of infection within the household for one-third of the infants. Thus, a sizeable fraction of the infections in infants might have been caused by contacts outside the household. In contrast, the infants might have also been infected by asymptomatically infected household members. In view of the fact that day care attendance in the Netherlands typically begins at age 3 months, we believe that the effect of casual contacts outside the household on the probability of infection of the infant may have been limited.

Second, the analyses are based on 140 households, of which 128 were included on the basis of the presence of an infected infant, and 12 on the basis of an infected mother, father, or sibling. The 128 households with an infected infant provide evidence of which household contact was the most likely source of infection of the infant. However, they do not allow us to estimate the absolute probability of infection of the infant. Hence, information on the absolute rates of infection of the infant is based on just 12 households, and therefore the transmission rates to infants cannot readily be estimated with precision. A more balanced dataset, in which more households are included on the basis of an infected household contact other than the infant, would enable a more precise estimation of probability of infection of the infant. For logistical and practical reasons, however, this was not possible for the current study.

Third, our analyses are based only on those households in which PCR and serology were performed on all household members, and for which all infected persons (as determined by PCR/serology) showed clear symptoms.10 This was done so that the primary case (or cases) could be identified within the household. Asymptomatically or subclinically infected persons may transmit pertussis to infants, and it is of some interest to evaluate the role of asymptomatically infected persons in the household transmission rates.23,24 However, given that (1) asymptomatically infected persons were rare (42 out of 299 infected persons [14%] in the household study), (2) just 36 out of 164 households had to be excluded because of an asymptomatically infected person, and (3) attack rates in households with an asymptomatically infected person were not different from those in households with only symptomatic cases, we believe that the potential for asymptomatic cases to have a large effect on the parameter estimates is small.10

We recently showed that 9% of the Dutch population ≥9 years of age had an antipertussis toxin IgG antibody concentration indicative of a recent infection.7 Moreover, more than 2% of a tested cohort of pregnant women in the Netherlands had serological evidence of pertussis infection during pregnancy.25 These figures indicate that even in a small country like the Netherlands (~16 million inhabitants, ~180,000 births per year) several thousand vulnerable newborns may be at risk of being infected by their mother. In principle, vaccination of mothers during pregnancy could help to protect infants from birth until immunity is induced by active vaccination.26 However, safety concerns make this strategy difficult to realize. A recent study showed that cocooning was accepted by and successfully implemented among postpartum women in the United States.27 An alternative approach would be to add general adolescent or adult booster vaccination programs to existing childhood vaccination programs.28–33 The advantages of general vaccination campaigns over specifically targeting vaccination to households with a newborn would be that the former strategy could potentially reduce transmission levels in the population as a whole. However, vaccination campaigns specifically targeted at families with newborn children would probably be more cost-effective.

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We thank Jacco Wallinga and Annelie Vink for helpful comments on a draft of the manuscript. Two anonymous reviewers are gratefully acknowledged for constructive comments.

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A Call For Nominations: The 2013 Rothman EPIDEEMIOLOGY Prize

EPIDEMIOLOGY presents an annual award for the best paper published by the journal during the previous year. This prize of $3000 and a plaque goes to the author whose paper is selected by the Editors and the Editorial Board for its originality, importance, clarity of thought, and excellence in writing.

With this issue, we close our 2012 volume. We invite our readers to nominate papers published during the past year. Please e-mail your nominations to Allen Wilcox, Editor-in-Chief:

Nominations must be received no later than 31 December 2012. The winner will be announced in our September 2013 issue and at the 2013 annual meeting of the American College of Epidemiology.

This award is made possible by an endowment from Hoffman-LaRoche Ltd., managed by the American College of Epidemiology.

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