Abstract
Pertussis has resurged in many countries where it was once regarded as under control, with the recent outbreaks showing a shift in incidence towards teens and older individuals. Here, using an age-stratified transmission model, we tested two potential causes for underlying changes in pertussis transmission dynamics. We did so assuming hypothesized mechanisms supporting present-day pertussis epidemiology: (I) improved diagnostics, (II) acellular vaccines leading to asymptomatic transmission (III) both. We used the relative risks and odds ratio methods to examine the impact of these differing assumptions on signatures of relative roles of key age groups through time, allowing us to explore those age cohorts that disproportionately account for transmission. Our findings show that for epidemics after the vaccine switch, a scenario with increased adult reporting and no asymptomatic transmission reflect a loss of signal, where no age group appears to be key. While scenarios with asymptomatic transmission, reflect a population where children (1-10 years old) are still disproportionally at risk. These results demonstrate that understanding the underlying transmission mechanisms in a population are paramount for vaccination policies in attaining herd immunity and eventually eradication.
Introduction
Pertussis is a highly transmissible vaccine-preventable respiratory disease [1, 2, 3, 4]. With the implementation of routine immunization in the 1950s with whole-cell pertussis (DTP) vaccines, pertussis incidence decreased considerably [5, 6, 7] allowing this disease to become a candidate for eradication. However, recently, countries boasting high pertussis vaccine coverage, such as the UK and the US, have experienced increased incidence accompanied with infant pertussis-linked deaths [4, 7, 8, 9, 10].
Historically considered a childhood disease, these resurgence events are characterized by a remarkable shift in the age-distribution of cases [11, 2, 4, 9, 10]. This is reflected by the increasing incidence in adolescents and adults that may currently be contributing disproportionately to transmission, perhaps due to higher contact rates or lower immunity [12, 13, 14, 15, 10]. Thus, subsequently being over-represented in incidence reports as an epidemic takes off.
Potential explanations for these patterns include improved diagnostic testing, leading to better surveillance and higher reporting [8, 16, 17], and the switch from the DTP to acellular pertussis vaccines (DTaP) [18, 19, 20]. Reporting rates for pertussis cases vary by age group, thus the leading to ambiguity of age-related transmission roles [21]. There is a growing concern that the DTaP vaccine might be an insufficient control measure [17]. In animal models, it has been suggested that acellular vaccines may not prevent infection and, additionally, allow for asymptomatic transmission [22]. This pattern of resurgence could also be consistent with the long-term dynamical consequences of lower vaccination coverage, resulting in a build-up of susceptible adults who were neither vaccinated nor infected [8].
The uncertainty surrounding the role of different age cohorts further complicates matters. We investigate potential changes in age-specific drivers of pertussis transmission by performing a simulation study, based on an age-structured model of pertussis transmission that incorporates England and Wales demography and contact patterns, historical immunization practices, the introduction of serological and PCR diagnostic methods in 2001 and the switch to the acellular vaccine (DTaP) in 2004.
Focusing on two different epidemics - before and after changes in vaccine and diagnostics - we evaluate scenarios of asymptomatic transmission and increased adult reporting. For the different scenarios, we attempt to characterize the role of different age groups by comparing the patterns of incidence before and after an epidemic peak. For the different scenarios, we use relative risk and odds ratio analyses - which calculate the ratio of the probability of an event occurring in one group to the probability of it occurring in another group [23]. We thus try to identify age groups at higher risk, suggestive of enhanced susceptibility to pertussis infection and/or higher contact rates [21]. Measuring age cohorts’ risks in the different scenarios, will further allows us to understand the knock-on consequences at the population level of changes in both vaccine and diagnostics.
Contrasting these different scenarios and odds ratio measures with actual incidence reports, for a given country, we may be able to better understand recent epidemiological data and the underlying transmission dynamics. Thus, detecting possible age cohorts driving transmission could be crucial for an adaptive assessment of control policies.
Methods
Model formulation
A baseline model of pertussis transmission
We implemented an age-structured, compartmental model of pertussis transmission, building on previously proposed models that have carried out statistical fitting of transmission models to pertussis incidence reports [24, 25, 26, 27]. The model is an extension of the classic SIR model with routine vaccination, implemented as a system of ordinary differential equations. It incorporates empirical age-specific contact rates from the POLYMOD study in Great Britain [28].
Our model is comprised of 18 age classes: 12 1-month infant age classes and 1-4 years, 5-9 years, 10-14 years, 15-19 years, 20-44 years, 45+ years. Individuals are born susceptible (at a rate μ). Susceptible individuals become exposed through contact with infectious individuals and become infectious. After recovering, individuals are immune to further infection. We assume infection-derived immunity to be practically life lifelong, based on previous epidemiological studies of pertussis in England and Wales [24], Sweden [25] and Thailand [26], which found that repeat infections contributed very little to transmission [29]. Individuals in the routine vaccinated class (V) may lose immunity at rate ϵ. This rate of waning is exponentially distributed, meaning that many will lose immunity faster than the population average. We assume routine vaccination to also afford protection lasting, on average, 75 years, while being aware that there is considerable discussion regarding the nature and duration of pertussis vaccine protection [30, 31, 20]. The average infectious period (1/γ) was fixed at 21 days [8, 32]. The per capita birth and death rates were fixed at μ = 1/75 per year. Individuals who are infected, have a coarse age-specific reporting probability ι of their infection status being recorded (Table 1). We assumed a basic reproduction number, R0 of 10 [20]. The model equations and associated parameter values are presented in detail in the Supplementary materials and in Table 1.
At time ta we introduce vaccination. Individuals may be vaccinated with either whole cell (before time tb) or acellular vaccine (after time tb). The model explicitly models acellular vaccine replacing whole cell vaccine. Routine infant vaccination occurs at 2, 4, and 6 months of age in order to mimic the protective effects afforded following the receipt of three doses of pertussis vaccine. It is implemented by moving, with probability ρ (corresponding to the vaccine coverage), those susceptible individuals who age out of their 2-, 4-, or 6-month age categories into the vaccinated (V) class.
Contact network data and R0 estimation
Our model incorporated empirical age-specific contact rates from the POLYMOD study in Great Britain [28], corrected for reciprocity as detailed Riolo et al. [27]. We constructed a WAIFW (Who Acquires Infection From Whom) matrix, to describe the transmission rate between different age groups (Figure S1). The Basic Reproduction Number, R0, for our model was calculated using the Next Generation Method [33]. See supplementary materials for details.
Model scenarios
Scenario I - Baseline model with no changes in reporting and a change in vaccine from whole cell to acellular.
Scenario II - Asymptomatic carriage after time tb, to simulate a vaccination switch from DTP to DTaP. An added compartment to the baseline model: Infected Asymptomatic (A). Individuals who are vaccinated with Tdap may become infectious but will not show symptoms.
Scenario III - Increased adult reporting after tc, to simulate introduction of PCR testing (from 10% to 20%).
Scenario IV - Both asymptomatic carriage after time tb and increased adult reporting after tc.
Reporting probability
From the simulated data at each time t, for both scenarios - with and without asymptomatic transmission - we sampled the true infections It to mimic under reporting, assuming sampling is negative-binomially distributed. where Ct are the case reports, ι changes depending on the age class, and also in a scenario with changes in reporting in the older age classes at specific year in time (ι from 10% to 20%).
Asymptomatic carriage
Individuals vaccinated with DTaP move into a vaccinated class where they can become asymptomatically infected. We assume no difference in transmissibility between symptomatic and asymptomatic individuals in scenarios II and IV. In scenarios V and VI, asymptomatic individuals are as infectious than non vaccinated infected individuals, but the infectious period is doubled.
Age specific relative risks during an outbreak
We attempted to characterize the role of different age groups by comparing the patterns of incidence before and after the epidemic peak [21]. We do this for all scenarios.
Defining periods
We defined the peak week as the calendar week in two specific outbreak years: one in the period before implementation of increased reporting in adults and before switching vaccination types (associated with asymptomatic carriage). Because the data are noisy and do not have a consistently timed annual peak, we characterized the pre- and post-peak periods (time windows) by smoothing the data using a cubic spline with 3 knots. The pre-peak is “take off” period before the peak of the epidemic. The post-peak is the “tail” of the epidemic, it was determined by the same method using the cut off week with the emergence of a smaller peak in incidence. This choice of spline for determining pre and post windows was validated by a generalized additive model (GAM) [34] and by segmented regression [35] (Refer to supplementary materials for details and figure S5).
Relative risks calculation
Additionally we estimated the relative role that different age groups play in the transmission of pertussis infection, as previously used by Worby and colleagues [21]. The population was split into groups. We estimate the relative risk for each age group defined as: Where B(i) is the proportion of the cases in age group i over all the cases in the pre-peak period and A (i) is the proportion for the cases in that same age group i over all cases during the post-peak period.
In the pre- and post-peak periods, we calculate the fraction (ratio) of cases which occur in each age group. We estimate the relative risk for each age group i as ratio of the fraction of pre-peak cases in age group i to the fraction of post-peak cases in age group i. This depicts a probability of a specific group being at high risk before the epidemic takes off when compared to post peak period. Thus comparing the periods before and after the epidemic’s peak. This allows us to account for difference in overall incidence between age groups and between pre- and post-peak periods. The 95% confidence intervals were calculated for relative risk following Lachin [23], where ln(RR(i)) is approximately normal.
Odds ratio calculation
In order to compare the extent to which different age groups are overrepresented in the pre-peak period, we can look at the odds-ratio between pairs of these relative risks of two different age groups. This gives us a relative measure of effect, allowing us to compare between age groups.
We estimate the odds ratio to characterize which age group when compared with another age group shows a more pronounced susceptibles’ depletion during the period approaching the outbreak - pre-peak period: where i and j are age groups as define for the previous methods. The 95% confidence intervals were calculated for odds ratios following Lachin [23], where ln(OR(i,j)) is approximately normal.
Results
Baseline Scenario - No changes in adult reporting, no asymptomatic transmission
The simulated time series show noo changes in either vaccination or adult reporting.
Odds ratios
Baseline scenario: Peak week
Two outbreaks in detail are show here, before and after vaccine swith from DTP to DTaP. In both periods peak week is at week 28, with the epoch before vaccine switch showing higher incidence fore younger age classes. The ascending period and descending windows of the after vaccine switch are a few weeks larger, as calculated using the GAM methodology (Figure S5).
Before the vaccine switch (DTP)
Table 2 provides a pairwise comparison of age groups, the odds ratios (OR), possibly indicating that young children (1-10-year-olds) were a key group in the epidemic. Worby et al.[21] described this higher risk as a measure for experiencing a significant depletion of susceptible pool during the outbreak take-off (pre-peak) period when compared to the other age groups, with risks among 1-10 years old significantly higher.
After the vaccine switch (4 years with DTaP)
Table 3 provides a pairwise comparison of age groups, the odds ratios (OR), possibly indicating that young children (10-15-year-olds) were a key group in the epidemic. In 1982 the pre-peak relative risk of an age group was higher the closer that group was to ages 1-10 years old, suggesting that school-aged children were on the leading edge of the outbreak.
Discussion
Needs updating
Are the odds ratios used by Worby et al. [21] really a measure of susceptible depletion, as postulated by them? Or simply a feature of the fact of contacts shaping the transmission dynamics and also increase reporting?
Can asymptomatic carriage [17], as a consequence of introduction of acellular vaccine, explain he breakdown in signal of specific age groups?
Can an increase in reporting probability of adults explain he breakdown in signal of specific age groups?
Determine by simulation how different scenarios affect the transmission dynamics and information regarding specific age groups
Calculate odds ratios and evaluate assumptions, in the context of contact rates
The relative impact of different age groups in epidemics in not well understood. We set out to test whether the observed changes in core groups could be due to asymptomatic transmission in infectious individuals who had been vaccinated with the DTaP vaccine (as suggested by [22, 17, 10]). We report the relative risks and odds ratio examining the impact of these differing assumptions on signatures of relative roles of key age groups through time. We assume that odds ratio are suggestive of driver role of a particular age group[21].
Our simulation study examined scenarios revealed that:
Scenario I- No asymptomatic transmission even after vaccination switch from DTP to DTaP (ie, both vaccines are transmission blocking). There are no changes to the adult reporting model (Figures 1 and 2).
Scenario II - Asymptomatic transmission can result following vaccination DTaP. We added a compartment to the baseline model: Infected Asymptomatic (A). Individuals who are vaccinated with Tdap may become infectious but will not show symptoms. There are no changes to the adult reporting model. This scenario with asymptomatic carriage (II), identified the 1-5 years of age as having a higher relative risk when compared to the other age groups (Figures S2 and S6 and Table S1).
Scenario III - No asymptomatic transmission in DTaP vaccinees. Increased adult reporting after the introduction of serological/PCR testing (Figures S3 and S7 and Table S2).The odds ratio results, for epidemics after the vaccine switch, that best reflect the loss of signal we observed in the actual data for England and Wales [36], are those for scenario III (increased adult reporting, no asymptomatic transmission).
Scenario IV - Both asymptomatic transmission after the vaccine switch and increased adult reporting after the introduction of serological/PCR testing. This scenario (both changes) shows age groups 1-10 years of age as being at higher risk, with 10-15 also with higher risk, possibly reflecting the roles these groups play in driving the epidemic (Figures S4 and S8 and Table S3).
Our results provide a cross-scenario comparison of the relative roles of different age cohorts during epidemics. Our estimates of the simulated results illustrate variability in the relative roles of each age group during different scenario pertussis epidemics, and for the most part yield consistent evidence for a leading role of school age children in propagating the pertussis epidemics.
Footnotes
↵* E-mail: anabento{at}uga.edu