Exploring the cause of the pertussis resurgence in England following the COVID-19 pandemic: a mathematical modelling study

Abstract

Background

In 2024 England, in common with many other countries, experienced a pertussis resurgence the cause of which is unclear. We used a pertussis transmission model, previously developed to investigate the cause of the pertussis resurgence in England in 2012, to explore potential factors contributing to the increase in pertussis cases observed in England in 2024.

Methods

An age-stratified dynamic transmission model fitted to pertussis notification data from England between 1953 and 2013 was run until 2034 with and without changes in social mixing as estimated from Google mobility and school attendance data during the COVID-19 pandemic. The model assumes vaccination protects better against disease than pertussis infection, and that infected vaccinees can transmit if asymptomatic or with only mild/atypical symptoms. Infection is assumed to result in protection against clinical symptoms and infection, and provide more durable immunity than vaccination. Counterfactual scenarios were run to explore the effect of reductions in vaccine coverage during the pandemic and of the addition in 2014 of boosters in the 2nd year of life and in adolescence.

Results

A resurgence was only generated with reduced social mixing and could not be explained by short-term reductions in vaccine coverage. Additional boosters from 2014 would not have prevented a resurgence. Peaks of increased pertussis incidence are predicted over the next decade. The parameter sets that generated a resurgence in 2024 had the shortest duration of acellular vaccine protection, median 5 years with 90% protection against infection.

Conclusion

This modelling study implicates reduced mixing in England during the COVID-19 pandemic as the cause of the pertussis resurgence in 2024 together with the short duration of protection from acellular vaccine. Interruption of the background rate of natural boosting during the pandemic increased the pool of susceptible individuals resulting in increased transmission post-pandemic with clinical cases in those with waned vaccine–induced protection and the unvaccinated, including infants of unvaccinated mothers. In countries using acellular pertussis vaccines, infection continues to play an important role in maintaining population immunity around an endemic equilibrium. Improved pertussis vaccines that provide more complete and more durable protection against infection are needed to improve pertussis control.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12879-026-12521-5.

Introduction

Pertussis is a highly transmissible respiratory infection which remains endemic despite longstanding immunisation programmes that have achieved high coverage. Infants too young to be vaccinated are most at risk of severe disease with high case fatality rates even in countries with advanced health care systems [1]. Many countries experienced an increase in pertussis incidence some years after changing from whole cell pertussis (wP) to acellular pertussis (aP) vaccines which was likely attributable to the shorter duration of protection and lower efficacy against infection of aP than wP vaccines [2, 3]. This resulted in a higher endemic level of pertussis transmission in aP-using countries which could not be wholly mitigated by adding additional aP boosters to the immunisation programme [2, 3]. In response to the pertussis resurgence in the UK in 2012 that followed the change from wP to aP vaccine in 2004, the UK introduced a maternal pertussis immunisation programme which was shown to be highly effective at preventing pertussis cases and associated deaths in infants too young to be vaccinated [4, 5]. Many aP-using countries subsequently introduced a maternal programme which is now recommended by WHO as the most effective and cost-effective way of protecting vulnerable young infants [2].

In the first quarter of 2024 five infant deaths from pertussis were reported in England together with an increase in pertussis cases in all age groups [6]. The European Centre for Disease prevention and Control (ECDC) also reported an increase in pertussis cases in all but two of the 27 European countries submitting surveillance reports to ECDC in the first quarter of 2024 [7]. The resurgences in England and other European countries occurred after a period of reduced incidence associated with the social distancing measures introduced during the COVID-19 pandemic. Increases in pertussis incidence in 2023-24 have also been reported in other countries including North America, Brazil, Australia, Israel and China [7]. These resurgences have occurred in countries with and without maternal pertussis vaccination programmes and in countries with vaccination schedules that recommended booster doses in adolescence and at regular intervals during adult life.

A number of factors have been suggested as potentially contributing to the increase in pertussis cases reported in 2023-24 including improvements in sensitivity of surveillance methods, low vaccine coverage, occurrence of natural epidemic peaks and waning immunity together with what has been described as a “bounce back” after the period of reduced transmission during the COVID-19 pandemic [7–10]. We used a pertussis transmission model previously developed to explore the cause of the 2012 resurgence [11] to explore potential factors associated with the pertussis resurgence in England in 2024; these include the impact of the changes in population mixing that resulted from the social distancing measures imposed to reduce SARS-CoV-2 transmission in 2020 and 2022 [12], a drop in vaccine coverage associated with the COVID-19 pandemic and the failure to introduce aP-containing booster doses in the second year of life and in adolescence in England which were explored as policy options following the 2012 pertussis resurgence but not implemented [11].

Methods

Model structure and assumptions

We used a previously described age-structured, compartmental deterministic model to explore the effect of the COVID-19 social distancing measures on pertussis transmission dynamics in the post COVID-19 period [11]. The model distinguishes between natural and vaccine-induced immunity and between protection against clinical disease and infection. The model assumes that natural immunity completely protects against both clinically-typical pertussis symptoms and infection whereas vaccination completely protects clinically-typical pertussis but only provides partial protection against acquiring and transmitting infection. We also assume that both natural and vaccine-induced immunity wane with time and that, if re-infected, an individual has a lower probability of developing clinically typical disease.

In the model, infants are born susceptible (S1) to pertussis and acquire natural immunity (R) according to the age-dependent force of infection (FOI), λ. A primary infection in an unvaccinated individual results in a proportion developing clinically typical pertussis a proportion of which gets notified; individuals whose infection does not result in a notified case may or may not have pertussis symptoms but can still transmit. The proportion of all primary infections that is notified is α₁. Following a primary infection natural immunity wanes to a secondary susceptible state (S2) in which individuals can become re-infected according to the same FOI as for a primary infection. The proportion of secondary infections that result in notified pertussis (α₂) is lower than α₁ as fewer infections produce clinically typical symptoms. After recovery from a primary or secondary infection individuals re-enter the R compartment. Vaccinated individuals prior to waning are assumed to be completely protected against notified pertussis but can still be infected, though with a reduced FOI reflecting the efficacy of the vaccine against infection. After clearing infection, vaccinated individuals enter the R compartment from which protection wanes to S2; without infection vaccine protection also wanes to S2. An aP booster is assumed to restore waned protection to the vaccine-protected compartment which gives protection against clinical disease but only partial protection against infection. On waning, boosted individuals enter S2. A summary of the transitions between compartments for aP vaccinated cohorts is shown in Fig. 1.

Fig. 1.

Flow diagram of the pertussis transmission dynamic model capturing the impact of acellular pertussis vaccination. Legend. S1: Susceptible to a first infection, λ: Force of infection, I1: Infectious with a first infection, α₁: the proportion) of first infections developing notified pertussis, R: Natural Immunity, S2: Susceptible to a secondary infection, I2: Infectious with a secondary infection, α₂; the proportion of secondary infections developing notified pertussis, S_aP: Susceptible to infection while acellular pertussis vaccine protected against clinical disease, VE: Vaccine Efficacy against infection, I_aP: Infectious with a first infection while protected by acellular vaccine against clinical disease (* there is no α parameter as this is set to 0). Green lines show vaccination, red lines show acquisition of infection, light blue lines show acquisition of natural immunity after clearing infection, and dark blue lines show waning of natural immunity or vaccine protection

Model fitting

In this exploratory study we used the previously estimated transmission and vaccine parameters from Choi et al. [11]. The FOI in unvaccinated individuals was estimated from a static model fitted to pre-vaccination age-stratified pertussis notification data for 1956 with the parameters relating to natural and vaccine-induced protection estimated by fitting a dynamic model to age-stratified annual notification data for England from 1956 to 2013 using historical coverage data for primary and booster doses [11]. The wP vaccine was used up to 2004 when it was fully replaced by aP vaccine. From 2001 onwards the aP booster was in use in pre-school children. The following parameters were estimated by selecting the 5% best fitting parameter sets; average duration of natural immunity; efficacy of wP and aP vaccines (VE) against infection while still vaccine-protected ; average duration of protection of wP and aP against infection and clinical disease; α₁, and the ratio α₂/α₁. The following constraints were applied during the fitting: duration of natural immunity should not be less than that of wP and the duration of wP protection against infection should not be less than that of aP for which a minimum duration of 5 years was assumed based on aP effectiveness studies. The range of parameter values for natural and vaccine-induced immunity explored during the fitting in Choi et al. [11] is shown in Table S8. The parameter ranges for the (658) 5% best fitting parameter sets taken from Choi et al. [11] are shown in Table 1. These 658 parameters were then used to describe the uncertainty (minimum to maximum range) of the model outputs for the long-term simulations for the current analyses.

Table 1.

Estimated parameter values (median and quantiles) from pertussis model in Choi et al. [11]

Parameter	Quantiles
	0.025	0.25	0.5 (Median)	0.75	0.975
Duration* natural protection (Years)	19.75	30	35	45	50
Duration* of wP protection (Years)	15	22.5	25	27.5	30
Duration* of aP protection (Years)	5	7.5	12.5	20	27.5
Efficacy wP vaccine against infection (VE)	0.8	0.8	0.8	0.8	0.9
Efficacy aP vaccine against infection (VE)	0.6	0.7	0.7	0.8	0.9
α1**	0.1449	0.1455	0.1457	0.1457	0.146
α2**	0.0016	0.0016	0.0021	0.0029	0.0048

^* Average duration of protection assuming an exponential decay

** α₁ is percentage of first infections in an unvaccinated individual that are notified; α₂ is the percentage of infections in vaccinated individuals with waned protection or reinfections in unvaccinated individuals that are notified

A fuller description of the model structure, data and fitting procedure is given in the Supplementary Appendix Section S2, together with the model equations.

Mixing matrix

The mixing matrix between age groups used for the fitting and for model predictions up to February 2020 was from the POLYMOD survey carried out in England in 2006 supplemented by an additional contact study in infants under one year of age who were under-represented in POLYMOD [13, 14]. From March 2020 the mixing matrix was scaled to reflect the reduced mixing that was associated with the social distancing measures that were imposed in England between March 2020 and October 2022 to reduce SARS-CoV-2 transmission, using the same approach as described in Birrell et al. [12], (see the section on contact matrices in the supplementary materials of Birrell et al. for a detailed description). In summary, that method followed the approach of van Leeuwen et al. [15] in which contacts in each location (e.g. work, home, leisure etc.) in the POLYMOD survey were associated with one or more activities (e.g. school, social visits etc.) as defined in the time-use survey (UKTUS) [16]; the resulting mapping is shown in Table S1 of van Leuuwen et al. [15]. Activities were then linearly scaled based on bi-weekly Google Mobility data, and school attendance data. For example, school associated contacts were scaled linearly based on the school attendance data, and social visits were scaled based on the Google Mobility data for leisure activities as described in Birrell et al. [12]. This results in a weekly scaling matrix, where each element represents the relative number of contacts between the associated age groups, which can then be elementwise multiplied with the base contact matrix as shown in Fig S1. Annual population sizes between 1956 and projected out to 2030 [17] were implemented to produce realistic mixing patterns with the 2030 population used for model simulations out to 2034.

Model scenarios

The model was run from 1956 to 2034 with the assumption that coverage for primary (96%) and booster (86%) doses from 2013 was the same as that in England in 2013. The following model scenarios were investigated: continuing with the existing primary immunisation and pre-school booster programme with and without a change in population mixing due to the COVID-19 social distancing measures; assuming a drop of 10% in coverage of the primary and pre-school booster programme between January 2020 to December 2022 but without a change in social mixing; and with and without the addition in 2014 of an adolescent booster with 86% coverage and a booster dose at 18 months with 91% coverage. Coverage assumed for the 18 month and adolescent booster was respectively the primary vaccination coverage and pre-school booster coverage in England in 2020.

Results

The pertussis notifications between 1956 and 2024 and the changes to the pertussis vaccination programme over the period are shown in Fig. 2; the exact dates of the COVID-19 lockdowns in England are provided in a foot note. The resurgence in 2024 resulted in the largest number of notified cases since the change to aP vaccine in 2004.

Fig. 2.

Number of notified cases (NOIDS) of pertussis by age group and pertussis vaccine coverage at 24 months by vaccine type for the primary course, and for the pre-school acellular vaccine booster from 1956 to 2024. Note: First lockdown: from 26 March 2020 to 4 July 2020, second lockdown: from 5 November 2020 to 2 December 2020, third lockdown: from 6 January 2021 to 8 March 2021

The projected pertussis cases out to 2034 under different model scenarios are shown in Fig. 3. There is no predicted resurgence after the Covid-19 pandemic without the reduced social mixing during the pandemic (Fig. 3A). The year in which the model predicted a resurgence varied with the choice of parameter sets, with some sets generating a resurgence in 2024 while others generating a resurgence starting in later years, with the median for all 658 parameter sets showing a resurgence in 2026 (Fig. 3B). In order to explore which vaccine parameter values generate an early resurgence, those parameter sets that gave the highest 10% of predicted overall cases in 2024 (66 out of 658 parameter sets) were selected and compared with parameter sets that predicted less than one case in 2024 (n = 273) (Fig. 3C and D respectively).The median duration of acellular vaccine protection for the parameter sets that generated a resurgence in 2024 was 5 years with a VE against infection of 0.9; in contrast for those that predicted a later resurgence the median duration of protection was 17.5 years with a VE of 0.7 (Supplementary Appendix Tables S1 and S2). With the shorter duration of vaccine protection peaks of increased incidence are predicted to continue for a decade (Fig. 3C). Without the change in social mixing a drop of 10% in coverage for the primary and pre-school booster doses during the COVID-19 pandemic would not have generated a resurgence (Fig. 3E). If an 18 month and 14 year booster programme had been introduced in 2014 the model predicts that there would still have been a resurgence after the COVID-19 pandemic, although the median number of cases in 2024 is predicted to be around 5000 cases lower (Fig. 3F).

Fig. 3.

Predicted overall notifications under different model scenarios. Legend. Graphs show model outputs for pertussis notifications all ages combined from 2006 to 2034 under the existing primary aP schedule at 2,3,4 months with a single booster before school entry. The median is shown as a black line (minimum to maximum range in the grey shaded area) of the predicted annual pertussis notifications. Blue dots show NOIDs cases reported up to week 52 2024. (A) Counterfactual scenario without reduced population mixing during the COVID-19 pandemic using all 658 best fitting parameter sets from Choi et al. [11]); (B) With reduced population mixing during the pandemic (all 658 parameter sets); (C) With reduced population mixing during the pandemic and restriction of parameter sets to those that generate the top 10% of cases in 2024 (n = 66); (D) With reduced population mixing during the pandemic and restriction of parameter sets to those that predict < 1 case in 2024 (n = 273); (E) 66 parameter sets with top 10% cases in 2024 without any change in population mixing but with a 10% drop in coverage for the primary and pre-school booster doses from January 2020 to December 2022; (F): 66 parameter sets with top 10% cases in 2024 with a change in population mixing during the COVID-19 pandemic and with the counterfactual scenario of introducing additional aP vaccine boosters at 18 months and 14 years of age in 2014

The predicted cases by age group out to 2034 with the restricted parameter sets that produced the top 10% of overall cases in 2024 are shown in Fig. 4. A resurgence in 2024 is predicted in all age groups with the biggest increases in those under 10 years of age. Apart from 15 to 24 year olds the first three post-pandemic peaks exceed those in the immediate pre-pandemic period.

Fig. 4.

Model outputs by age-group under the existing schedule with reduced population mixing during the pandemic. Legend. Graphs show the median as a black line (minimum to maximum range in the grey shaded area) of the predicted annual pertussis notifications with restriction of parameter sets to those that generate the top 10% of notifications in 2024 (n = 66)

The proportions of the population in the different model compartments by age from the model outputs between 2000/01 and 2040/41 are shown in Supplementary Appendix Fig S2. The infectious proportion decreased from 2020 due to social distancing, with a resulting increase in the susceptible proportion and a reduction in the proportion with natural immunity, most marked in the 5–9 and 10–14 age groups. Following the relaxation of social distancing measures, the infectious proportion increased as the larger pool of susceptibles facilitated transmission.

The age-breakdown of the notified cases predicted by the model in 2024 with the 66 selected parameter sets compared with the NOIDs cases is shown in Fig. 5. Although the overall shape of the age distribution was similar between the model prediction and the NOIDS data, the model underestimated the cases in most age groups.

Fig. 5.

Predicted number of notified pertussis cases by age group in 2024 in England. Legend. Graphs show medians (error bars minimum to maximum range) of the model predictions with the reductions in population mixing during the COVID-19 pandemic [12] and NOIDs cases for 2024

Discussion

This modelling study implicates the social distancing measures imposed during the COVID-19 pandemic as the cause of the pertussis resurgence in England that started in 2024. Our model predicted increases in cases across the age range consistent with the observed disease trends [18]. The model predicted a resurgence without introducing in the model any drop in vaccine coverage associated with the pandemic. Implementing a 10% coverage drop for both the primary and pre-school booster doses for 3 years from January 2020 without reduced mixing did not produce a resurgence comparable to that seen in England in 2024. Our model predicted a resurgence following the reduced population mixing that occurred during the pandemic even under the counterfactual scenario in which 18 month and adolescent aP boosters were added to the national programme in 2014. This is consistent with the resurgences seen in settings where these additional boosters were already part of the schedule [7].

In constructing our model we based the vaccine parameters on the protection against disease and infection documented in epidemiological studies and the baboon pertussis challenge model [2, 3]. The epidemiological studies have shown more rapid waning of protection against clinical disease [2] with acellular than whole cell vaccines. In the baboon challenge model aP vaccines provide good protection against disease but no protection against infection or transmission [3] with robust protection against infection only being generated after one or more pertussis infections [19]. While these animal studies have provided valuable insights into the key differences between aP and wP vaccines and pertussis infection, epidemiological studies in countries that have introduced aP vaccination programmes do provide evidence of reduced transmission indicative of some protection from aP vaccines against transmission [20–23]. In our model we reflected these properties by allowing acellular vaccinees to be susceptible to infection while still protected against notified (i.e. clinically typical) pertussis, and to have a shorter duration of protection than whole cell vaccinees or those who have experienced natural infection. Infection in an acellular vaccinee therefore acts as a booster generating more durable protection against further infection without necessarily resulting in notified pertussis. The COVID-19 social distancing measures supressed this background rate of boosting allowing a pool of infection-susceptible acellular vaccinees to accumulate during the pandemic thereby disturbing the endemic equilibrium that existed before the COVID pandemic. On resumption of normal mixing patterns, transmission of pertussis increased and is predicted to exhibit cycles of increased oscillation before resuming the pre-COVID equilibrium with clinical cases apparent in unvaccinated individuals, including infants of unvaccinated mothers, and those whose protection against clinically typical disease has waned. Based on the timing of the resurgence in England our model implies that it was driven by short average duration of protection from aP vaccine (around 5 years) rather than poor protection against infection which was estimated to be around 90% prior to waning.

The strength of our study is that we used an existing pertussis transmission model that reproduced the resurgence in England in 2012 which followed the change from wP to aP vaccines [11] and correctly predicted the higher endemic level of transmission in England in all age groups since 2012 [24]. While our model did not include a maternal immunisation component, vaccination of pregnant women would have a negligible impact on overall transmission. The modifications to the mixing patterns that were incorporated to capture the restrictions imposed during the COVID-19 pandemic were based on empirical data and were used by modelling groups to refine model predictions on the impact of the evolving pandemic on cases and deaths [12, 15].

A limitation of our model is that the range of aP parameter values that fitted the observed notification patterns in England over the period 1956 to 2013 was wide (Table 1). More formal fitting of the model to notifications data up to 2024 would have allowed better refinement of the parameter values but the objective of the study was to explore which factors would generate a resurgence rather than to produce precise predictions. However, by selecting the parameter sets that gave the top 10% of overall cases in 2024, further refinement of the most likely parameter values for the degree and duration of protection afforded by aP vaccines was possible. Despite this restriction, there was still a wide range of model outputs with some showing no post-pandemic resurgence (Fig. 3C).

A further limitation is that our model parameters α₁ and α₂ (which reflect the proportion of infections notified respectively in unvaccinated and previously infected/vaccinated individuals) are assumed to be constant over time. However, since 2013 the proportion of cases that are notified has increased due to the routine availability of oral fluid testing for raised IgG levels to pertussis toxin that are indicative of recent infection [25]. The improvements in notification efficiency resulting from oral fluid IgG testing have been most marked in those aged 10 years and over in whom pertussis may be mild or clinically atypical [26]. If our model had been fitted to NOIDs data since 2013 with age-dependent α₁ and α₂ parameters, it is probable that these estimated parameter values would have been higher for those aged 10 years and over. This may explain in part the underestimation of cases in those aged 10 years and above predicted by the model when compared with NOIDs cases in 2024. In addition, as media coverage and health warnings about the pertussis resurgence increased during 2024, notification efficiency improved as evidenced by the 2 fold higher number of notified than laboratory confirmed cases in 2024 whereas, since the introduction of PCR and serological diagnosis in 2001, laboratory confirmed cases have consistently exceeded notifications [27]. While this change in notification efficiency will have exaggerated the size of the resurgence it was not the cause of the increase in reported cases in 2024.

Another factor that will have changed over time is population mixing patterns between 1956 and 2013, the period over which the model was fitted to notification data. For the mixing matrix over this period we used the POLYMOD survey conducted in 2006 in England [13] in the absence of data on how mixing patterns have changed in the population over the fitting period. The changes in population mixing during the COVID-19 lockdowns were based on Google Mobility and school attendance data, and there may be potential biases inherent in these proxies. Further exploration of the impact of various contact assumptions on the COVID-19 model has shown that the matrices fitted well, albeit when used in a different more complex model [28]. Since we used our pertussis model as an exploratory tool, such potential biases are unlikely to have a material impact on our conclusions.

We did not consider virulence evolution as a factor contributing to the pertussis resurgence in England. While one study found a temporal association between emergence of a ptxP3-ERBP lineage of B. pertussis with high virulence and macrolides resistance and the 2023 pertussis resurgence in Northern China [29], virulence evolution was not identified as a factor contributing to the resurgence in England or elsewhere in the wake of the COVID-19 pandemic [30].

Our model was originally developed to investigate the cause of the pertussis resurgence in England in 2012. At around the same time, a number of other groups developed pertussis transmission models to investigate the cause of the resurgences being reported in other aP-using countries. In common with our model, most of these models include waning immunity and allow for a substantial component of pertussis transmission to be driven by infections that are not reflected in notified disease [31–34]. Differences with our model include allowing for the proportion of infections that are notified to be age-dependent [34] and for the use of sero-epidemiological data to estimate the incidence of boosting in the population by detection of high IgG levels to pertussis toxin [31], features that could potentially be incorporated in future iterations of our model. To date however we are unaware of any publications using such models to investigate the post-COVID-19 resurgences now being reported.

The model predicts that peaks with an elevated incidence of pertussis are likely to occur over the next decade in England as the epidemiology of pertussis returns to the pre-pandemic equilibrium. It is therefore essential to achieve and sustain high levels of maternal immunisation to protect vulnerable infants too young to be vaccinated. Coverage of the maternal immunisation programme in England for 2023 to March 2024 was only 58.6%, a fall of 15.8% since 2017 [18]. With an effectiveness of around 92% [18], 90% coverage of the maternal programme could prevent 83% of the cases predicted by our model in infants under 3 months of age in the coming years. The effect of the resurgence would also have been mitigated somewhat had additional 18 month and adolescent boosters been in place since 2014. The short duration of protection of 5 years estimated by the model for aP vaccine supports the recommendation that those who have regular contact with pregnant women or vulnerable infants in the hospital or community setting should receive 5-yearly booster doses, not only for their own protection but potentially to reduce onward transmission [35].

Our modelling analysis, together with other assessments [36], indicate the extent of pertussis infection that occurs despite high vaccine coverage and the deficiencies of the current generation of aP vaccines in providing durable, sterilising immunity. Research efforts are underway to develop improved pertussis vaccines by incorporating novel adjuvants to elicit persisting immunological memory [35] or by using intranasal administration of a live attenuated B. pertussis strain to generate mucosal responses that can protect against transmission [37]. Optimising the deployment of such new pertussis vaccines, for example as boosters or in place of the current generation of aP vaccines, will require further refinement of pertussis transmission models to better capture the impact of improved surveillance methods and to validate the model predictions against direct measures of pertussis incidence such as those available from seroepidemiology.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

YHC and EM designed the study; YHC built the pertussis model and ran the simulations; EvL constructed the scaling matrix for the reduced social mixing during the COVID-19 pandemic; EM wrote the first draft of the paper; all authors critically reviewed and revised the paper, and approved the final version for submission.

Funding

UKHSA and the National Institute for Health Research grant reference NIHR200929.

Data availability

The data files including notification data by age group and vaccine coverage, and code for the model can be accessed at https://url.uk.m.mimecastprotect.com/s/4pI9CY58PIKPq0rU0fouxeQuq?domain=zenodo.org.

Declarations

Ethical approval

The data used for fitting the pertussis model is routinely available anonymised notification data. Ethics approval for the study was there not required.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.