Deciphering the impacts of vaccination and immunity on pertussis epidemiology in Thailand

Pertussis vaccines, epidemiology and evolution

Pertussis, which is caused by Bordetella pertussis, has plagued humans for at least 800 years, is highly infectious and can be fatal in the unvaccinated, especially very young infants. Although the rollout of whole-cell pertussis (wP) vaccines in the 1940s and 1950s was associated with a drastic drop in incidence, concerns regarding the reactogenicity of wP vaccines led to the development of a new generation of safer, acellular (aP) vaccines that have been adopted mainly in high-income countries. Over the past 20 years, some countries that boast high aP coverage have experienced a resurgence in pertussis, which has led to substantial debate over the basic immunology, epidemiology and evolutionary biology of the bacterium. Controversy surrounds the duration of natural immunity and vaccine-derived immunity, the ability of vaccines to prevent transmission and severe disease, and the impact of evolution on evading vaccine immunity. Resolving these issues is made challenging by incomplete detection of pertussis cases, the absence of a serological marker of immunity, modest sequencing of the bacterial genome and heterogeneity in diagnostic methods of surveillance. In this Review, we lay out the complexities of contemporary pertussis and, where possible, propose a parsimonious explanation for apparently incongruous observations.

A perturbative approach to the analysis of many-compartment models characterized by the presence of waning immunity

The waning of immunity after recovery or vaccination is a major factor accounting for the severity and prolonged duration of an array of epidemics, ranging from COVID-19 to diphtheria and pertussis. To study the effectiveness of different immunity level-based vaccination schemes in mitigating the impact of waning immunity, we construct epidemiological models that mimic the latter's effect. The total susceptible population is divided into an arbitrarily large number of discrete compartments with varying levels of disease immunity. We then vaccinate various compartments within this framework, comparing the value of [Formula: see text] and the equilibria locations for our systems to determine an optimal immunization scheme under natural constraints. Relying on perturbative analysis, we establish a number of results concerning the location, existence, and uniqueness of the system's endemic equilibria, as well as results on disease-free equilibria. We use numerical techniques to supplement our analytical ones, applying our model to waning immunity dynamics in pertussis, among other diseases. Our analytical results are applicable to a wide range of systems composed of arbitrarily many ODEs.

Cost-Utility Analysis of Universal Maternal Pertussis Immunisation in Thailand: A Comparison of Two Model Structures

OBJECTIVES

This study aimed to assess the cost-effectiveness of introducing universal maternal pertussis immunisation under the national vaccine programme in Thailand.

METHODS

We conducted a cost-utility analysis from a societal perspective to compare maternal vaccination with (1) TdaP vaccine, (2) Td vaccine and aP vaccine, and (3) Td vaccine only. We constructed two decision-tree models with Markov elements, each following a different clinical pathway, to allow us to examine structural uncertainty. Costs were converted to 2021 Thai Baht (THB) and a discount rate of 3% was applied to health and cost outcomes, with sensitivity analysis at 0% and 6%. Parameter uncertainty was investigated through deterministic and probabilistic sensitivity analysis, with expected value of perfect information analysis.

RESULTS

Maternal pertussis vaccination would avert 27 cases and up to one death per year. The incremental cost-effectiveness ratio (ICER) for adding aP to the maternal immunisation schedule is 2,184,025 THB/QALY and the ICER for replacing maternal Td vaccination with TdaP is 3,198,101 THB/QALY. Maternal pertussis vaccination only becomes favourable in the probabilistic sensitivity analysis at cost-effectiveness thresholds above 6,000,000 THB/QALY, far above the Thai threshold of 160,000 THB/QALY. If incidence is less than 397 cases per 100,000, maternal pertussis vaccination will not be cost-effective in Thailand, within the plausible range for vaccine effectiveness and probability of hospitalisation. Budget impact is dominated by vaccination costs, which represent 12% and 18% of the 2021 national vaccine programme budget for introducing aP vaccine or for switching Td with TdaP vaccine, respectively.

CONCLUSIONS

We have found that maternal pertussis immunisation is not cost-effective in Thailand. Although there may be substantial under-reporting of pertussis cases, comparison with hospital data suggests that most under-reported cases are not hospitalised and therefore have negligible impact on our results. However, considerations such as affordability and local manufacturing may also be important for national immunisation programme decision-making.

Evaluation of Whole-Cell and Acellular Pertussis Vaccines in the Context of Long-Term Herd Immunity

After the pertussis vaccine had been introduced in the 1940s and was shown to be very successful in reducing the morbidity and mortality associated with the disease, the possibility of improving both vaccine composition and vaccination schedules has become the subject of continuous interest. As a result, we are witnessing a considerable heterogeneity in pertussis vaccination policies, which remains beyond universal consensus. Many pertussis-related deaths still occur in low- and middle-income countries; however, these deaths are attributable to gaps in vaccination coverage and limited access to healthcare in these countries, rather than to the poor efficacy of the first generation of pertussis vaccine consisting in inactivated and detoxified whole cell pathogen (wP). In many, particularly high-income countries, a switch was made in the 1990s to the use of acellular pertussis (aP) vaccine, to reduce the rate of post-vaccination adverse events and thereby achieve a higher percentage of children vaccinated. However the epidemiological data collected over the past few decades, even in those high-income countries, show an increase in pertussis prevalence and morbidity rates, triggering a wide-ranging debate on the causes of pertussis resurgence and the effectiveness of current pertussis prevention strategies, as well as on the efficacy of available pertussis vaccines and immunization schedules. The current article presents a systematic review of scientific reports on the evaluation of the use of whole-cell and acellular pertussis vaccines, in the context of long-term immunity and vaccines efficacy.

Immunological heterogeneity informs estimation of the durability of vaccine protection

Deciphering the properties of vaccines against an emerging pathogen is essential for optimizing immunization strategies. Early after vaccine roll-out, however, uncertainties about vaccine immunity raise the question of how much time is needed to estimate these properties, particularly the durability of vaccine protection. Here we designed a simulation study, based on a generic transmission model of vaccination, to simulate the impact of a breadth of vaccines with different mean (range: 10 months-2 years) and variability (coefficient of variation range: 50-100%) of the duration of protection. Focusing on the dynamics of SARS-CoV-2 in the year after start of mass immunization in Germany as a case study, we then assessed how confidently the duration of protection could be estimated under a range of epidemiological scenarios. We found that lower mean and higher heterogeneity facilitated estimation of the duration of vaccine protection. Across the vaccines tested, rapid waning and high heterogeneity permitted complete identification of the duration of protection; by contrast, slow waning and low heterogeneity allowed only estimation of the fraction of vaccinees with rapid loss of immunity. These findings suggest that limited epidemiological data can inform the duration of vaccine immunity. More generally, they highlight the need to carefully consider immunological heterogeneity when designing transmission models to evaluate vaccines.

Dissecting recurrent waves of pertussis across the boroughs of London

Pertussis has resurfaced in the UK, with incidence levels not seen since the 1980s. While the fundamental causes of this resurgence remain the subject of much conjecture, the study of historical patterns of pathogen diffusion can be illuminating. Here, we examined time series of pertussis incidence in the boroughs of Greater London from 1982 to 2013 to document the spatial epidemiology of this bacterial infection and to identify the potential drivers of its percolation. The incidence of pertussis over this period is characterized by 3 distinct stages: a period exhibiting declining trends with 4-year inter-epidemic cycles from 1982 to 1994, followed by a deep trough until 2006 and the subsequent resurgence. We observed systematic temporal trends in the age distribution of cases and the fade-out profile of pertussis coincident with increasing national vaccine coverage from 1982 to 1990. To quantify the hierarchy of epidemic phases across the boroughs of London, we used the Hilbert transform. We report a consistent pattern of spatial organization from 1982 to the early 1990s, with some boroughs consistently leading epidemic waves and others routinely lagging. To determine the potential drivers of these geographic patterns, a comprehensive parallel database of borough-specific features was compiled, comprising of demographic, movement and socio-economic factors that were used in statistical analyses to predict epidemic phase relationships among boroughs. Specifically, we used a combination of a feed-forward neural network (FFNN), and SHapley Additive exPlanations (SHAP) values to quantify the contribution of each covariate to model predictions. Our analyses identified a number of predictors of a borough's historical epidemic phase, specifically the age composition of households, the number of agricultural and skilled manual workers, latitude, the population of public transport commuters and high-occupancy households. Univariate regression analysis of the 2012 epidemic identified the ratio of cumulative unvaccinated children to the total population and population of Pakistan-born population to have moderate positive and negative association, respectively, with the timing of epidemic. In addition to providing a comprehensive overview of contemporary pertussis transmission in a large metropolitan population, this study has identified the characteristics that determine the spatial spread of this bacterium across the boroughs of London.

The impact of infection-derived immunity on disease dynamics

When modeling infectious diseases, it is common to assume that infection-derived immunity is either (1) non-existent or (2) perfect and lifelong. However there are many diseases in which infection-derived immunity is known to be present but imperfect. There are various ways in which infection-derived immunity can fail, which can ultimately impact the probability that an individual be reinfected by the same pathogen, as well as the long-run population-level prevalence of the pathogen. Here we discuss seven different models of imperfect infection-derived immunity, including waning, leaky and all-or-nothing immunity. For each model we derive the probability that an infected individual becomes reinfected during their lifetime, given that the system is at endemic equilibrium. This can be thought of as the impact that each of these infection-derived immunity failures have on reinfection. This measure is useful because it provides us with a way to compare different modes of failure of infection-derived immunity.

Durability of protection after 5 doses of acellular pertussis vaccine among 5-9 year old children in King County, Washington

PURPOSE

Waning of immunity after vaccination with the acellular Pertussis (aP) vaccine has been proposed as one of the main reasons for pertussis resurgence in the US. In this study, we estimated time-varying vaccine effectiveness after 5 doses of aP vaccine.

METHODS

We conducted a retrospective cohort study among children 5-9 years old (born between 2008 and 2012) living in King County, Washington, USA, who participated in the Washington State Immunization Information System. We estimated time-varying vaccine effectiveness after 5 doses of aP using smoothed scaled Schoenfeld residuals obtained from fitting Cox proportional hazards models to the data as well as piecewise constant Poisson regression.

RESULTS

There were 55 pertussis cases in this cohort, of whom 22 (40%) were fully-vaccinated and 33 (60%) were under-vaccinated. Vaccine effectiveness (VE) remained high for up to 42 months after the fifth dose (VE(t) = 89%; 95% CI: 64%, 97%) as estimated using survival analysis methods and up to 4 years (VE(t) = 93%; 95% CI: 67%, 98%) as estimated using Poisson regression.

CONCLUSION

We did not find evidence for waning of vaccine effectiveness for up to four years after 5 doses of aP among 5 -9 years old children in King County, WA.

Cost-effectiveness of maternal pertussis immunization: Implications of a dynamic transmission model for low- and middle-income countries

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(84) Low- and middle-income countries (LMICs) have experienced a resurgence of pertussis.

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(74) Maternal aP immunization could prevent pertussis among very young infants.

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(84) A dynamic transmission model was used to evaluate maternal aP immunization in LMICs.

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(82) Maternal aP is cost-effective when infant vaccination coverage is moderate or low.

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(85) Maternal aP immunization is not cost-effective in LMICs with infant coverage 90-95%.

Objective

This study evaluates the cost-effectiveness of maternal acellular pertussis (aP) immunization in low- and middle-income countries using a dynamic transmission model.

Methods

We developed a dynamic transmission model to simulate the impact of infant vaccination with whole-cell pertussis (wP) vaccine with and without maternal aP immunization. The model was calibrated to Brazilian surveillance data and then used to project health outcomes and costs under alternative strategies in Brazil, and, after adjusting model parameter values to reflect their conditions, in Nigeria and Bangladesh. The primary measure of cost-effectiveness is incremental cost (2014 USD) per disability-adjusted life-year (DALY).

Results

The dynamic model shows that maternal aP immunization would be cost-effective in Brazil, a middle-income country, under the base-case assumptions, but would be very expensive at infant vaccination coverage in and above the threshold range necessary to eliminate the disease (90–95%). At 2007 infant coverage (DTP1 90%, DTP3 61% at 1 year of age), maternal immunization would cost < $4,000 per DALY averted. At high infant coverage, such as Brazil in 1996 (DTP1 94%, DTP3 74% at 1 year), cost/DALY increases to $1.27 million. When the model’s time horizon was extended from 2030 to 2100, cost/DALY increased under both infant coverage levels, but more steeply with high coverage. The results were moderately sensitive to discount rate, maternal vaccine price, and maternal aP coverage and were robust using the 100 best-fitting parameter sets. Scenarios representing low-income countries showed that maternal aP immunization could be cost-saving in countries with low infant coverage, such as Nigeria, but very expensive in countries, such as Bangladesh, with high infant coverage.

Conclusion

A dynamic model, which captures the herd immunity benefits of pertussis vaccination, shows that, in low- and middle-income countries, maternal aP immunization is cost-effective when infant vaccination coverage is moderate, even cost-saving when it is low, but not cost-effective when coverage levels pass 90–95%.

Comparison of static and dynamic models of maternal immunization to prevent infant pertussis in Brazil

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Dynamic transmission models of infectious disease capture the herd immunity effects of vaccination.

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We compared dynamic and static models of maternal acellular pertussis (aP) immunization built with Brazilian data.

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At infant vaccine coverage < 90–95%, both models estimate that maternal immunization is cost-effective.

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Only the dynamic model shows that maternal immunization is not cost-effective at infant coverage > 90–95%.

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The background effect of routine infant vaccination is critical to the cost-effectiveness of maternal aP immunization.

Background

This paper compares cost-effectiveness results from two models of maternal immunization to prevent pertussis in infants in Brazil, one static, one dynamic, to explore when static models are adequate for public health decisions and when the extra effort required by dynamic models is worthwhile.

Methods

We defined two scenarios to explore key differences between static and dynamic models, herd immunity and time horizon. Scenario 1 evaluates the incremental cost/DALY of maternal acellular pertussis (aP) immunization as routine infant vaccination coverage ranges from low/moderate up to, and above, the threshold at which herd immunity begins to eliminate pertussis. Scenario 2 compares cost-effectiveness estimates over the models’ different time horizons. Maternal vaccine prices of $9.55/dose (base case) and $1/dose were evaluated.

Results

The dynamic model shows that maternal immunization could be cost-saving as well as life-saving at low levels of infant vaccination coverage. When infant coverage reaches the threshold range (90–95%), it is expensive: the dynamic model estimates that maternal immunization costs $2 million/DALY at infant coverage > 95% and maternal vaccine price of $9.55/dose; at $1/dose, cost/DALY is $200,000. By contrast, the static model estimates costs/DALY only modestly higher at high than at low infant coverage. When the models’ estimates over their different time horizons are compared at infant coverage < 90–95%, their projections fall in the same range.

Conclusions

Static models may serve to explore an intervention’s cost-effectiveness against infectious disease: the direction and principal drivers of change were the same in both models. When, however, an intervention too small to have significant herd immunity effects itself, such as maternal aP immunization, takes place against a background of vaccination in the rest of the population, a dynamic model is crucial to accurate estimates of cost-effectiveness. This finding is particularly important in the context of widely varying routine infant vaccination rates globally.

Clinical Trial registry

Clinical Trial registry name and registration number: Not applicable.

Modeling the cost-effectiveness of maternal acellular pertussis immunization (aP) in different socioeconomic settings: A dynamic transmission model of pertussis in three Brazilian states

OBJECTIVES

Using dynamic transmission models we evaluated the health and cost outcomes of adding acellular pertussis (aP) vaccination of pregnant women to infant vaccination in three Brazilian states that represent different socioeconomic conditions. The primary objective was to determine whether the same model structure could be used to represent pertussis disease dynamics in differing socioeconomic conditions.

METHODS

We tested three model structures (SIR, SIRS, SIRSIs) to represent population-level transmission in three socio-demographically distinct Brazilian states: São Paulo, Paraná and Bahia. Two strategies were evaluated: infant wP vaccination alone versus maternal aP immunization plus infant wP vaccination. Model projections for 2014-2029 include outpatient and inpatient pertussis cases, pertussis deaths, years of life lost, disability-adjusted life-years (DALYs) lost, and costs (in 2014 USD) of maternal aP vaccination, infant vaccination, and pertussis medical treatment. Incremental cost per DALY averted is presented from the perspective of the Brazilian National Health System.

RESULTS

Based on goodness-of-fit statistics, the SIRSIs model fit best, although it had only a modest improvement in statistical quantitative assessments relative to the SIRS model. For all three Brazilian states, maternal aP immunization led to higher costs but also saved infant lives and averted DALYs. The 2014 USD cost/DALY averted was $3068 in Sao Paulo, $2962 in Parana, and $2022 in Bahia. These results were robust in sensitivity analyses with the incremental cost-effectiveness ratios exceeding per capita gross regional product only when the probability that a pertussis case is reported was assumed higher than base case implying more overt cases and deaths and therefore more medical costs.

CONCLUSIONS

The same model structure fit all three states best, supporting the idea that the disease behaves similarly across different socioeconomic conditions. We also found that immunization of pregnant women with aP is cost-effective in diverse Brazilian states.

A computational framework for modeling and studying pertussis epidemiology and vaccination

BACKGROUND

Emerging and re-emerging infectious diseases such as Zika, SARS, ncovid19 and Pertussis, pose a compelling challenge for epidemiologists due to their significant impact on global public health. In this context, computational models and computer simulations are one of the available research tools that epidemiologists can exploit to better understand the spreading characteristics of these diseases and to decide on vaccination policies, human interaction controls, and other social measures to counter, mitigate or simply delay the spread of the infectious diseases. Nevertheless, the construction of mathematical models for these diseases and their solutions remain a challenging tasks due to the fact that little effort has been devoted to the definition of a general framework easily accessible even by researchers without advanced modelling and mathematical skills.

RESULTS

In this paper we describe a new general modeling framework to study epidemiological systems, whose novelties and strengths are: (1) the use of a graphical formalism to simplify the model creation phase; (2) the implementation of an R package providing a friendly interface to access the analysis techniques implemented in the framework; (3) a high level of portability and reproducibility granted by the containerization of all analysis techniques implemented in the framework; (4) a well-defined schema and related infrastructure to allow users to easily integrate their own analysis workflow in the framework. Then, the effectiveness of this framework is showed through a case of study in which we investigate the pertussis epidemiology in Italy.

CONCLUSIONS

We propose a new general modeling framework for the analysis of epidemiological systems, which exploits Petri Net graphical formalism, R environment, and Docker containerization to derive a tool easily accessible by any researcher even without advanced mathematical and computational skills. Moreover, the framework was implemented following the guidelines defined by Reproducible Bioinformatics Project so it guarantees reproducible analysis and makes simple the developed of new user-defined workflows.

The impact of past vaccination coverage and immunity on pertussis resurgence

The resurgence of pertussis over the past decades has resulted in incidence levels not witnessed in the United States since the 1950s. The underlying causes have been the subject of much speculation, with particular attention paid to the shortcomings of the latest generation of vaccines. We formulated transmission models comprising competing hypotheses regarding vaccine failure and challenged them to explain 16 years of highly resolved incidence data from Massachusetts, United States. Our results suggest that the resurgence of pertussis is a predictable consequence of incomplete historical coverage with an imperfect vaccine that confers slowly waning immunity. We found evidence that the vaccine itself is effective at reducing overall transmission, yet that routine vaccination alone would be insufficient for elimination of the disease. Our results indicated that the core transmission group is schoolchildren. Therefore, efforts aimed at curtailing transmission in the population at large, and especially in vulnerable infants, are more likely to succeed if targeted at schoolchildren, rather than adults.

Pertussis in the Association of Southeast Asian Nations: epidemiology and challenges

Pertussis is a highly infectious respiratory disease caused by Bordetella pertussis. Infants and young children are particularly at risk of severe and life-threatening disease. Infectious older individuals may transmit Bordetella pertussis to unprotected infants. Pertussis control measures have even failed in some countries with high pertussis vaccination coverage rates, leading to increased incidence rates. In 2014, this caused the World Health Organization to declare pertussis resurgent in some countries and led to recommendations regarding pertussis surveillance and national immunization programs. Despite the resurgence of pertussis, epidemiology of the disease in Southeast Asia has received little attention. In this narrative review, we describe pertussis surveillance systems, control measures, epidemiologic trends, and region-specific pertussis research in Southeast Asia. We also make recommendations for the intensification of pertussis surveillance and research in the region.

Response to Comment on "The impact of past vaccination coverage and immunity on pertussis resurgence"

We present new evidence that the immunity conferred against pertussis by the DTaP acellular vaccine wanes more slowly than widely believed.

Evidence of cryptic incidence in childhood diseases

Persistence and extinction are key processes in infectious disease dynamics that, owing to incomplete reporting, are seldom directly observable. For fully immunizing diseases, reporting probabilities can be readily estimated from demographic records and case reports. Yet reporting probabilities are not sufficient to unambiguously reconstruct disease incidence from case reports. Here, we focus on disease presence (i.e. marginal probability of non-zero incidence), which provides an upper bound on the marginal probability of disease extinction. We examine measles and pertussis in pre-vaccine era United States (US) cities, and describe a conserved scaling relationship between population size, reporting probability and observed presence (i.e. non-zero case reports). We use this relationship to estimate disease presence given perfect reporting, and define cryptic presence as the difference between estimated and observed presence. We estimate that, in early twentieth century US cities, pertussis presence was higher than measles presence across a range of population sizes, and that cryptic presence was common in small cities with imperfect reporting. While the methods employed here are specific to fully immunizing diseases, our results suggest that cryptic incidence deserves careful attention, particularly in diseases with low case counts, poor reporting and longer infectious periods.

Modeling and inference for infectious disease dynamics: a likelihood-based approach

Likelihood-based statistical inference has been considered in most scientific fields involving stochastic modeling. This includes infectious disease dynamics, where scientific understanding can help capture biological processes in so-called mechanistic models and their likelihood functions. However, when the likelihood of such mechanistic models lacks a closed-form expression, computational burdens are substantial. In this context, algorithmic advances have facilitated likelihood maximization, promoting the study of novel data-motivated mechanistic models over the last decade. Reviewing these models is the focus of this paper. In particular, we highlight statistical aspects of these models like overdispersion, which is key in the interface between nonlinear infectious disease modeling and data analysis. We also point out potential directions for further model exploration.

Morbidity and Mortality Due to Bordetella pertussis: A Significant Pathogen in West Africa?

In the absence of specific surveillance platforms for pertussis and availability of suitable diagnostics at the hospital level, reliable data that describe morbidity and mortality from pertussis are difficult to obtain in any setting, as is the case in West Africa. Here, we summarize the available evidence of the burden of pertussis in the region, given historical data, and describe recent and ongoing epidemiological studies that offer opportunities for additional data collection. The available seroepidemiological data provide evidence of ongoing circulation of Bordetella pertussis in the region. Due to the lack of systematic and targeted surveillance with laboratory confirmation of B. pertussis infection, we cannot definitively conclude that pertussis disease is well controlled in West Africa. However, based on observations by clinicians and ongoing demographic surveillance systems that capture morbidity and mortality data in general terms, currently there is no evidence that pertussis causes a significant burden of disease in young children in West Africa.

What Is Wrong with Pertussis Vaccine Immunity? The Problem of Waning Effectiveness of Pertussis Vaccines

Pertussis is resurgent in some countries, particularly those in which children receive acellular pertussis (aP) vaccines in early infancy and boosters later in life. Immunologic studies show that, whereas whole-cell pertussis (wP) vaccines orient the immune system toward Th1/Th17 responses, acellular pertussis vaccines orient toward Th1/Th2 responses. Although aP vaccines do provide protection during the first years of life, the change in T-cell priming results in waning effectiveness of aP as early as 2-3 years post-boosters. Although other factors, such as increased virulence of pertussis strains, better diagnosis, and better surveillance may play a role, the increase in pertussis appears to be the result of waning immunity. In addition, studies in baboon models, requiring confirmation in humans, show that aP is less able to prevent nasopharyngeal colonization of Bordetella pertussis than wP or natural infection.

A second-order iterated smoothing algorithm

Simulation-based inference for partially observed stochastic dynamic models is currently receiving much attention due to the fact that direct computation of the likelihood is not possible in many practical situations. Iterated filtering methodologies enable maximization of the likelihood function using simulation-based sequential Monte Carlo filters. Doucet et al. (2013) developed an approximation for the first and second derivatives of the log likelihood via simulation-based sequential Monte Carlo smoothing and proved that the approximation has some attractive theoretical properties. We investigated an iterated smoothing algorithm carrying out likelihood maximization using these derivative approximations. Further, we developed a new iterated smoothing algorithm, using a modification of these derivative estimates, for which we establish both theoretical results and effective practical performance. On benchmark computational challenges, this method beat the first-order iterated filtering algorithm. The method's performance was comparable to a recently developed iterated filtering algorithm based on an iterated Bayes map. Our iterated smoothing algorithm and its theoretical justification provide new directions for future developments in simulation-based inference for latent variable models such as partially observed Markov process models.

The relationship between mucosal immunity, nasopharyngeal carriage, asymptomatic transmission and the resurgence of Bordetella pertussis

The incidence of whooping cough in the US has been rising slowly since the 1970s, but the pace of this has accelerated sharply since acellular pertussis vaccines replaced the earlier whole cell vaccines in the late 1990s. A similar trend occurred in many other countries, including the UK, Canada, Australia, Ireland, and Spain, following the switch to acellular vaccines. The key question is why. Two leading theories (short duration of protective immunologic persistence and evolutionary shifts in the pathogen to evade the vaccine) explain some but not all of these shifts, suggesting that other factors may also be important.

In this synthesis, we argue that sterilizing mucosal immunity that blocks or abbreviates the duration of nasopharyngeal carriage of Bordetella pertussis and impedes person-to-person transmission (including between asymptomatically infected individuals) is a critical factor in this dynamic. Moreover, we argue that the ability to induce such mucosal immunity is fundamentally what distinguishes whole cell and acellular pertussis vaccines and may be pivotal to understanding much of the resurgence of this disease in many countries that adopted acellular vaccines. Additionally, we offer the hypothesis that observed herd effects generated by acellular vaccines may reflect a modification of disease presentation leading to reduced potential for transmission by those already infected, as opposed to inducing resistance to infection among those who have been exposed.

Effects of reactive social distancing on the 1918 influenza pandemic

The 1918 influenza pandemic was characterized by multiple epidemic waves. We investigated reactive social distancing, a form of behavioral response where individuals avoid potentially infectious contacts in response to available information on an ongoing epidemic or pandemic. We modelled its effects on the three influenza waves in the United Kingdom. In previous studies, human behavioral response was modelled by a Power function of the proportion of recent influenza mortality in a population, and by a Hill function, which is a function of the number of recent influenza mortality. Using a simple epidemic model with a Power function and one common set of parameters, we provided a good model fit for the observed multiple epidemic waves in London boroughs, Birmingham and Liverpool. We further applied the model parameters from these three cities to all 334 administrative units in England and Wales and including the population sizes of individual administrative units. We computed the Pearson's correlation between the observed and simulated for each administrative unit. We found a median correlation of 0.636, indicating that our model predictions are performing reasonably well. Our modelling approach is an improvement from previous studies where separate models are fitted to each city. With the reduced number of model parameters used, we achieved computational efficiency gain without over-fitting the model. We also showed the importance of reactive behavioral distancing as a potential non-pharmaceutical intervention during an influenza pandemic. Our work has both scientific and public health significance.

Monte Carlo profile confidence intervals for dynamic systems

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable. When Monte Carlo error can be made small, by sufficiently exhaustive computation, then the standard theory and practice of likelihood-based inference applies. As datasets become larger, and models more complex, situations arise where no reasonable amount of computation can render Monte Carlo error negligible. We develop profile likelihood methodology to provide frequentist inferences that take into account Monte Carlo uncertainty. We investigate the role of this methodology in facilitating inference for computationally challenging dynamic latent variable models. We present examples arising in the study of infectious disease transmission, demonstrating our methodology for inference on nonlinear dynamic models using genetic sequence data and panel time-series data. We also discuss applicability to nonlinear time-series and spatio-temporal data.

Mathematical modeling of diphtheria transmission in Thailand

In this work, a mathematical model for describing diphtheria transmission in Thailand is proposed. Based on the course of diphtheria infection, the population is divided into 8 epidemiological classes, namely, susceptible, symptomatic infectious, asymptomatic infectious, carrier with full natural-acquired immunity, carrier with partial natural-acquired immunity, individual with full vaccine-induced immunity, and individual with partial vaccine-induced immunity. Parameter values in the model were either directly obtained from the literature, estimated from available data, or estimated by means of sensitivity analysis. Numerical solutions show that our model can correctly describe the decreasing trend of diphtheria cases in Thailand during the years 1977-2014. Furthermore, despite Thailand having high DTP vaccine coverage, our model predicts that there will be diphtheria outbreaks after the year 2014 due to waning immunity. Our model also suggests that providing booster doses to some susceptible individuals and those with partial immunity every 10 years is a potential way to inhibit future diphtheria outbreaks.

Demographic transition and the dynamics of measles in six provinces in China: A modeling study

BACKGROUND

Industrialization and demographic transition generate nonstationary dynamics in human populations that can affect the transmission and persistence of infectious diseases. Decades of increasing vaccination and development have led to dramatic declines in the global burden of measles, but the virus remains persistent in much of the world. Here we show that a combination of demographic transition, as a result of declining birth rates, and reduced measles prevalence, due to improved vaccination, has shifted the age distribution of susceptibility to measles throughout China.

METHODS AND FINDINGS

We fit a novel time-varying catalytic model to three decades of age-specific measles case reporting in six provinces in China to quantify the change in the age-specific force of infection for measles virus over time. We further quantified the impact of supplemental vaccination campaigns on the reduction of susceptible individuals. The force of infection of measles has declined dramatically (90%-97% reduction in transmission rate) in three industrialized eastern provinces during the last decade, driving a concomitant increase in both the relative proportion and absolute number of adult cases, while three central and western provinces exhibited dynamics consistent with endemic persistence (24%-73% reduction in transmission rate). The reduction in susceptible individuals due to supplemental vaccination campaigns is frequently below the nominal campaign coverage, likely because campaigns necessarily vaccinate those who may already be immune. The impact of these campaigns has significantly improved over time: campaigns prior to 2005 were estimated to have achieved less than 50% reductions in the proportion susceptible in the target age classes, but campaigns from 2005 onwards reduced the susceptible proportion by 32%-87%. A limitation of this study is that it relies on case surveillance, and thus inference may be biased by age-specific variation in measles reporting.

CONCLUSIONS

The age distribution of measles cases changes in response to both demographic and vaccination processes. Combining both processes in a novel catalytic model, we illustrate that age-specific incidence patterns reveal regional differences in the progress to measles elimination and the impact of vaccination controls in China. The shift in the age distribution of measles susceptibility in response to demographic and vaccination processes emphasizes the importance of progressive control strategies and measures to evaluate program success that anticipate and react to this transition in observed incidence.

Forecasting Epidemiological Consequences of Maternal Immunization

BACKGROUND

 The increase in the incidence of whooping cough (pertussis) in many countries with high vaccination coverage is alarming. Maternal pertussis immunization has been proposed as an effective means of protecting newborns during the interval between birth and the first routine dose. However, there are concerns regarding potential interference between maternal antibodies and the immune response elicited by the routine schedule, with possible long-term population-level effects.

METHODS

 We formulated a transmission model comprising both primary routine and maternal immunization. This model was examined to evaluate the long-term epidemiological effects of routine and maternal immunization, together with consequences of potential immune interference scenarios.

RESULTS

 Overall, our model demonstrates that maternal immunization is an effective strategy in reducing the incidence of pertussis in neonates prior to the onset of the primary schedule. However, if maternal antibodies lead to blunting, incidence increases among older age groups. For instance, our model predicts that with 60% routine and maternal immunization coverage and 30% blunting, the incidence among neonates (0-2 months) is reduced by 43%. Under the same scenario, we observe a 20% increase in incidence among children aged 5-10 years. However, the downstream increase in the older age groups occurs with a delay of approximately a decade or more.

CONCLUSIONS

 Maternal immunization has clear positive effects on infant burden of disease, lowering mean infant incidence. However, if maternally derived antibodies adversely affect the immunogenicity of the routine schedule, we predict eventual population-level repercussions that may lead to an overall increase in incidence in older age groups.

The pertussis enigma: reconciling epidemiology, immunology and evolution

Pertussis, a highly contagious respiratory infection, remains a public health priority despite the availability of vaccines for 70 years. Still a leading cause of mortality in developing countries, pertussis has re-emerged in several developed countries with high vaccination coverage. Resurgence of pertussis in these countries has routinely been attributed to increased awareness of the disease, imperfect vaccinal protection or high infection rates in adults. In this review, we first present 1980-2012 incidence data from 63 countries and show that pertussis resurgence is not universal. We further argue that the large geographical variation in trends probably precludes a simple explanation, such as the transition from whole-cell to acellular pertussis vaccines. Reviewing available evidence, we then propose that prevailing views on pertussis epidemiology are inconsistent with both historical and contemporary data. Indeed, we summarize epidemiological evidence showing that natural infection and vaccination both appear to provide long-term protection against transmission and disease, so that previously infected or vaccinated adults contribute little to overall transmission at a population level. Finally, we identify several promising avenues that may lead to a consistent explanation of global pertussis epidemiology and to more effective control strategies.

Using age-stratified incidence data to examine the transmission consequences of pertussis vaccination

Pertussis is a highly infectious respiratory disease that has been on the rise in many countries worldwide over the past several years. The drivers of this increase in pertussis incidence remain hotly debated, with a central and long-standing hypothesis that questions the ability of vaccines to eliminate pertussis transmission rather than simply modulate the severity of disease. In this paper, we present age-structured case notification data from all provinces of Thailand between 1981 and 2014, a period during which vaccine uptake rose substantially, permitting an evaluation of the transmission impacts of vaccination. Our analyses demonstrate decreases in incidence across all ages with increased vaccine uptake - an observation that is at odds with pertussis case notification data in a number of other countries. To explore whether these observations are consistent with a rise in herd immunity and a reduction in bacterial transmission, we analyze an age-structured model that incorporates contrasting hypotheses concerning the immunological and transmission consequences of vaccines. Our results lead us to conclude that the most parsimonious explanation for the combined reduction in incidence and the shift to older age groups in the Thailand data is vaccine-induced herd immunity.

Pertussis immunity and epidemiology: mode and duration of vaccine-induced immunity

The resurgence of pertussis in some countries that maintain high vaccination coverage has drawn attention to gaps in our understanding of the epidemiological effects of pertussis vaccines. In particular, major questions surround the nature, degree and durability of vaccine protection. To address these questions, we used mechanistic transmission models to examine regional time series incidence data from Italy in the period immediately following the introduction of acellular pertussis (aP) vaccine. Our results concur with recent animal-challenge experiments wherein infections in aP-vaccinated individuals proved as transmissible as those in naive individuals but much less symptomatic. On the other hand, the data provide evidence for vaccine-driven reduction in susceptibility, which we quantify via a synthetic measure of vaccine impact. As to the precise nature of vaccine failure, the data do not allow us to distinguish between leakiness and waning of vaccine immunity, or some combination of these. Across the range of well-supported models, the nature and duration of vaccine protection, the age profile of incidence and the range of projected epidemiological futures differ substantially, underscoring the importance of the remaining unknowns. We identify key data gaps: sources of data that can supply the information needed to eliminate these remaining uncertainties.

Pertussis models to inform vaccine policy

Pertussis remains a challenging public health problem with many aspects of infection, disease and immunity poorly understood. Initially controlled by mass vaccination, pertussis resurgence has occurred in some countries with well-established vaccination programs, particularly among adolescents and young adults. Several studies have used mathematical models to investigate drivers of pertussis epidemiology and predict the likely impact of different vaccination strategies. We reviewed a number of these models to evaluate their suitability to answer questions of public health importance regarding optimal vaccine scheduling. We critically discuss the approaches adopted and the impact of chosen model structures and assumptions on study conclusions. Common limitations were a lack of contemporary, population relevant data for parameterization and a limited understanding of the relationship between infection and disease. We make recommendations for future model development and suggest epidemiologic data collections that would facilitate efforts to reduce uncertainty and improve the robustness of model-derived conclusions.

Pertussis Across the Globe: Recent Epidemiologic Trends From 2000 to 2013

Pertussis has reemerged as a problem across the world. To better understand the nature of the resurgence, we reviewed recent epidemiologic data and we report disease trends from across the world. Published epidemiologic data from January 2000 to July 2013 were obtained via PubMed searches and open-access websites. Data on vaccine coverage and reported pertussis cases from 2000 through 2012 from the 6 World Health Organization regions were also reviewed. Findings are confounded not only by the lack of systematic and comparable observations in many areas of the world but also by the cyclic nature of pertussis with peaks occurring every 3-5 years. It appears that pertussis incidence has increased in school-age children in North America and western Europe, where acellular pertussis vaccines are used, but an increase has also occurred in some countries that use whole-cell vaccines. Worldwide, pertussis remains a serious health concern, especially for infants, who bear the greatest disease burden. Factors that may contribute to the resurgence include lack of booster immunizations, low vaccine coverage, improved diagnostic methods, and genetic changes in the organism. To better understand the epidemiology of pertussis and optimize disease control, it is important to improve surveillance worldwide, irrespective of pertussis vaccine types and schedules used in each country.

Conserved patterns of incomplete reporting in pre-vaccine era childhood diseases

Incomplete observation is an important yet often neglected feature of observational ecological timeseries. In particular, observational case report timeseries of childhood diseases have played an important role in the formulation of mechanistic dynamical models of populations and metapopulations. Yet to our knowledge, no comprehensive study of childhood disease reporting probabilities (commonly referred to as reporting rates) has been conducted to date. Here, we provide a detailed analysis of measles and whooping cough reporting probabilities in pre-vaccine United States cities and states, as well as measles in cities of England and Wales. Overall, we find the variability between locations and diseases greatly exceeds that between methods or time periods. We demonstrate a strong relationship within location between diseases and within disease between geographical areas. In addition, we find that demographic covariates such as ethnic composition and school attendance explain a non-trivial proportion of reporting probability variation. Overall, our findings show that disease reporting is both variable and non-random and that completeness of reporting is influenced by disease identity, geography and socioeconomic factors. We suggest that variations in incomplete observation can be accounted for and that doing so can reveal ecologically important features that are otherwise obscured.

Combating pertussis resurgence: One booster vaccination schedule does not fit all

Pertussis has reemerged as a major public health concern in many countries where it was once considered well controlled. Although the mechanisms responsible for continued pertussis circulation and resurgence remain elusive and contentious, many countries have nevertheless recommended booster vaccinations, the timing and number of which vary widely. Here, using a stochastic, age-stratified transmission model, we searched for cost-effective booster vaccination strategies using a genetic algorithm. We did so assuming four hypothesized mechanisms underpinning contemporary pertussis epidemiology: (I) insufficient coverage, (II) frequent primary vaccine failure, (III) waning of vaccine-derived protection, and (IV) vaccine "leakiness." For scenarios I-IV, successful booster strategies were identified and varied considerably by mechanism. Especially notable is the inability of booster schedules to alleviate resurgence when vaccines are leaky. Critically, our findings argue that the ultimate effectiveness of vaccine booster schedules will likely depend on correctly pinpointing the causes of resurgence, with misdiagnosis of the problem epidemiologically ineffective and economically costly.

Inference for dynamic and latent variable models via iterated, perturbed Bayes maps

Iterated filtering algorithms are stochastic optimization procedures for latent variable models that recursively combine parameter perturbations with latent variable reconstruction. Previously, theoretical support for these algorithms has been based on the use of conditional moments of perturbed parameters to approximate derivatives of the log likelihood function. Here, a theoretical approach is introduced based on the convergence of an iterated Bayes map. An algorithm supported by this theory displays substantial numerical improvement on the computational challenge of inferring parameters of a partially observed Markov process.

EPIDEMIOLOGICAL CONSEQUENCES OF IMPERFECT VACCINES FOR IMMUNIZING INFECTIONS

The control of some childhood diseases has proven to be difficult even in countries that maintain high vaccination coverage. This may be due to the use of imperfect vaccines and there has been much discussion on the different modes by which vaccines might fail. To understand the epidemiological implications of some of these different modes, we performed a systematic analysis of a model based on the standard SIR equations with a vaccinated component that permits vaccine failure in degree ("leakiness"), take ("all-or-nothingness") and duration (waning of vaccine-derived immunity). The model was first considered as a system of ordinary differential equations, then extended to a system of partial differential equations to accommodate age structure. We derived analytic expressions for the steady states of the system and the final age distributions in the case of homogenous contact rates. The stability of these equilibria are determined by a threshold parameter R_p , a function of the vaccine failure parameters and the coverage p. The value of p for which R_p = 1 yields the critical vaccination ratio, a measure of herd immunity. Using this concept we can compare vaccines that confer the same level of herd immunity to the population but may fail at the individual level in different ways. For any fixed R_p > 1, the leaky model results in the highest prevalence of infection, while the all-or-nothing and waning models have the same steady state prevalence. The actual composition of a vaccine cannot be determined on the basis of steady state levels alone, however the distinctions can be made by looking at transient dynamics (such as after the onset of vaccination), the mean age of infection, the age distributions at steady state of the infected class, and the effect of age-specific contact rates.

Estimation of the underlying burden of pertussis in adolescents and adults in Southern Ontario, Canada

Despite highly successful vaccination programs and high vaccine uptake, both endemic pertussis and periodic pertussis outbreaks continue to occur. The under-recognized role of adolescents and adults in disease transmission, due to waning immunity following natural infection and vaccination, and reduced likelihood of correct diagnosis, may contribute to pertussis persistence. We constructed a mathematical model to describe the transmission of pertussis in Southern Ontario in both pre-vaccine and vaccine eras, to estimate the underlying burden of pertussis in the population. The model was well calibrated using the best available data on pertussis in the pre-vaccination (1880–1929) and vaccination (1993–2004) eras in Ontario. Pertussis under-reporting by age group was estimated by comparing model-projected incidence to reported laboratory-confirmed cases for Greater Toronto. Best-fit model estimates gave a basic reproductive number of approximately 10.6, (seasonal range 9.9 to 11.5). Under-reporting increased with age, and approximately >95% of infections in children were caused by infections in persons with waning immunity to pertussis following prior infection or vaccination. A well-calibrated model suggests that under-recognized cases of pertussis in older individuals are likely to be an important driver of ongoing pertussis outbreaks in children. Model projections strongly support enhancement of booster vaccination efforts in adults.