Immune boosting explains regime-shifts in prevaccine-era pertussis dynamics

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.

An immuno-epidemiological model for transient immune protection: A case study for viral respiratory infections

The dynamics of infectious disease in a population critically involves both within-host pathogen replication and between host pathogen transmission. While modeling efforts have recently explored how within-host dynamics contribute to shaping population transmission, fewer have explored how ongoing circulation of an epidemic infectious disease can impact within-host immunological dynamics. We present a simple, influenza-inspired model that explores the potential for re-exposure during a single, ongoing outbreak to shape individual immune response and epidemiological potential in non-trivial ways. We show how even a simplified system can exhibit complex ongoing dynamics and sensitive thresholds in behavior. We also find epidemiological stochasticity likely plays a critical role in reinfection or in the maintenance of individual immunological protection over time.

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.

Fluctuation theory of immune response: A statistical mechanical approach to understand pathogen induced T-cell population dynamics

In this period of intense interest in human immunity, we attempt here to quantify the immune response against pathogen invasion through T-cell population dynamics. Borrowing concepts from equilibrium statistical mechanics, we introduce a new description of the immune response function (IMRF) in terms of fluctuations in the population number of relevant biological cells (effector and regulatory T-cells). We use a coarse-grained chemical reaction network model (CG-CRNM) to calculate the number fluctuations and show that the response function derived as such can, indeed, capture the crossover observed in a T-cell driven immune response. We employ the network model to learn the effect of vitamin-D as an immunomodulator. We solve our CG-CRNM using a stochastic Gillespie algorithm. Depending on the effector T-cell concentration, we can classify immune regulation regimes into three categories: weak, strong, and moderate. The IMRF is found to behave differently in these three regimes. A damped cross-regulatory behavior found in the dynamics of effector and regulatory T-cell concentration in the diseased states correlates well with the same found in a cohort of patients with specific malignancies and autoimmune diseases. Importantly, the crossover from the weakly regulated steady state to the other (the strongly regulated) is accompanied by a divergence-like growth in the fluctuation of both the effector and the regulatory T-cell concentration, characteristic of a dynamic phase transition. We believe such steady-state IMRF analyses could help not only to phase-separate different immune stages but also aid in the valuable connection between autoimmunity, optimal vitamin-D, and consequences of immunosuppressive stress and malignancy.

Waning immunity and re-emergence of measles and mumps in the vaccine era

Vaccine-preventable diseases (VPD) including measles and mumps have been re-emerging in countries with sustained high vaccine coverage. For mumps, waning immunity has been recognized as a major contributor to recent outbreaks. Although unvaccinated individuals account for most cases in recent measles outbreaks, the role of immune waning remains unclear. Accumulating serological and epidemiological evidence suggests that natural immunity induced by infection may be more durable compared to vaccine-induced immunity. As the proportion of population immunity via vaccination gradually increases and boosting through natural exposures becomes rare, risk of outbreaks may increase. Mechanistic insights into the coupled immuno-epidemiological dynamics of waning and boosting will be important to understand optimal vaccination strategies to combat VPD re-emergence and achieve eradication.

Critical transitions in malaria transmission models are consistently generated by superinfection

The history of modelling vector-borne infections essentially begins with the papers by Ross on malaria. His models assume that the dynamics of malaria can most simply be characterized by two equations that describe the prevalence of malaria in the human and mosquito hosts. This structure has formed the central core of models for malaria and most other vector-borne diseases for the past century, with additions acknowledging important aetiological details. We partially add to this tradition by describing a malaria model that provides for vital dynamics in the vector and the possibility of super-infection in the human host: reinfection of asymptomatic hosts before they have cleared a prior infection. These key features of malaria aetiology create the potential for break points in the prevalence of infected hosts, sudden transitions that seem to characterize malaria's response to control in different locations. We show that this potential for critical transitions is a general and underappreciated feature of any model for vector-borne diseases with incomplete immunity, including the canonical Ross-McDonald model. Ignoring these details of the host's immune response to infection can potentially lead to serious misunderstanding in the interpretation of malaria distribution patterns and the design of control schemes for other vector-borne diseases. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

The Challenge of Quantifying Synchrony in Malaria Parasites

Malaria infection is often accompanied by periodic fevers, triggered by synchronous cycles of parasite replication within the host. The degree of synchrony in parasite development influences the efficacy of drugs and immune defenses and is therefore relevant to host health and infectiousness. Synchrony is thought to vary over the course of infection and across different host-parasite genotype or species combinations, but the evolutionary significance - if any - of this diversity remains elusive. Standardized methods are lacking, but the most common metric for quantifying synchrony is the percentage of parasites in a particular developmental stage. We use a heuristic model to show that this metric is often unacceptably biased. Methodological challenges must be addressed to characterize diverse patterns of synchrony and their consequences for disease severity and spread.

Humanised monoclonal antibodies neutralise pertussis toxin by receptor blockade and reduced retrograde trafficking

Pertussis toxin (PTx) is a major protective antigen produced by Bordetella pertussis that is included in all current acellular vaccines. Of several well‐characterized monoclonal antibodies binding this toxin, the humanised hu1B7 and hu11E6 antibodies are highly protective in multiple in vitro and in vivo assays. In this study, we determine the molecular mechanisms of protection mediated by these antibodies. Neither antibody directly binds the B. pertussis bacterium nor supports antibody‐dependent complement cytotoxicity. Both antibodies, either individually or as a cocktail, form multivalent complexes with soluble PTx that bind the FcγRIIb receptor more tightly than antibody alone, suggesting that the antibodies may accelerate PTx clearance via immune complex formation. However, a receptor binding assay and cellular imaging indicate that the main mechanism used by hu11E6 is competitive inhibition of PTx binding to its cellular receptor. In contrast, the main hu1B7 neutralising mechanism appears to be inhibition of PTx internalisation and retrograde trafficking. We assessed the effects of hu1B7 on PTx retrograde trafficking in CHO‐K1 cells using quantitative immunofluorescence microscopy. In the absence of hu1B7 or after incubation with an isotype control antibody, PTx colocalizes to organelles in a manner consistent with retrograde transport. However, after preincubation with hu1B7, PTx appears restricted to the membrane surface with colocalization to organelles associated with retrograde transport significantly reduced. Together, these data support a model whereby hu11E6 and hu1B7 interfere with PTx receptor binding and PTx retrograde trafficking, respectively.

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.

Species interactions may help explain the erratic periodicity of whooping cough dynamics

Incidence of whooping cough exhibits variable dynamics across time and space. The periodicity of this disease varies from annual to five years in different geographic regions in both developing and developed countries. Many hypotheses have been put forward to explain this variability such as nonlinearity and seasonality, stochasticity, variable recruitment of susceptible individuals via birth, immunization, and immune boosting. We propose an alternative hypothesis to describe the variability in periodicity - the intricate dynamical variability of whooping cough may arise from interactions between its dominant etiological agents of Bordetella pertussis and Bordetella parapertussis. We develop a two-species age-structured model, where two pathogens are allowed to interact by age-dependent convalescence of individuals with severe illness from infections. With moderate strength of interactions, the model exhibits multi-annual coexisting attractors that depend on the R₀ of the two pathogens. We also examine how perturbation from case importation and noise in transmission may push the system from one dynamical regime to another. The coexistence of multi-annual cycles and the behavior of switching between attractors suggest that variable dynamics of whopping cough could be an emergent property of its multi-agent etiology.

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.

Limits to Causal Inference with State-Space Reconstruction for Infectious Disease

Infectious diseases are notorious for their complex dynamics, which make it difficult to fit models to test hypotheses. Methods based on state-space reconstruction have been proposed to infer causal interactions in noisy, nonlinear dynamical systems. These “model-free” methods are collectively known as convergent cross-mapping (CCM). Although CCM has theoretical support, natural systems routinely violate its assumptions. To identify the practical limits of causal inference under CCM, we simulated the dynamics of two pathogen strains with varying interaction strengths. The original method of CCM is extremely sensitive to periodic fluctuations, inferring interactions between independent strains that oscillate with similar frequencies. This sensitivity vanishes with alternative criteria for inferring causality. However, CCM remains sensitive to high levels of process noise and changes to the deterministic attractor. This sensitivity is problematic because it remains challenging to gauge noise and dynamical changes in natural systems, including the quality of reconstructed attractors that underlie cross-mapping. We illustrate these challenges by analyzing time series of reportable childhood infections in New York City and Chicago during the pre-vaccine era. We comment on the statistical and conceptual challenges that currently limit the use of state-space reconstruction in causal inference.

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.

Old Disease and New Challenges: Major Obstacles of Current Strategies in the Prevention of Pertussis

Context

Universal immunization against Bordetella pertussis has partially controlled the burden of the disease and its transmission. However, according to recent data, the epidemiology of this vaccine-preventable disease has changed. Now, younger infants, adolescents, and adults are at greater risk of infection. This article has studied the interaction between the various factors involved in the changing epidemiology of pertussis and the major obstacles faced by the current strategies in its prevention.

Evidence Acquisition

In this narrative review, the most recently published sources of information on pertussis control measures, consisting of textbooks and articles, have been reviewed. We focused on the more recent data about the changing epidemiology or pertussis in Scopus through the use of the MeSH-term words [pertussis] or [whooping cough] and [epidemiology] or [outbreak] or [resurgence], but our search was not restricted to this particular strategy; we also tried to find all of the most recent available data in the general field through other means.

Results

Primary and booster doses of the pertussis vaccine seem to partially control transmission of the disease, but despite the different preventive strategies available, pertussis continues to cause mortality and morbidity among high-risk groups.

Conclusions

Adding booster doses of acellular pertussis vaccine to the current national immunization practices with whole-cell vaccines for young adults and pregnant women seems to be a good option for controlling mortality and morbidity among high-risk groups such as very young infants.

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.

Persistent Chaos of Measles Epidemics in the Prevaccination United States Caused by a Small Change in Seasonal Transmission Patterns

Epidemics of infectious diseases often occur in predictable limit cycles. Theory suggests these cycles can be disrupted by high amplitude seasonal fluctuations in transmission rates, resulting in deterministic chaos. However, persistent deterministic chaos has never been observed, in part because sufficiently large oscillations in transmission rates are uncommon. Where they do occur, the resulting deep epidemic troughs break the chain of transmission, leading to epidemic extinction, even in large cities. Here we demonstrate a new path to locally persistent chaotic epidemics via subtle shifts in seasonal patterns of transmission, rather than through high-amplitude fluctuations in transmission rates. We base our analysis on a comparison of measles incidence in 80 major cities in the prevaccination era United States and United Kingdom. Unlike the regular limit cycles seen in the UK, measles cycles in US cities consistently exhibit spontaneous shifts in epidemic periodicity resulting in chaotic patterns. We show that these patterns were driven by small systematic differences between countries in the duration of the summer period of low transmission. This example demonstrates empirically that small perturbations in disease transmission patterns can fundamentally alter the regularity and spatiotemporal coherence of epidemics.

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.

Defining long-term drivers of pertussis resurgence, and optimal vaccine control strategies

Pertussis resurgence has been reported from several developed countries with long-standing immunisation programs. Among these, Australia in 2003 discontinued an 18 months (fourth) booster dose in favour of an adolescent (fifth) dose. We developed a model to evaluate determinants of resurgence in Australia and alternative vaccine strategies for mitigation. Novel characteristics of our model included the use of seroepidemiologic data for calibration, and broad investigation of variables relevant to transmission of, and protection against, pertussis. We simulated multiple parameter combinations, retaining those consistent with observed data for subsequent use in predictive models comparing alternative vaccination schedules. Reproducing the early control of pertussis followed by late resurgence observed in Australia required natural immunity to last decades longer than vaccine-acquired immunity, with mean duration exceeding 50 years in almost 90% of simulations. Replacement of the dose at 18 months with an adolescent dose in 2003 resulted in a 40% increase in infections in the age group 18-47 months by 2013. A six dose strategy (2, 4, 6, 18 months, 4 and 15 years) yielded a reduction in infection incidence (pre-school 43%, infants 8%) greater than any alternative strategies considered for timing of five administered doses. Our finding that natural immunity drives long-term trends in pertussis cycles is relevant to a range of pertussis strategies and provides the necessary context in which to consider maternal vaccination. Comparatively short-lived vaccine-acquired immunity requires multiple boosters over the first two decades of life to maximise reduction in infections.

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.

Dynamical crises, multistability and the influence of the duration of immunity in a seasonally-forced model of disease transmission

BACKGROUND

Highly successful strategies to make populations more resilient to infectious diseases, such as childhood vaccinations programs, may nonetheless lead to unpredictable outcomes due to the interplay between seasonal variations in transmission and a population's immune status.

METHODS

Motivated by the study of diseases such as pertussis we introduce a seasonally-forced susceptible-infectious-recovered model of disease transmission with waning and boosting of immunity. We study the system's dynamical properties using a combination of numerical simulations and bifurcation techniques, paying particular attention to the properties of the initial condition space.

RESULTS

We find that highly unpredictable behaviour can be triggered by changes in biologically relevant model parameters such as the duration of immunity. In the particular system we analyse--used in the literature to study pertussis dynamics--we identify the presence of an initial-condition landscape containing three coexisting attractors. The system's response to interventions which perturb population immunity (e.g. vaccination "catch-up" campaigns) is therefore difficult to predict.

CONCLUSION

Given the increasing use of models to inform policy decisions regarding vaccine introduction and scheduling and infectious diseases intervention policy more generally, our findings highlight the importance of thoroughly investigating the dynamical properties of those models to identify key areas of uncertainty. Our findings suggest that the often stated tension between capturing biological complexity and utilising mathematically simple models is perhaps more nuanced than generally suggested. Simple dynamical models, particularly those which include forcing terms, can give rise to incredibly complex behaviour.

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.