Resolving the impact of waiting time distributions on the persistence of measles

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.

Transmission models indicate Ebola virus persistence in non-human primate populations is unlikely

Infectious diseases that kill their hosts may persist locally only if transmission is appropriately balanced by susceptible recruitment. Great apes die of Ebola virus disease (EVD) and have transmitted ebolaviruses to people. However, understanding the role that apes and other non-human primates play in maintaining ebolaviruses in Nature is hampered by a lack of data. Recent serological findings suggest that few non-human primates have antibodies to EVD-causing viruses throughout tropical Africa, suggesting low transmission rates and/or high EVD mortality (Ayouba A et al. 2019 J. Infect. Dis. 220, 1599-1608 (doi:10.1093/infdis/jiz006); Mombo IM et al. 2020 Viruses 12, 1347 (doi:10.3390/v12121347)). Here, stochastic transmission models of EVD in non-human primates assuming high case-fatality probabilities and experimentally observed or field-observed parameters did not allow viral persistence, suggesting that non-human primate populations are highly unlikely to sustain EVD-causing infection for prolonged periods. Repeated introductions led to declining population sizes, similar to field observations of apes, but not viral persistence.

A new formulation of compartmental epidemic modelling for arbitrary distributions of incubation and removal times

The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are more flexible, yet do not allow for arbitrary distributions. We present a new formulation, focussing on the SEIR concept that allows to include general distributions of incubation and removal times. We compare the solution to two types of agent-based model simulations, a spatially homogeneous one where infection occurs by proximity, and a model on a scale-free network with varying clustering properties, where the infection between any two agents occurs via their link if it exists. We find good agreement in both cases. Furthermore a family of asymptotic solutions of the equations is found in terms of a logistic curve, which after a non-universal time shift, fits extremely well all the microdynamical simulations. The formulation allows for a simple numerical approach; software in Julia and Python is provided.

Assessing the potential impact of transmission during prolonged viral shedding on the effect of lockdown relaxation on COVID-19

A key parameter in epidemiological modeling which characterizes the spread of an infectious disease is the generation time, or more generally the distribution of infectiousness as a function of time since infection. There is increasing evidence supporting a prolonged viral shedding window for COVID-19, but the transmissibility in this phase is unclear. Based on this, we develop a generalized Susceptible-Exposed-Infected-Resistant (SEIR) model including an additional compartment of chronically infected individuals who can stay infectious for a longer duration than the reported generation time, but with infectivity reduced to varying degrees. Using the incidence and fatality data from different countries, we first show that such an assumption also yields a plausible model in explaining the data observed prior to the easing of the lockdown measures (relaxation). We then test the predictive power of this model for different durations and levels of prolonged infectiousness using the incidence data after the introduction of relaxation in Switzerland, and compare it with a model without the chronically infected population to represent the models conventionally used. We show that in case of a gradual easing on the lockdown measures, the predictions of the model including the chronically infected population vary considerably from those obtained under a model in which prolonged infectiousness is not taken into account. Although the existence of a chronically infected population still remains largely hypothetical, we believe that our results provide tentative evidence to consider a chronically infected population as an alternative modeling approach to better interpret the transmission dynamics of COVID-19.

Disease control across urban-rural gradients

Controlling the regional re-emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) after its initial spread in ever-changing personal contact networks and disease landscapes is a challenging task. In a landscape context, contact opportunities within and between populations are changing rapidly as lockdown measures are relaxed and a number of social activities re-activated. Using an individual-based metapopulation model, we explored the efficacy of different control strategies across an urban-rural gradient in Wales, UK. Our model shows that isolation of symptomatic cases or regional lockdowns in response to local outbreaks have limited efficacy unless the overall transmission rate is kept persistently low. Additional isolation of non-symptomatic infected individuals, who may be detected by effective test-and-trace strategies, is pivotal to reducing the overall epidemic size over a wider range of transmission scenarios. We define an 'urban-rural gradient in epidemic size' as a correlation between regional epidemic size and connectivity within the region, with more highly connected urban populations experiencing relatively larger outbreaks. For interventions focused on regional lockdowns, the strength of such gradients in epidemic size increased with higher travel frequencies, indicating a reduced efficacy of the control measure in the urban regions under these conditions. When both non-symptomatic and symptomatic individuals are isolated or regional lockdown strategies are enforced, we further found the strongest urban-rural epidemic gradients at high transmission rates. This effect was reversed for strategies targeted at symptomatic individuals only. Our results emphasize the importance of test-and-trace strategies and maintaining low transmission rates for efficiently controlling SARS-CoV-2 spread, both at landscape scale and in urban areas.

Estimating epidemic coupling between populations from the time to invasion

Identifying the mechanisms by which diseases spread among populations is important for understanding and forecasting patterns of epidemics and pandemics. Estimating transmission coupling among populations is challenging because transmission events are difficult to observe in practice, and connectivity among populations is often obscured by local disease dynamics. We consider the common situation in which an epidemic is seeded in one population and later spreads to a second population. We present a method for estimating transmission coupling between the two populations, assuming they can be modelled as susceptible-infected-removed (SIR) systems. We show that the strength of coupling between the two populations can be estimated from the time taken for the disease to invade the second population. Confidence in the estimate is low if only a single invasion event has been observed, but is substantially improved if numerous independent invasion events are observed. Our analysis of this simplest, idealized scenario represents a first step toward developing and verifying methods for estimating epidemic coupling among populations in an ever-more-connected global human population.

Beyond the SNP Threshold: Identifying Outbreak Clusters Using Inferred Transmissions

Whole-genome sequencing (WGS) is increasingly used to aid the understanding of pathogen transmission. A first step in analyzing WGS data is usually to define "transmission clusters," sets of cases that are potentially linked by direct transmission. This is often done by including two cases in the same cluster if they are separated by fewer single-nucleotide polymorphisms (SNPs) than a specified threshold. However, there is little agreement as to what an appropriate threshold should be. We propose a probabilistic alternative, suggesting that the key inferential target for transmission clusters is the number of transmissions separating cases. We characterize this by combining the number of SNP differences and the length of time over which those differences have accumulated, using information about case timing, molecular clock, and transmission processes. Our framework has the advantage of allowing for variable mutation rates across the genome and can incorporate other epidemiological data. We use two tuberculosis studies to illustrate the impact of our approach: with British Columbia data by using spatial divisions; with Republic of Moldova data by incorporating antibiotic resistance. Simulation results indicate that our transmission-based method is better in identifying direct transmissions than a SNP threshold, with dissimilarity between clusterings of on average 0.27 bits compared with 0.37 bits for the SNP-threshold method and 0.84 bits for randomly permuted data. These results show that it is likely to outperform the SNP-threshold method where clock rates are variable and sample collection times are spread out. We implement the method in the R package transcluster.

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.

Comparative epidemiology of poliovirus transmission

Understanding the determinants of polio transmission and its large-scale epidemiology remains a public health priority. Despite a 99% reduction in annual wild poliovirus (WPV) cases since 1988, tackling the last 1% has proven difficult. We identified key covariates of geographical variation in polio transmission patterns by relating country-specific annual disease incidence to demographic, socio-economic and environmental factors. We assessed the relative contributions of these variables to the performance of computer-generated models for predicting polio transmission. We also examined the effect of spatial coupling on the polio extinction frequency in islands relative to larger land masses. Access to sanitation, population density, forest cover and routine vaccination coverage were the strongest predictors of polio incidence, however their relative effect sizes were inconsistent geographically. The effect of climate variables on polio incidence was negligible, indicating that a climate effect is not identifiable at the annual scale, suggesting a role for climate in shaping the transmission seasonality rather than intensity. We found polio fadeout frequency to depend on both population size and demography, which should therefore be considered in policies aimed at extinction. Our comparative epidemiological approach highlights the heterogeneity among polio transmission determinants. Recognition of this variation is important for the maintenance of population immunity in a post-polio era.

High turnover drives prolonged persistence of influenza in managed pig herds

Pigs have long been hypothesized to play a central role in the emergence of novel human influenza A virus (IAV) strains, by serving as mixing vessels for mammalian and avian variants. However, the key issue of viral persistence in swine populations at different scales is ill understood. We address this gap using epidemiological models calibrated against seroprevalence data from Dutch finishing pigs to estimate the ‘critical herd size’ (CHS) for IAV persistence. We then examine the viral phylogenetic evidence for persistence by comparing human and swine IAV. Models suggest a CHS of approximately 3000 pigs above which influenza was likely to persist, i.e. orders of magnitude lower than persistence thresholds for IAV and other acute viruses in humans. At national and regional scales, we found much stronger empirical signatures of prolonged persistence of IAV in swine compared with human populations. These striking levels of persistence in small populations are driven by the high recruitment rate of susceptible piglets, and have significant implications for management of swine and for overall patterns of genetic diversity of IAV.

Detecting signals of chronic shedding to explain pathogen persistence: Leptospira interrogans in California sea lions

Identifying mechanisms driving pathogen persistence is a vital component of wildlife disease ecology and control. Asymptomatic, chronically infected individuals are an oft‐cited potential reservoir of infection, but demonstrations of the importance of chronic shedding to pathogen persistence at the population‐level remain scarce.

Studying chronic shedding using commonly collected disease data is hampered by numerous challenges, including short‐term surveillance that focuses on single epidemics and acutely ill individuals, the subtle dynamical influence of chronic shedding relative to more obvious epidemic drivers, and poor ability to differentiate between the effects of population prevalence of chronic shedding vs. intensity and duration of chronic shedding in individuals.

We use chronic shedding of Leptospira interrogans serovar Pomona in California sea lions (Zalophus californianus) as a case study to illustrate how these challenges can be addressed. Using leptospirosis‐induced strands as a measure of disease incidence, we fit models with and without chronic shedding, and with different seasonal drivers, to determine the time‐scale over which chronic shedding is detectable and the interactions between chronic shedding and seasonal drivers needed to explain persistence and outbreak patterns.

Chronic shedding can enable persistence of L. interrogans within the sea lion population. However, the importance of chronic shedding was only apparent when surveillance data included at least two outbreaks and the intervening inter‐epidemic trough during which fadeout of transmission was most likely. Seasonal transmission, as opposed to seasonal recruitment of susceptibles, was the dominant driver of seasonality in this system, and both seasonal factors had limited impact on long‐term pathogen persistence.

We show that the temporal extent of surveillance data can have a dramatic impact on inferences about population processes, where the failure to identify both short‐ and long‐term ecological drivers can have cascading impacts on understanding higher order ecological phenomena, such as pathogen persistence.

A 'post-honeymoon' measles epidemic in Burundi: mathematical model-based analysis and implications for vaccination timing

Using a mathematical model with realistic demography, we analyze a large outbreak of measles in Muyinga sector in rural Burundi in 1988–1989. We generate simulated epidemic curves and age × time epidemic surfaces, which we qualitatively and quantitatively compare with the data. Our findings suggest that supplementary immunization activities (SIAs) should be used in places where routine vaccination cannot keep up with the increasing numbers of susceptible individuals resulting from population growth or from logistical problems such as cold chain maintenance. We use the model to characterize the relationship between SIA frequency and SIA age range necessary to suppress measles outbreaks. If SIAs are less frequent, they must expand their target age range.

Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis

The devastation caused by periodic measles outbreaks motivated efforts over more than a century to mathematically model measles disease and transmission. Following the identification of rubella, which similarly presents with fever and rash and causes congenital rubella syndrome (CRS) in infants born to women first infected with rubella early in pregnancy, modelers also began to characterize rubella disease and transmission. Despite the relatively large literature, no comprehensive review to date provides an overview of dynamic transmission models for measles and rubella developed to support risk and policy analysis. This systematic review of the literature identifies quantitative measles and/or rubella dynamic transmission models and characterizes key insights relevant for prospective modeling efforts. Overall, measles and rubella represent some of the relatively simplest viruses to model due to their ability to impact only humans and the apparent life-long immunity that follows survival of infection and/or protection by vaccination, although complexities arise due to maternal antibodies and heterogeneity in mixing and some models considered potential waning immunity and reinfection. This review finds significant underreporting of measles and rubella infections and widespread recognition of the importance of achieving and maintaining high population immunity to stop and prevent measles and rubella transmission. The significantly lower transmissibility of rubella compared to measles implies that all countries could eliminate rubella and CRS by using combination of measles- and rubella-containing vaccines (MRCVs) as they strive to meet regional measles elimination goals, which leads to the recommendation of changing the formulation of national measles-containing vaccines from measles only to MRCV as the standard of care.

Effects of memory on the shapes of simple outbreak trees

Genomic tools, including phylogenetic trees derived from sequence data, are increasingly used to understand outbreaks of infectious diseases. One challenge is to link phylogenetic trees to patterns of transmission. Particularly in bacteria that cause chronic infections, this inference is affected by variable infectious periods and infectivity over time. It is known that non-exponential infectious periods can have substantial effects on pathogens’ transmission dynamics. Here we ask how this non-Markovian nature of an outbreak process affects the branching trees describing that process, with particular focus on tree shapes. We simulate Crump-Mode-Jagers branching processes and compare different patterns of infectivity over time. We find that memory (non-Markovian-ness) in the process can have a pronounced effect on the shapes of the outbreak’s branching pattern. However, memory also has a pronounced effect on the sizes of the trees, even when the duration of the simulation is fixed. When the sizes of the trees are constrained to a constant value, memory in our processes has little direct effect on tree shapes, but can bias inference of the birth rate from trees. We compare simulated branching trees to phylogenetic trees from an outbreak of tuberculosis in Canada, and discuss the relevance of memory to this dataset.

The probability of epidemic fade-out is non-monotonic in transmission rate for the Markovian SIR model with demography

Epidemic fade-out refers to infection elimination in the trough between the first and second waves of an outbreak. The number of infectious individuals drops to a relatively low level between these waves of infection, and if elimination does not occur at this stage, then the disease is likely to become endemic. For this reason, it appears to be an ideal target for control efforts. Despite this obvious public health importance, the probability of epidemic fade-out is not well understood. Here we present new algorithms for approximating the probability of epidemic fade-out for the Markovian SIR model with demography. These algorithms are more accurate than previously published formulae, and one of them scales well to large population sizes. This method allows us to investigate the probability of epidemic fade-out as a function of the effective transmission rate, recovery rate, population turnover rate, and population size. We identify an interesting feature: the probability of epidemic fade-out is very often greatest when the basic reproduction number, R0, is approximately 2 (restricting consideration to cases where a major outbreak is possible, i.e., R0>1). The public health implication is that there may be instances where a non-lethal infection should be allowed to spread, or antiviral usage should be moderated, to maximise the chance of the infection being eliminated before it becomes endemic.

Simple Approximations for Epidemics with Exponential and Fixed Infectious Periods

Analytical approximations have generated many insights into the dynamics of epidemics, but there is only one well-known approximation which describes the dynamics of the whole epidemic. In addition, most of the well-known approximations for different aspects of the dynamics are for the classic susceptible-infected-recovered model, in which the infectious period is exponentially distributed. Whilst this assumption is useful, it is somewhat unrealistic. Equally reasonable assumptions are that the infectious period is finite and fixed or that there is a distribution of infectious periods centred round a nonzero mean. We investigate the effect of these different assumptions on the dynamics of the epidemic by deriving approximations to the whole epidemic curve. We show how the well-known sech-squared approximation for the infective population in 'weak' epidemics (where the basic reproduction rate R₀ ≈ 1) can be extended to the case of an arbitrary distribution of infectious periods having finite second moment, including as examples fixed and gamma-distributed infectious periods. Further, we show how to approximate the time course of a 'strong' epidemic, where R₀ ≫ 1, demonstrating the importance of estimating the infectious period distribution early in an epidemic.

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.

A century of transitions in New York City's measles dynamics

Infectious diseases spreading in a human population occasionally exhibit sudden transitions in their qualitative dynamics. Previous work has successfully predicted such transitions in New York City's historical measles incidence using the seasonally forced susceptible-infectious-recovered (SIR) model. This work relied on a dataset spanning 45 years (1928-1973), which we have extended to 93 years (1891-1984). We identify additional dynamical transitions in the longer dataset and successfully explain them by analysing attractors and transients of the same mechanistic epidemiological model.

The effect of seasonal birth pulses on pathogen persistence in wild mammal populations

The notion of a critical community size (CCS), or population size that is likely to result in long-term persistence of a communicable disease, has been developed based on the empirical observations of acute immunizing infections in human populations, and extended for use in wildlife populations. Seasonal birth pulses are frequently observed in wildlife and are expected to impact infection dynamics, yet their effect on pathogen persistence and CCS have not been considered. To investigate this issue theoretically, we use stochastic epidemiological models to ask how host life-history traits and infection parameters interact to determine pathogen persistence within a closed population. We fit seasonal birth pulse models to data from diverse mammalian species in order to identify realistic parameter ranges. When varying the synchrony of the birth pulse with all other parameters being constant, our model predicted that the CCS can vary by more than two orders of magnitude. Tighter birth pulses tended to drive pathogen extinction by creating large amplitude oscillations in prevalence, especially with high demographic turnover and short infectious periods. Parameters affecting the relative timing of the epidemic and birth pulse peaks determined the intensity and direction of the effect of pre-existing immunity in the population on the pathogen's ability to persist beyond the initial epidemic following its introduction.

Eight challenges in modelling disease ecology in multi-host, multi-agent systems

Many disease systems exhibit complexities not captured by current theoretical and empirical work. In particular, systems with multiple host species and multiple infectious agents (i.e., multi-host, multi-agent systems) require novel methods to extend the wealth of knowledge acquired studying primarily single-host, single-agent systems. We outline eight challenges in multi-host, multi-agent systems that could substantively increase our knowledge of the drivers and broader ecosystem effects of infectious disease dynamics.

Assembling evidence for identifying reservoirs of infection

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We review the problem of identifying reservoirs of infection for multihost pathogens and provide an overview of current approaches and future directions.

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We provide a conceptual framework for classifying patterns of incidence and prevalence.

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We review current methods that allow us to characterise the components of reservoir-target systems.

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Ecological theory offers promising new ways to prioritise populations when designing interventions.

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We propose using interventions as quasi-experiments embedded in adaptive management frameworks.

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Integration of data and analysis provides powerful new opportunities for studying multihost systems.

Many pathogens persist in multihost systems, making the identification of infection reservoirs crucial for devising effective interventions. Here, we present a conceptual framework for classifying patterns of incidence and prevalence, and review recent scientific advances that allow us to study and manage reservoirs simultaneously. We argue that interventions can have a crucial role in enriching our mechanistic understanding of how reservoirs function and should be embedded as quasi-experimental studies in adaptive management frameworks. Single approaches to the study of reservoirs are unlikely to generate conclusive insights whereas the formal integration of data and methodologies, involving interventions, pathogen genetics, and contemporary surveillance techniques, promises to open up new opportunities to advance understanding of complex multihost systems.

Dynamics of infectious diseases

Modern infectious disease epidemiology has a strong history of using mathematics both for prediction and to gain a deeper understanding. However the study of infectious diseases is a highly interdisciplinary subject requiring insights from multiple disciplines, in particular a biological knowledge of the pathogen, a statistical description of the available data and a mathematical framework for prediction. Here we begin with the basic building blocks of infectious disease epidemiology--the SIS and SIR type models--before considering the progress that has been made over the recent decades and the challenges that lie ahead. Throughout we focus on the understanding that can be developed from relatively simple models, although accurate prediction will inevitably require far greater complexity beyond the scope of this review. In particular, we focus on three critical aspects of infectious disease models that we feel fundamentally shape their dynamics: heterogeneously structured populations, stochasticity and spatial structure. Throughout we relate the mathematical models and their results to a variety of real-world problems.

Characterizing the dynamics of rubella relative to measles: the role of stochasticity

Rubella is a completely immunizing and mild infection in children. Understanding its behaviour is of considerable public health importance because of congenital rubella syndrome, which results from infection with rubella during early pregnancy and may entail a variety of birth defects. The recurrent dynamics of rubella are relatively poorly resolved, and appear to show considerable diversity globally. Here, we investigate the behaviour of a stochastic seasonally forced susceptible-infected-recovered model to characterize the determinants of these dynamics and illustrate patterns by comparison with measles. We perform a systematic analysis of spectra of stochastic fluctuations around stable attractors of the corresponding deterministic model and compare them with spectra from full stochastic simulations in large populations. This approach allows us to quantify the effects of demographic stochasticity and to give a coherent picture of measles and rubella dynamics, explaining essential differences in the recurrent patterns exhibited by these diseases. We discuss the implications of our findings in the context of vaccination and changing birth rates as well as the persistence of these two childhood infections.

Persistence in epidemic metapopulations: quantifying the rescue effects for measles, mumps, rubella and whooping cough

Metapopulation rescue effects are thought to be key to the persistence of many acute immunizing infections. Yet the enhancement of persistence through spatial coupling has not been previously quantified. Here we estimate the metapopulation rescue effects for four childhood infections using global WHO reported incidence data by comparing persistence on island countries vs all other countries, while controlling for key variables such as vaccine cover, birth rates and economic development. The relative risk of extinction on islands is significantly higher, and approximately double the risk of extinction in mainland countries. Furthermore, as may be expected, infections with longer infectious periods tend to have the strongest metapopulation rescue effects. Our results quantitate the notion that demography and local community size controls disease persistence.

Probabilistic measures of persistence and extinction in measles (meta)populations

Persistence and extinction are fundamental processes in ecological systems that are difficult to accurately measure due to stochasticity and incomplete observation. Moreover, these processes operate on multiple scales, from individual populations to metapopulations. Here, we examine an extensive new data set of measles case reports and associated demographics in pre-vaccine era US cities, alongside a classic England & Wales data set. We first infer the per-population quasi-continuous distribution of log incidence. We then use stochastic, spatially implicit metapopulation models to explore the frequency of rescue events and apparent extinctions. We show that, unlike critical community size, the inferred distributions account for observational processes, allowing direct comparisons between metapopulations. The inferred distributions scale with population size. We use these scalings to estimate extinction boundary probabilities. We compare these predictions with measurements in individual populations and random aggregates of populations, highlighting the importance of medium-sized populations in metapopulation persistence.

Resolving pertussis immunity and vaccine effectiveness using incidence time series

Resolving the long-term, population-level consequence of vaccine-induced immunity to pertussis is a key challenge for control strategies and vaccine development. Controlled vaccine efficacy studies provide invaluable information; however, they are limited in scope by their sample size and follow-up duration. Long-term time series of incidence data collected by public health institutions provide insight at a broader scale, especially when the data are spatially explicit and age stratified. By using modern ecological and statistical methodolgies, which are reviewed in this paper, new insights into the duration of transmission-blocking immunity and the age-specific patterns of transmission can be gained. Recent advances in computing power and statistical software development will increasingly make these methods available to public health practitioners, vaccine developers and academics alike.

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

Pertussis is a highly infectious respiratory disease that is currently responsible for nearly 300,000 annual deaths worldwide, primarily in infants in developing countries. Despite sustained high vaccine uptake, a resurgence in pertussis incidence has been reported in a number of countries. This resurgence has led to critical questions regarding the transmission impacts of vaccination and pertussis immunology. We analyzed pertussis incidence in Thailand--both age-stratified and longitudinal aggregate reports--over the past 30 y. To dissect the contributions of waning pertussis immunity and repeat infections to pertussis epidemiology in Thailand following a pronounced increase in vaccine uptake, we used likelihood-based statistical inference methods to evaluate the support for multiple competing transmission models. We found that, in contrast to other settings, there is no evidence for pertussis resurgence in Thailand, with each model examined pointing to a substantial rise in herd immunity over the past 30 y. Using a variety of empirical metrics, we verified our findings by documenting signatures of changing herd immunity over the study period. Importantly, this work leads to the conclusion that repeat infections have played little role in shaping pertussis epidemiology in Thailand. Our results are surprisingly emphatic in support of measurable impact of herd immunity given the uncertainty associated with pertussis epidemiology.

Effects of the infectious period distribution on predicted transitions in childhood disease dynamics

The population dynamics of infectious diseases occasionally undergo rapid qualitative changes, such as transitions from annual to biennial cycles or to irregular dynamics. Previous work, based on the standard seasonally forced 'susceptible-exposed-infectious-removed' (SEIR) model has found that transitions in the dynamics of many childhood diseases result from bifurcations induced by slow changes in birth and vaccination rates. However, the standard SEIR formulation assumes that the stage durations (latent and infectious periods) are exponentially distributed, whereas real distributions are narrower and centred around the mean. Much recent work has indicated that realistically distributed stage durations strongly affect the dynamical structure of seasonally forced epidemic models. We investigate whether inferences drawn from previous analyses of transitions in patterns of measles dynamics are robust to the shapes of the stage duration distributions. As an illustrative example, we analyse measles dynamics in New York City from 1928 to 1972. We find that with a fixed mean infectious period in the susceptible-infectious-removed (SIR) model, the dynamical structure and predicted transitions vary substantially as a function of the shape of the infectious period distribution. By contrast, with fixed mean latent and infectious periods in the SEIR model, the shapes of the stage duration distributions have a less dramatic effect on model dynamical structure and predicted transitions. All these results can be understood more easily by considering the distribution of the disease generation time as opposed to the distributions of individual disease stages. Numerical bifurcation analysis reveals that for a given mean generation time the dynamics of the SIR and SEIR models for measles are nearly equivalent and are insensitive to the shapes of the disease stage distributions.

Estimating the probability of a major outbreak from the timing of early cases: an indeterminate problem?

Conservation biologists, as well as veterinary and public health officials, would benefit greatly from being able to forecast whether outbreaks of infectious disease will be major. For values of the basic reproductive number (R₀) between one and two, infectious disease outbreaks have a reasonable chance of either fading out at an early stage or, in the absence of intervention, spreading widely within the population. If it were possible to predict when fadeout was likely to occur, the need for costly precautionary control strategies could be minimized. However, the predictability of even simple epidemic processes remains largely unexplored. Here we conduct an examination of simulated data from the early stages of a fatal disease outbreak and explore how observable information might be useful for predicting major outbreaks. Specifically, would knowing the time of deaths for the first few cases allow us to predict whether an outbreak will be major? Using two approaches, trajectory matching and discriminant function analysis, we find that even in our best-case scenario (with accurate knowledge of epidemiological parameters, and precise times of death), it was not possible to reliably predict the outcome of a stochastic Susceptible-Exposed–Infectious-Recovered (SEIR) process.

Estimating the hidden burden of bovine tuberculosis in Great Britain

The number of cattle herds placed under movement restrictions in Great Britain (GB) due to the suspected presence of bovine tuberculosis (bTB) has progressively increased over the past 25 years despite an intensive and costly test-and-slaughter control program. Around 38% of herds that clear movement restrictions experience a recurrent incident (breakdown) within 24 months, suggesting that infection may be persisting within herds. Reactivity to tuberculin, the basis of diagnostic testing, is dependent on the time from infection. Thus, testing efficiency varies between outbreaks, depending on weight of transmission and cannot be directly estimated. In this paper, we use Approximate Bayesian Computation (ABC) to parameterize two within-herd transmission models within a rigorous inferential framework. Previous within-herd models of bTB have relied on ad-hoc methods of parameterization and used a single model structure (SORI) where animals are assumed to become detectable by testing before they become infectious. We study such a conventional within-herd model of bTB and an alternative model, motivated by recent animal challenge studies, where there is no period of epidemiological latency before animals become infectious (SOR). Under both models we estimate that cattle-to-cattle transmission rates are non-linearly density dependent. The basic reproductive ratio for our conventional within-herd model, estimated for scenarios with no statutory controls, increases from 1.5 (0.26-4.9; 95% CI) in a herd of 30 cattle up to 4.9 (0.99-14.0) in a herd of 400. Under this model we estimate that 50% (33-67) of recurrent breakdowns in Britain can be attributed to infection missed by tuberculin testing. However this figure falls to 24% (11-42) of recurrent breakdowns under our alternative model. Under both models the estimated extrinsic force of infection increases with the burden of missed infection. Hence, improved herd-level testing is unlikely to reduce recurrence unless this extrinsic infectious pressure is simultaneously addressed.

Direct and indirect effects of rotavirus vaccination: comparing predictions from transmission dynamic models

Early observations from countries that have introduced rotavirus vaccination suggest that there may be indirect protection for unvaccinated individuals, but it is unclear whether these benefits will extend to the long term. Transmission dynamic models have attempted to quantify the indirect protection that might be expected from rotavirus vaccination in developed countries, but results have varied. To better understand the magnitude and sources of variability in model projections, we undertook a comparative analysis of transmission dynamic models for rotavirus. We fit five models to reported rotavirus gastroenteritis (RVGE) data from England and Wales, and evaluated outcomes for short- and long-term vaccination effects. All of our models reproduced the important features of rotavirus epidemics in England and Wales. Models predicted that during the initial year after vaccine introduction, incidence of severe RVGE would be reduced 1.8–2.9 times more than expected from the direct effects of the vaccine alone (28–50% at 90% coverage), but over a 5-year period following vaccine introduction severe RVGE would be reduced only by 1.1–1.7 times more than expected from the direct effects (54–90% at 90% coverage). Projections for the long-term reduction of severe RVGE ranged from a 55% reduction at full coverage to elimination with at least 80% coverage. Our models predicted short-term reductions in the incidence of RVGE that exceeded estimates of the direct effects, consistent with observations from the United States and other countries. Some of the models predicted that the short-term indirect benefits may be offset by a partial shifting of the burden of RVGE to older unvaccinated individuals. Nonetheless, even when such a shift occurs, the overall reduction in severe RVGE is considerable. Discrepancies among model predictions reflect uncertainties about age variation in the risk and reporting of RVGE, and the duration of natural and vaccine-induced immunity, highlighting important questions for future research.

The population ecology of infectious diseases: pertussis in Thailand as a case study

Many of the fundamental concepts in studying infectious diseases are rooted in population ecology. We describe the importance of population ecology in exploring central issues in infectious disease research including identifying the drivers and dynamics of host-pathogen interactions and pathogen persistence, and evaluating the success of public health policies. The use of ecological concepts in infectious disease research is demonstrated with simple theoretical examples in addition to an analysis of case notification data of pertussis, a childhood respiratory disease, in Thailand as a case study. We stress that further integration of these fields will have significant impacts in infectious diseases research.

The impact of school holidays on the social mixing patterns of school children

School holidays are recognised to be of great epidemiological importance for a wide range of infectious diseases; this is postulated to be because the social mixing patterns of school children - a key population group - change significantly during the holiday period. However, there is little direct quantitative evidence to confirm this belief. Here, we present the results of a prospective survey designed to provide a detailed comparison of social mixing patterns of school children during school terms and during the school holidays. Paired data were collected, with participants recording their social contacts once during term time and once during the holiday period. We found that the daily number of recorded encounters approximately halved during the holidays, and that the number of close contact encounters fell by approximately one third. The holiday period also saw a change in the age structure of children's social contacts, with far fewer contacts of their own age, but an increase in the number of encounters with adults, particularly older adults. A greater amount of mixing between children at different schools was recorded during the holiday. We suggest, therefore, that whilst infections may spread rapidly within schools during term time, in the holiday period there are increased opportunities for transmission to other schools and other age groups.

Natural immune boosting in pertussis dynamics and the potential for long-term vaccine failure

Incidence of whooping cough, unlike many other childhood diseases for which there is an efficacious vaccine, has been increasing over the past twenty years despite high levels of vaccine coverage. Its reemergence has been particularly noticeable among teenagers and adults. Many hypotheses have been put forward to explain these two patterns, but parsimonious reconciliation of clinical data on the limited duration of immunity with both pre- and postvaccine era age-specific incidence remains a challenge. We consider the immunologically relevant, yet epidemiologically largely neglected, possibility that a primed immune system can respond to a lower dose of antigen than a naive one. We hypothesize that during the prevaccine era teenagers' and adults' primed immunity was frequently boosted by reexposure, so maintaining herd immunity in the face of potentially eroding individual immunity. In contrast, low pathogen circulation in the current era, except during epidemic outbreaks, allows immunity to be lost before reexposure occurs. We develop and analyze an age-structured model that encapsulates this hypothesis. We find that immune boosting must be more easily triggered than primary infection to account for age-incidence data. We make age-specific and dynamical predictions through bifurcation analysis and simulation. The boosting model proposed here parsimoniously captures four key features of pertussis data from highly vaccinated countries: (i) the shift in age-specific incidence, (ii) reemergence with high vaccine coverage, (iii) the possibility for cyclic dynamics in the pre- and postvaccine eras, and (iv) the apparent shift from susceptible-infectious-recovered (SIR)-like to susceptible-infectious-recovered-susceptible (SIRS)-like phenomenology of infection and immunity to Bordetella pertussis.

Origin of measles virus: divergence from rinderpest virus between the 11th and 12th centuries

Measles, caused by measles virus (MeV), is a common infection in children. MeV is a member of the genus Morbillivirus and is most closely related to rinderpest virus (RPV), which is a pathogen of cattle. MeV is thought to have evolved in an environment where cattle and humans lived in close proximity. Understanding the evolutionary history of MeV could answer questions related to divergence times of MeV and RPV. We investigated divergence times using relaxed clock Bayesian phylogenetics. Our estimates reveal that MeV had an evolutionary rate of 6.0-6.5 x 10(-4) substitutions/site/year. It was concluded that the divergence time of the most recent common ancestor of current MeV was the early 20th century. And, divergence between MeV and RPV occurred around the 11th to 12th centuries. The result was unexpected because emergence of MeV was previously considered to have occurred in the prehistoric age. MeV may have originated from virus of non-human species and caused emerging infectious diseases around the 11th to 12th centuries. In such cases, investigating measles would give important information about the course of emerging infectious diseases.

Plug-and-play inference for disease dynamics: measles in large and small populations as a case study

Statistical inference for mechanistic models of partially observed dynamic systems is an active area of research. Most existing inference methods place substantial restrictions upon the form of models that can be fitted and hence upon the nature of the scientific hypotheses that can be entertained and the data that can be used to evaluate them. In contrast, the so-called plug-and-play methods require only simulations from a model and are thus free of such restrictions. We show the utility of the plug-and-play approach in the context of an investigation of measles transmission dynamics. Our novel methodology enables us to ask and answer questions that previous analyses have been unable to address. Specifically, we demonstrate that plug-and-play methods permit the development of a modelling and inference framework applicable to data from both large and small populations. We thereby obtain novel insights into the nature of heterogeneity in mixing and comment on the importance of including extra-demographic stochasticity as a means of dealing with environmental stochasticity and model misspecification. Our approach is readily applicable to many other epidemiological and ecological systems.