Joint modelling of serological and hospitalization data reveals that high levels of pre-existing immunity and school holidays shaped the influenza A pandemic of 2009 in The Netherlands

Obtaining a quantitative understanding of the transmission dynamics of influenza A is important for predicting healthcare demand and assessing the likely impact of intervention measures. The pandemic of 2009 provides an ideal platform for developing integrative analyses as it has been studied intensively, and a wealth of data sources is available. Here, we analyse two complementary datasets in a disease transmission framework: cross-sectional serological surveys providing data on infection attack rates, and hospitalization data that convey information on the timing and duration of the pandemic. We estimate key epidemic determinants such as infection and hospitalization rates, and the impact of a school holiday. In contrast to previous approaches, our novel modelling of serological data with mixture distributions provides a probabilistic classification of individual samples (susceptible, immune and infected), propagating classification uncertainties to the transmission model and enabling serological classifications to be informed by hospitalization data. The analyses show that high levels of immunity among persons 20 years and older provide a consistent explanation of the skewed attack rates observed during the pandemic and yield precise estimates of the probability of hospitalization per infection (1–4 years: 0.00096 (95%CrI: 0.00078–0.0012); 5–19 years: 0.00036 (0.00031–0.0044); 20–64 years: 0.0015 (0.00091–0.0020); 65+ years: 0.0084 (0.0028–0.016)). The analyses suggest that in The Netherlands, the school holiday period reduced the number of infectious contacts between 5- and 9-year-old children substantially (estimated reduction: 54%; 95%CrI: 29–82%), thereby delaying the unfolding of the pandemic in The Netherlands by approximately a week.     

An avian influenza model with latency and vaccination

Avian influenza, caused by influenza A viruses, has received worldwide attention in recent years. The viruses can spread from birds to humans as well as transmit among human hosts. In this study, we formulate a mathematical model for avian influenza that includes bird-human interaction and that incorporates the effects of infection latency and human vaccination. We investigate the essential dynamics of the model through an equilibrium analysis. Meanwhile, we explore effective vaccination strategy to control avian influenza outbreaks using optimal control theory. Our results indicate that strategically deployed human vaccination can significantly reduce the numbers of exposed and infectious people.     

The global spread of drug-resistant influenza

Resistance to oseltamivir, the most widely used influenza antiviral drug, spread to fixation in seasonal influenza A(H1N1) between 2006 and 2009. This sudden rise in resistance seemed puzzling given the low overall level of the oseltamivir usage and the lack of a correlation between local rates of resistance and oseltamivir usage. We used a stochastic simulation model and deterministic approximations to examine how such events can occur, and in particular to determine how the rate of fixation of the resistant strain depends both on its fitness in untreated hosts as well as the frequency of antiviral treatment. We found that, for the levels of antiviral usage in the population, the resistant strain will eventually spread to fixation, if it is not attenuated in transmissibility relative to the drug-sensitive strain, but not at the speed observed in seasonal H1N1. The extreme speed with which the resistance spread in seasonal H1N1 suggests that the resistant strain had a transmission advantage in untreated hosts, and this could have arisen from genetic hitchhiking, or from the mutations responsible for resistance and compensation. Importantly, our model also shows that resistant virus will fail to spread if it is even slightly less transmissible than its sensitive counterpart—a finding of relevance given that resistant pandemic influenza (H1N1) 2009 may currently suffer from a small, but nonetheless experimentally perceptible reduction in transmissibility.     

Quantifying social distancing arising from pandemic influenza.

Local epidemic curves during the 1918-1919 influenza pandemic were often characterized by multiple epidemic waves. Identifying the underlying cause(s) of such waves may help manage future pandemics. We investigate the hypothesis that these waves were caused by people avoiding potentially infectious contacts-a behaviour termed 'social distancing'. We estimate the effective disease reproduction number and from it infer the maximum degree of social distancing that occurred during the course of the multiple-wave epidemic in Sydney, Australia. We estimate that, on average across the city, people reduced their infectious contact rate by as much as 38%, and that this was sufficient to explain the multiple waves of this epidemic. The basic reproduction number, R0, was estimated to be in the range of 1.6-2.0 with a preferred estimate of 1.8, in line with other recent estimates for the 1918-1919 influenza pandemic. The data are also consistent with a high proportion (more than 90%) of the population being initially susceptible to clinical infection, and the proportion of infections that were asymptomatic (if this occurs) being no higher than approximately 9%. The observed clinical attack rate of 36.6% was substantially lower than the 59% expected based on the estimated value of R0, implying that approximately 22% of the population were spared from clinical infection. This reduction in the clinical attack rate translates to an estimated 260 per 100000 lives having been saved, and suggests that social distancing interventions could play a major role in mitigating the public health impact of future influenza pandemics.     

Demographic buffering: titrating the effects of birth rate and imperfect immunity on epidemic dynamics

Host demography can alter the dynamics of infectious disease. In the case of perfectly immunizing infections, observations of strong sensitivity to demographic variation have been mechanistically explained through analysis of the susceptible–infected–recovered (SIR) model that assumes lifelong immunity following recovery from infection. When imperfect immunity is incorporated into this framework via the susceptible–infected–recovered–susceptible (SIRS) model, with individuals regaining full susceptibility following recovery, we show that rapid loss of immunity is predicted to buffer populations against the effects of demographic change. However, this buffering is contrary to the dependence on demography recently observed for partially immunizing infections such as rotavirus and respiratory syncytial virus. We show that this discrepancy arises from a key simplification embedded in the SIR(S) framework, namely that the potential for differential immune responses to repeat exposures is ignored. We explore the minimum additional immunological information that must be included to reflect the range of observed dependencies on demography. We show that including partial protection and lower transmission following primary infection is sufficient to capture more realistic reduced levels of buffering, in addition to changes in epidemic timing, across a range of partially and fully immunizing infections. Furthermore, our results identify key variables in this relationship, including R₀.     

A dose and time response Markov model for the in-host dynamics of infection with intracellular bacteria following inhalation: with application to Francisella tularensis

In a novel approach, the standard birth–death process is extended to incorporate a fundamental mechanism undergone by intracellular bacteria, phagocytosis. The model accounts for stochastic interaction between bacteria and cells of the immune system and heterogeneity in susceptibility to infection of individual hosts within a population. Model output is the dose–response relation and the dose-dependent distribution of time until response, where response is the onset of symptoms. The model is thereafter parametrized with respect to the highly virulent Schu S4 strain of Francisella tularensis, in the first such study to consider a biologically plausible mathematical model for early human infection with this bacterium. Results indicate a median infectious dose of about 23 organisms, which is higher than previously thought, and an average incubation period of between 3 and 7 days depending on dose. The distribution of incubation periods is right-skewed up to about 100 organisms and symmetric for larger doses. Moreover, there are some interesting parallels to the hypotheses of some of the classical dose–response models, such as independent action (single-hit model) and individual effective dose (probit model). The findings of this study support experimental evidence and postulations from other investigations that response is, in fact, influenced by both in-host and between-host variability.     

A two-tiered model for simulating the ecological and evolutionary dynamics of rapidly evolving viruses, with an application to influenza

Understanding the epidemiological and evolutionary dynamics of rapidly evolving pathogens is one of the most challenging problems facing disease ecologists today. To date, many mathematical and individual-based models have provided key insights into the factors that may regulate these dynamics. However, in many of these models, abstractions have been made to the simulated sequences that limit an effective interface with empirical data. This is especially the case for rapidly evolving viruses in which de novo mutations result in antigenically novel variants. With this focus, we present a simple two-tiered ‘phylodynamic’ model whose purpose is to simulate, along with case data, sequence data that will allow for a more quantitative interface with observed sequence data. The model differs from previous approaches in that it separates the simulation of the epidemiological dynamics (tier 1) from the molecular evolution of the virus''s dominant antigenic protein (tier 2). This separation of phenotypic dynamics from genetic dynamics results in a modular model that is computationally simpler and allows sequences to be simulated with specifications such as sequence length, nucleotide composition and molecular constraints. To illustrate its use, we apply the model to influenza A (H3N2) dynamics in humans, influenza B dynamics in humans and influenza A (H3N8) dynamics in equine hosts. In all three of these illustrative examples, we show that the model can simulate sequences that are quantitatively similar in pattern to those empirically observed. Future work should focus on statistical estimation of model parameters for these examples as well as the possibility of applying this model, or variants thereof, to other host–virus systems.     

Essential epidemiological mechanisms underpinning the transmission dynamics of seasonal influenza

Seasonal influenza has considerable impact around the world, both economically and in mortality among risk groups, but there is considerable uncertainty as to the essential mechanisms and their parametrization. In this paper, we identify a number of characteristic features of influenza incidence time series in temperate regions, including ranges of annual attack rates and outbreak durations. By constraining the output of simple models to match these characteristic features, we investigate the role played by population heterogeneity, multiple strains, cross-immunity and the rate of strain evolution in the generation of incidence time series. Results indicate that an age-structured model with non-random mixing and co-circulating strains are both required to match observed time-series data. Our work gives estimates of the seasonal peak basic reproduction number, R₀, in the range 1.6–3. Estimates of R₀ are strongly correlated with the timescale for waning of immunity to current circulating seasonal influenza strain, which we estimate is between 3 and 8 years. Seasonal variation in transmissibility is largely confined to 15–30% of its mean value. While population heterogeneity and cross-immunity are required mechanisms, the degree of heterogeneity and cross-immunity is not tightly constrained. We discuss our findings in the context of other work fitting to seasonal influenza data.     

An explicit immunogenetic model of gastrointestinal nematode infection in sheep

Gastrointestinal nematodes are a global cause of disease and death in humans, wildlife and livestock. Livestock infection has historically been controlled with anthelmintic drugs, but the development of resistance means that alternative controls are needed. The most promising alternatives are vaccination, nutritional supplementation and selective breeding, all of which act by enhancing the immune response. Currently, control planning is hampered by reliance on the faecal egg count (FEC), which suffers from low accuracy and a nonlinear and indirect relationship with infection intensity and host immune responses. We address this gap by using extensive parasitological, immunological and genetic data on the sheep–Teladorsagia circumcincta interaction to create an immunologically explicit model of infection dynamics in a sheep flock that links host genetic variation with variation in the two key immune responses to predict the observed parasitological measures. Using our model, we show that the immune responses are highly heritable and by comparing selective breeding based on low FECs versus high plasma IgA responses, we show that the immune markers are a much improved measure of host resistance. In summary, we have created a model of host–parasite infections that explicitly captures the development of the adaptive immune response and show that by integrating genetic, immunological and parasitological understanding we can identify new immune-based markers for diagnosis and control.     

Transmission and control of an emerging influenza pandemic in a small-world airline network

The avian influenza virus H5N1 and the 2009 swine flu H1N1 are potentially serious pandemic threats to human health, and air travel readily facilitates the spread of infectious diseases. However, past studies have not yet incorporated the effects of air travel on the transmission of influenza in the construction of mathematical epidemic models. Therefore, this paper focused on the human-to-human transmission of influenza, and investigated the effects of air travel activities on an influenza pandemic in a small-world network. These activities of air travel include passengers’ consolidation, conveyance and distribution in airports and flights. Dynamic transmission models were developed to assess the expected burdens of the pandemic, with and without control measures. This study also investigated how the small-world properties of an air transportation network facilitate the spread of influenza around the globe. The results show that, as soon as the influenza is spread to the top 50 global airports, the transmission is greatly accelerated. Under the constraint of limited resources, a strategy that first applies control measures to the top 50 airports after day 13 and then soon afterwards to all other airports may result in remarkable containment effectiveness. As the infectiousness of the disease increases, it will expand the scale of the pandemic, and move the start time of the pandemic ahead.     

Towards a quantitative understanding of the within-host dynamics of influenza A infections

Although the influenza A virus has been extensively studied, a quantitative understanding of the infection dynamics is still lacking. To make progress in this direction, we designed several mathematical models and compared them with data from influenza A infections of mice. We find that the immune response (IR) plays an important part in the infection dynamics. Both an innate and an adaptive IR are required to provide adequate explanation of the data. In contrast, regrowth of epithelial cells did not seem to be an important mechanism on the time scale of the infection. We also find that different model variants for both innate and adaptive responses fit the data well, indicating the need for additional data to allow further model discrimination.     

The role of heterogeneity in contact timing and duration in network models of influenza spread in schools

Influenza poses a significant health threat to children, and schools may play a critical role in community outbreaks. Mathematical outbreak models require assumptions about contact rates and patterns among students, but the level of temporal granularity required to produce reliable results is unclear. We collected objective contact data from students aged 5–14 at an elementary school and middle school in the state of Utah, USA, and paired those data with a novel, data-based model of influenza transmission in schools. Our simulations produced within-school transmission averages consistent with published estimates. We compared simulated outbreaks over the full resolution dynamic network with simulations on networks with averaged representations of contact timing and duration. For both schools, averaging the timing of contacts over one or two school days caused average outbreak sizes to increase by 1–8%. Averaging both contact timing and pairwise contact durations caused average outbreak sizes to increase by 10% at the middle school and 72% at the elementary school. Averaging contact durations separately across within-class and between-class contacts reduced the increase for the elementary school to 5%. Thus, the effect of ignoring details about contact timing and duration in school contact networks on outbreak size modelling can vary across different schools.     

Variation in host susceptibility and infectiousness generated by co-infection: the myxoma-Trichostrongylus retortaeformis case in wild rabbits.

One of the conditions that can affect host susceptibility and parasite transmission is the occurrence of concomitant infections. Parasites interact directly or indirectly within an individual host and often these interactions are modulated by the host immune response. We used a free-living rabbit population co-infected with the nematode Trichostrongylus retortaeformis, which appears to stimulate an acquired immune response, and the immunosuppressive poxvirus myxoma. Modelling was used to examine how myxoma infection alters the immune-mediated establishment and death/expulsion of T. retortaeformis, and consequently affects parasite intensity and duration of the infection. Simulations were based on the general TH1-TH2 immunological paradigm that proposes the polarization of the host immune response towards one of the two subsets of T helper cells. Our findings suggest that myxoma infections contribute to alter host susceptibility to the nematode, as co-infected rabbits showed higher worm intensity compared with virus negative hosts. Results also suggest that myxoma disrupts the ability of the host to clear T. retortaeformis as worm intensities were consistently high and remained high in old rabbits. However, the co-infection model has to include some immune-mediated nematode regulation to be consistent with field data, indicating that the TH1-TH2 dichotomy is not complete. We conclude that seasonal myxoma outbreaks enhance host susceptibility to the nematode and generate highly infected hosts that remain infectious for a longer time. Finally, the virus-nematode co-infection increases heterogeneities among individuals and potentially has a large effect on parasite transmission.     

Insights into mucosal innate responses to Escherichia coli O157 : H7 colonization of cattle by mathematical modelling of excretion dynamics

Mathematical model-based statistical inference applied to within-host dynamics of infectious diseases can help dissect complex interactions between hosts and microbes. This work has applied advances in model-based inference to understand colonization of cattle by enterohaemorrhagic Escherichia coli O157 : H7 at the terminal rectum. A mathematical model was developed based on niche replication and transition rates at this site. A nested-model comparison, applied to excretion curves from 25 calves, was used to reduce complexity while maintaining integrity. We conclude that, 5–9 days post inoculation, the innate immune response negates bacterial replication on the epithelium and either reduces attachment to or increases detachment from the epithelium of the terminal rectum. Thus, we provide a broadly applicable model that gives novel insights into bacterial replication rates in vivo and the timing and impact of host responses.     

Bayesian data assimilation provides rapid decision support for vector-borne diseases

Predicting the spread of vector-borne diseases in response to incursions requires knowledge of both host and vector demographics in advance of an outbreak. Although host population data are typically available, for novel disease introductions there is a high chance of the pathogen using a vector for which data are unavailable. This presents a barrier to estimating the parameters of dynamical models representing host–vector–pathogen interaction, and hence limits their ability to provide quantitative risk forecasts. The Theileria orientalis (Ikeda) outbreak in New Zealand cattle demonstrates this problem: even though the vector has received extensive laboratory study, a high degree of uncertainty persists over its national demographic distribution. Addressing this, we develop a Bayesian data assimilation approach whereby indirect observations of vector activity inform a seasonal spatio-temporal risk surface within a stochastic epidemic model. We provide quantitative predictions for the future spread of the epidemic, quantifying uncertainty in the model parameters, case infection times and the disease status of undetected infections. Importantly, we demonstrate how our model learns sequentially as the epidemic unfolds and provide evidence for changing epidemic dynamics through time. Our approach therefore provides a significant advance in rapid decision support for novel vector-borne disease outbreaks.     

A combined within-host and between-hosts modelling framework for the evolution of resistance to antimalarial drugs

The spread of drug resistance represents a significant challenge to many disease control efforts. The evolution of resistance is a complex process influenced by transmission dynamics between hosts as well as infection dynamics within these hosts. This study aims to investigate how these two processes combine to impact the evolution of resistance in malaria parasites. We introduce a stochastic modelling framework combining an epidemiological model of Plasmodium transmission and an explicit within-human infection model for two competing strains. Immunity, treatment and resistance costs are included in the within-host model. We show that the spread of resistance is generally less likely in areas of intense transmission, and therefore of increased competition between strains, an effect exacerbated when costs of resistance are higher. We also illustrate how treatment influences the spread of resistance, with a trade-off between slowing resistance and curbing disease incidence. We show that treatment coverage has a stronger impact on disease prevalence, whereas treatment efficacy primarily affects resistance spread, suggesting that coverage should constitute the primary focus of control efforts. Finally, we illustrate the importance of feedbacks between modelling scales. Overall, our results underline the importance of concomitantly modelling the evolution of resistance within and between hosts.     

Estimating antiviral effectiveness against pandemic influenza using household data

Current estimates of antiviral effectiveness for influenza are based on the existing strains of the virus. Should a pandemic strain emerge, strain-specific estimates will be required as early as possible to ensure that antiviral stockpiles are used optimally and to compare the benefits of using antivirals as prophylaxis or to treat cases. We present a method to measure antiviral effectiveness using early pandemic data on household outbreak sizes, including households that are provided with antivirals for prophylaxis and those provided with antivirals for treatment only. We can assess whether antiviral drugs have a significant impact on susceptibility or on infectivity with the data from approximately 200 to 500 households with a primary case. Fewer households will suffice if the data can be collected before case numbers become high, and estimates are more precise if the study includes data from prophylaxed households and households where no antivirals are provided. Rates of asymptomatic infection and the level of transmissibility of the virus do not affect the accuracy of these estimates greatly, but the pattern of infectivity in the individual strongly influences the estimate of the effect of antivirals on infectivity. An accurate characterization of the infectiousness profile—informed by strain-specific data—is essential for measuring antiviral effectiveness.     

Transmission and dose�Cresponse experiments for social animals: a reappraisal of the colonization biology of Campylobacter jejuni in chickens

Dose–response experiments characterize the relationship between infectious agents and their hosts. These experiments are routinely used to estimate the minimum effective infectious dose for an infectious agent, which is most commonly characterized by the dose at which 50 per cent of challenged hosts become infected—the ID₅₀. In turn, the ID₅₀ is often used to compare between different agents and quantify the effect of treatment regimes. The statistical analysis of dose–response data typically makes the assumption that hosts within a given dose group are independent. For social animals, in particular avian species, hosts are routinely housed together in groups during experimental studies. For experiments with non-infectious agents, this poses no practical or theoretical problems. However, transmission of infectious agents between co-housed animals will modify the observed dose–response relationship with implications for the estimation of the ID₅₀ and the comparison between different agents and treatments. We derive a simple correction to the likelihood for standard dose–response models that allows us to estimate dose–response and transmission parameters simultaneously. We use this model to show that: transmission between co-housed animals reduces the apparent value of the ID₅₀ and increases the variability between replicates leading to a distinctive all-or-nothing response; in terms of the total number of animals used, individual housing is always the most efficient experimental design for ascertaining dose–response relationships; estimates of transmission from previously published experimental data for Campylobacter spp. in chickens suggest that considerable transmission occurred, greatly increasing the uncertainty in the estimates of dose–response parameters reported in the literature. Furthermore, we demonstrate that accounting for transmission in the analysis of dose–response data for Campylobacter spp. challenges our current understanding of the differing response of chickens with respect to host-age and in vivo passage of bacteria. Our findings suggest that the age-dependence of transmissibility between hosts—rather than their susceptibility to colonization—is the mechanism behind the ‘lag-phase’ reported in commercial flocks, which are typically found to be Campylobacter free for the first 14–21 days of life.     

A model for the spread and control of pandemic influenza in an isolated geographical region

In the event of an influenza pandemic, the most probable way in which the virus would be introduced to an isolated geographical area is by an infected traveller. We use a mathematical model, structured on the location at which infection occurs and based on published parameters for influenza, to describe an epidemic in a community of one million people. The model is then modified to reflect a variety of control strategies based on social distancing measures, targeted antiviral treatment and antiviral prophylaxis and home quarantine, and the effectiveness of the strategies is compared. The results suggest that the only single strategy that would be successful in preventing an epidemic (with R0=2.0) is targeted antiviral treatment and prophylaxis, and that closing schools combined with either closing work places or home quarantine would only prevent such an epidemic if these strategies were combined with a modest level of antiviral coverage.