Essential epidemiological mechanisms underpinning the transmission dynamics of seasonal influenza

Integrating dynamical modeling and phylogeographic inference to characterize global influenza circulation

Global seasonal influenza circulation involves a complex interplay between local (seasonality, demography, host immunity) and global factors (international mobility) shaping recurrent epidemic patterns. No studies so far have reconciled the two spatial levels, evaluating the coupling between national epidemics, considering heterogeneous coverage of epidemiological and virological data, integrating different data sources. We propose a novel combined approach based on a dynamical model of global influenza spread (GLEAM), integrating high-resolution demographic and mobility data, and a generalized linear model of phylogeographic diffusion that accounts for time-varying migration rates. Seasonal migration fluxes across global macro-regions simulated with GLEAM are tested as phylogeographic predictors to provide model validation and calibration based on genetic data. Seasonal fluxes obtained with a specific transmissibility peak time and recurrent travel outperformed the raw air-transportation predictor, previously considered as optimal indicator of global influenza migration. Influenza A subtypes supported autumn-winter reproductive number as high as 2.25 and an average immunity duration of 2 years. Similar dynamics were preferred by influenza B lineages, with a lower autumn-winter reproductive number. Comparing simulated epidemic profiles against FluNet data offered comparatively limited resolution power. The multiscale approach enables model selection yielding a novel computational framework for describing global influenza dynamics at different scales - local transmission and national epidemics vs. international coupling through mobility and imported cases. Our findings have important implications to improve preparedness against seasonal influenza epidemics. The approach can be generalized to other epidemic contexts, such as emerging disease outbreaks to improve the flexibility and predictive power of modeling.

Seasonality as a driver of pH1N12009 influenza vaccination campaign impact

Although the most recent respiratory virus pandemic was triggered by a Coronavirus, sustained and elevated prevalence of highly pathogenic avian influenza viruses able to infect mammalian hosts highlight the continued threat of pandemics of influenza A virus (IAV) to global health. Retrospective analysis of pandemic outcomes, including comparative investigation of intervention efficacy in different regions, provide important contributions to the evidence base for future pandemic planning. The swine-origin IAV pandemic of 2009 exhibited regional variation in onset, infection dynamics and annual infection attack rates (IARs). For example, the UK experienced three severe peaks of infection over two influenza seasons, whilst Australia experienced a single severe wave. We adopt a seasonally forced 2-subtype model for the transmission of pH1N12009 and seasonal H3N2 to examine the role vaccination campaigns may play in explaining differences in pandemic trajectories in temperate regions. Our model differentiates between the nature of vaccine- and infection-acquired immunity. In particular, we assume that immunity triggered by infection elicits heterologous cross-protection against viral shedding in addition to long-lasting neutralising antibody, whereas vaccination induces imperfect reduction in susceptibility. We employ an Approximate Bayesian Computation (ABC) framework to calibrate the model using data for pH1N12009 seroprevalence, relative subtype dominance, and annual IARs for Australia and the UK. Heterologous cross-protection substantially suppressed the pandemic IAR over the posterior, with the strength of protection against onward transmission inversely correlated with the initial reproduction number. We show that IAV pandemic timing relative to the usual seasonal influenza cycle influenced the size of the initial waves of pH1N12009 in temperate regions and the impact of vaccination campaigns.

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.

Repeatability and timing of tropical influenza epidemics

Much of the world experiences influenza in yearly recurring seasons, particularly in temperate areas. These patterns can be considered repeatable if they occur predictably and consistently at the same time of year. In tropical areas, including southeast Asia, timing of influenza epidemics is less consistent, leading to a lack of consensus regarding whether influenza is repeatable. This study aimed to assess repeatability of influenza in Vietnam, with repeatability defined as seasonality that occurs at a consistent time of year with low variation. We developed a mathematical model incorporating parameters to represent periods of increased transmission and then fitted the model to data collected from sentinel hospitals throughout Vietnam as well as four temperate locations. We fitted the model for individual (sub)types of influenza as well as all combined influenza throughout northern, central, and southern Vietnam. Repeatability was evaluated through the variance of the timings of peak transmission. Model fits from Vietnam show high variance (sd = 64-179 days) in peak transmission timing, with peaks occurring at irregular intervals and throughout different times of year. Fits from temperate locations showed regular, annual epidemics in winter months, with low variance in peak timings (sd = 32-57 days). This suggests that influenza patterns are not repeatable or seasonal in Vietnam. Influenza prevention in Vietnam therefore cannot rely on anticipation of regularly occurring outbreaks.

Competitive evolution of H1N1 and H3N2 influenza viruses in the United States: A mathematical modeling study

Seasonal influenza causes vast public health and economic impact globally. The prevention and control of the annual epidemics remain a challenge due to the antigenic evolution of the viruses. Here, we presented a novel modeling framework based on changes in amino acid sequences and relevant epidemiological data to retrospectively investigate the competitive evolution and transmission of H1N1 and H3N2 influenza viruses in the United States during October 2002 and April 2019. To do so, we estimated the time-varying disease transmission rate from the reported influenza cases and the time-varying antigenic change rate of the viruses from the changes in amino acid sequences. By incorporating the time-varying antigenic change rate into the transmission models, we found that the models could capture the evolutionary transmission dynamics of influenza viruses in the United States. Our modeling results also showed that the antigenic change of the virus plays an essential role in seasonal influenza dynamics.

From Outbreak to Near Disappearance: How Did Non-pharmaceutical Interventions Against COVID-19 Affect the Transmission of Influenza Virus?

Influenza shares the same putative transmission pathway with coronavirus disease 2019 (COVID-19), and causes tremendous morbidity and mortality annually globally. Since the transmission of COVID-19 in China, a series of non-pharmaceutical interventions (NPIs) against to the disease have been implemented to contain its transmission. Based on the surveillance data of influenza, Search Engine Index, and meteorological factors from 2011 to 2021 in Xi'an, and the different level of emergence responses for COVID-19 from 2020 to 2021, Bayesian Structural Time Series model and interrupted time series analysis were applied to quantitatively assess the impact of NPIs in sequent phases with different intensities, and to estimate the reduction of influenza infections. From 2011 to 2021, a total of 197,528 confirmed cases of influenza were reported in Xi'an, and the incidence of influenza continuously increased from 2011 to 2019, especially, in 2019-2020, when the incidence was up to 975.90 per 100,000 persons; however, it showed a sharp reduction of 97.68% in 2020-2021, and of 87.22% in 2021, comparing with 2019-2020. The highest impact on reduction of influenza was observed in the phase of strict implementation of NPIs with an inclusion probability of 0.54. The weekly influenza incidence was reduced by 95.45%, and an approximate reduction of 210,100 (95% CI: 125,100-329,500) influenza infections was found during the post-COVID-19 period. The reduction exhibited significant variations in the geographical, population, and temporal distribution. Our findings demonstrated that NPIs against COVID-19 had a long-term impact on the reduction of influenza transmission.

Increased urbanization reduced the effectiveness of school closures on seasonal influenza epidemics in China

BACKGROUND

School closure is a common mitigation strategy during severe influenza epidemics and pandemics. However, the effectiveness of this strategy remains controversial. In this study, we aimed to explore the effectiveness of school closure on seasonal influenza epidemics in provincial-level administrative divisions (PLADs) with varying urbanization rates in China.

METHODS

This study analyzed influenza surveillance data between 2010 and 2019 provided by the Chinese National Influenza Center. Taking into consideration the climate, this study included a region with 3 adjacent PLADs in Northern China and another region with 4 adjacent PLADs in Southern China. The effect of school closure on influenza transmission was evaluated by the reduction of the effective reproductive number of seasonal influenza during school winter breaks compared with that before school winter breaks. An age-structured Susceptible-Infected-Recovered-Susceptible (SIRS) model was built to model influenza transmission in different levels of urbanization. Parameters were determined using the surveillance data via robust Bayesian method.

RESULTS

Between 2010 and 2019, in the less urbanized provinces: Hebei, Zhejiang, Jiangsu and Anhui, during school winter breaks, the effective reproductive number of seasonal influenza epidemics reduced 14.6% [95% confidential interval (CI): 6.2-22.9%], 9.6% (95% CI: 2.5-16.6%), 7.3% (95% CI: 0.1-14.4%) and 8.2% (95% CI: 1.1-15.3%) respectively. However, in the highly urbanized cities: Beijing, Tianjin and Shanghai, it reduced only 5.2% (95% CI: -0.7-11.2%), 4.1% (95% CI: -0.9-9.1%) and 3.9% (95% CI: -1.6-9.4%) respectively. In China, urbanization is associated with decreased proportion of children and increased social contact. According to the SIRS model, both factors could reduce the impact of school closure on seasonal influenza epidemics, and the proportion of children in the population is thought to be the dominant influencing factor.

CONCLUSIONS

Effectiveness of school closure on the epidemics varies with the age structure in the population and social contact patterns. School closure should be recommended in the low urbanized regions in China in the influenza seasons.

Impact of biometeorological conditions and air pollution on influenza-like illnesses incidence in Warsaw

In order to assess the influence of atmospheric conditions and particulate matter (PM) on the seasonally varying incidence of influenza-like illnesses (ILI) in the capital of Poland-Warsaw, we analysed time series of ILI reported for the about 1.75 million residents in total and for different age groups in 288 approximately weekly periods, covering 6 years 2013-2018. Using Poisson regression, we predicted ILI by the Universal Thermal Climate Index (UTCI) as biometeorological indicator, and by PM2.5 and PM10, respectively, as air quality measures accounting for lagged effects spanning up to 3 weeks. Excess ILI incidence after adjusting for seasonal and annual trends was calculated by fitting generalized additive models. ILI morbidity increased with rising PM concentrations, for both PM2.5 and PM10, and with cooler atmospheric conditions as indicated by decreasing UTCI. While the PM effect focused on the actual reporting period, the atmospheric influence exhibited a more evenly distributed lagged effect pattern over the considered 3-week period. Though ILI incidence adjusted for population size significantly declined with age, age did not significantly modify the effect sizes of both PM and UTCI. These findings contribute to better understanding environmental conditionings of influenza seasonality in a temperate climate. This will be beneficial to forecasting future dynamics of ILI and to planning clinical and public health resources under climate change scenarios.

Influenza A(H1N1)pdm09 but not A(H3N2) virus infection induces durable sero-protection: results from the Ha Nam Cohort

Background

The extent to which influenza recurrence depends upon waning immunity from prior infection is undefined. We used antibody titers of Ha-Nam cohort participants to estimate protection curves and decay trajectories.

Methods

Households (270) participated in influenza-like–illness (ILI) surveillance and provided blood at intervals spanning laboratory–confirmed virus transmission. Sera were tested in hemagglutination inhibition assay. Infection was defined as influenza virus-positive ILI and/or seroconversion. Median protective titers were estimated using scaled-logistic regression to model pretransmission titer against infection status in that season, limiting analysis to households with infection(s). Titers were modelled against month since infection using mixed-effects linear regression to estimate decay and when titers fell below protection thresholds.

Results

From December 2008–2012, 295 and 314 participants were infected with H1N1pdm09-like and A/Perth/16/09-like (H3N2Pe09) viruses, respectively. The proportion protected rose more steeply with titer for H1N1pdm09 than for H3N2Pe09, and estimated 50% protection titers were 19.6 and 37.3, respectively. Postinfection titers started higher against H3N2Pe09 but decayed more steeply than against H1N1pdm09. Seroprotection was estimated to be sustained against H1N1pdm09 but to wane by 8-months for H3N2Pe09.

Conclusions

Estimates indicate that infection induces durable seroprotection against H1N1pdm09 but not H3N2Pe09, which could in part account for the younger age of A(H1N1) versus A(H3N2) cases.

First two months of the 2019 Coronavirus Disease (COVID-19) epidemic in China: real-time surveillance and evaluation with a second derivative model

Background

Similar to outbreaks of many other infectious diseases, success in controlling the novel 2019 coronavirus infection requires a timely and accurate monitoring of the epidemic, particularly during its early period with rather limited data while the need for information increases explosively.

Methods

In this study, we used a second derivative model to characterize the coronavirus epidemic in China with cumulatively diagnosed cases during the first 2 months. The analysis was further enhanced by an exponential model with a close-population assumption. This model was built with the data and used to assess the detection rate during the study period, considering the differences between the true infections, detectable and detected cases.

Results

Results from the second derivative modeling suggest the coronavirus epidemic as nonlinear and chaotic in nature. Although it emerged gradually, the epidemic was highly responsive to massive interventions initiated on January 21, 2020, as indicated by results from both second derivative and exponential modeling analyses. The epidemic started to decelerate immediately after the massive actions. The results derived from our analysis signaled the decline of the epidemic 14 days before it eventually occurred on February 4, 2020. Study findings further signaled an accelerated decline in the epidemic starting in 14 days on February 18, 2020.

Conclusions

The coronavirus epidemic appeared to be nonlinear and chaotic, and was responsive to effective interventions. The methods used in this study can be applied in surveillance to inform and encourage the general public, public health professionals, clinicians and decision-makers to take coordinative and collaborative efforts to control the epidemic.

Prediction of influenza peaks in Russian cities: Comparing the accuracy of two SEIR models

This paper is dedicated to the application of two types of SEIR models to the influenza outbreak peak prediction in Russian cities. The first one is a continuous SEIR model described by a system of ordinary differential equations. The second one is a discrete model formulated as a set of difference equations, which was used in the Baroyan-Rvachev modeling framework for the influenza outbreak prediction in the Soviet Union. The outbreak peak day and height predictions were performed by calibrating both models to varied-size samples of long-term data on ARI incidence in Moscow, Saint Petersburg, and Novosibirsk. The accuracy of the modeling predictions on incomplete data was compared with a number of other peak forecasting methods tested on the same dataset. The drawbacks of the described prediction approach and possible ways to overcome them are discussed.

Epidemic forecasts as a tool for public health: interpretation and (re)calibration

OBJECTIVE

Recent studies have used Bayesian methods to predict timing of influenza epidemics many weeks in advance, but there is no documented evaluation of how such forecasts might support the day-to-day operations of public health staff.

METHODS

During the 2015 influenza season in Melbourne, Australia, weekly forecasts were presented at Health Department surveillance unit meetings, where they were evaluated and updated in light of expert opinion to improve their accuracy and usefulness.

RESULTS

Predictive capacity of the model was substantially limited by delays in reporting and processing arising from an unprecedented number of notifications, disproportionate to seasonal intensity. Adjustment of the predictive algorithm to account for these delays and increased reporting propensity improved both current situational awareness and forecasting accuracy.

CONCLUSIONS

Collaborative engagement with public health practitioners in model development improved understanding of the context and limitations of emerging surveillance data. Incorporation of these insights in a quantitative model resulted in more robust estimates of disease activity for public health use. Implications for public health: In addition to predicting future disease trends, forecasting methods can quantify the impact of delays in data availability and variable reporting practice on the accuracy of current epidemic assessment. Such evidence supports investment in systems capacity.

Explaining the geographical origins of seasonal influenza A (H3N2)

Most antigenically novel and evolutionarily successful strains of seasonal influenza A (H3N2) originate in East, South and Southeast Asia. To understand this pattern, we simulated the ecological and evolutionary dynamics of influenza in a host metapopulation representing the temperate north, tropics and temperate south. Although seasonality and air traffic are frequently used to explain global migratory patterns of influenza, we find that other factors may have a comparable or greater impact. Notably, a region's basic reproductive number (R0) strongly affects the antigenic evolution of its viral population and the probability that its strains will spread and fix globally: a 17-28% higher R0 in one region can explain the observed patterns. Seasonality, in contrast, increases the probability that a tropical (less seasonal) population will export evolutionarily successful strains but alone does not predict that these strains will be antigenically advanced. The relative sizes of different host populations, their birth and death rates, and the region in which H3N2 first appears affect influenza's phylogeography in different but relatively minor ways. These results suggest general principles that dictate the spatial dynamics of antigenically evolving pathogens and offer predictions for how changes in human ecology might affect influenza evolution.

Human mobility networks and persistence of rapidly mutating pathogens

Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the dynamics of the outbreak, including pathogen's epidemiological traits (e.g. transmissibility, infectious period and duration of immunity), seasonality, interaction with other circulating strains and hosts' mixing and spatial fragmentation. Here, we study a susceptible-infected-recovered-susceptible model on a metapopulation where individuals are distributed in sub-populations connected via a network of mobility flows. Through extensive numerical simulations, we explore the phase space of pathogen's persistence and map the dynamical regimes of the pathogen following emergence. Our results show that spatial fragmentation and mobility play a key role in the persistence of the disease whose maximum is reached at intermediate mobility values. We describe the occurrence of different phenomena including local extinction and emergence of epidemic waves, and assess the conditions for large-scale spreading. Findings are highlighted in reference to previous studies and to real scenarios. Our work uncovers the crucial role of hosts' mobility on the ecological dynamics of rapidly mutating pathogens, opening the path for further studies on disease ecology in the presence of a complex and heterogeneous environment.

The optimal treatment of an infectious disease with two strains

This paper explores the optimal treatment of an infectious disease in a Susceptible-Infected-Susceptible model, where there are two strains of the disease and one strain is more infectious than the other. The strains are perfectly distinguishable, instantly diagnosed and equally costly in terms of social welfare. Treatment is equally costly and effective for both strains. Eradication is not possible, and there is no superinfection. In this model, we characterise two types of fixed points: coexistence equilibria, where both strains prevail, and boundary equilibria, where one strain is asymptotically eradicated and the other prevails at a positive level. We derive regimes of feasibility that determine which equilibria are feasible for which parameter combinations. Numerically, we show that optimal policy exhibits switch points over time, and that the paths to coexistence equilibria exhibit spirals, suggesting that coexistence equilibria are never the end points of optimal paths.

Detecting a trend change in cross-border epidemic transmission

A method for a system of Langevin equations is developed for detecting a trend change in cross-border epidemic transmission. The equations represent a standard epidemiological SIR compartment model and a meta-population network model. The method analyzes a time series of the number of new cases reported in multiple geographical regions. The method is applicable to investigating the efficacy of the implemented public health intervention in managing infectious travelers across borders. It is found that the change point of the probability of travel movements was one week after the WHO worldwide alert on the SARS outbreak in 2003. The alert was effective in managing infectious travelers. On the other hand, it is found that the probability of travel movements did not change at all for the flu pandemic in 2009. The pandemic did not affect potential travelers despite the WHO alert.

Substantial Influenza Vaccine Effectiveness in Households With Children During the 2013-2014 Influenza Season, When 2009 Pandemic Influenza A(H1N1) Virus Predominated

BACKGROUND

We examined the influenza vaccine effectiveness (VE) during the 2013-2014 influenza season, in which 2009 pandemic influenza A(H1N1) virus (influenza A[H1N1]pdm09) predominated. In 2 previous years when influenza A(H3N2) virus predominated, the VE was low and negatively affected by prior year vaccination.

METHODS

We enrolled and followed 232 households with 1049 members, including 618 children; specimens were collected from subjects with acute respiratory illnesses. The VE in preventing laboratory-confirmed influenza A(H1N1)pdm09 infection was estimated in adjusted models. Preseason hemagglutination-inhibition and neuraminidase-inhibition antibody titers were determined to assess susceptibility.

RESULTS

Influenza A(H1N1)pdm09 was identified in 25 households (10.8%) and 47 individuals (4.5%). Adjusted VE against infection with influenza A(H1N1)pdm09 was 66% (95% confidence interval [CI], 23%-85%), with similar point estimates in children and adults, and against both community-acquired and household-acquired infections. VE did not appear to be different for live-attenuated and inactivated vaccines among children aged 2-8 years, although numbers were small. VE was similar for subjects vaccinated in both current and prior seasons and for those vaccinated in the current season only; susceptibility titers were consistent with this observation.

CONCLUSIONS

Findings, including substantial significant VE and a lack of a negative effect of repeated vaccination on VE, were in contrast to those seen in prior seasons in which influenza A(H3N2) virus predominated.

Strain Interactions as a Mechanism for Dominant Strain Alternation and Incidence Oscillation in Infectious Diseases: Seasonal Influenza as a Case Study

Background

Many human infectious diseases are caused by pathogens that have multiple strains and show oscillation in infection incidence and alternation of dominant strains which together are referred to as epidemic cycling. Understanding the underlying mechanisms of epidemic cycling is essential for forecasting outbreaks of epidemics and therefore important for public health planning. Current theoretical effort is mainly focused on the factors that are extrinsic to the pathogens themselves (“extrinsic factors”) such as environmental variation and seasonal change in human behaviours and susceptibility. Nevertheless, co-circulation of different strains of a pathogen was usually observed and thus strains interact with one another within concurrent infection and during sequential infection. The existence of these intrinsic factors is common and may be involved in the generation of epidemic cycling of multi-strain pathogens.

Methods and Findings

To explore the mechanisms that are intrinsic to the pathogens themselves (“intrinsic factors”) for epidemic cycling, we consider a multi-strain SIRS model including cross-immunity and infectivity enhancement and use seasonal influenza as an example to parameterize the model. The Kullback-Leibler information distance was calculated to measure the match between the model outputs and the typical features of seasonal flu (an outbreak duration of 11 weeks and an annual attack rate of 15%). Results show that interactions among strains can generate seasonal influenza with these characteristic features, provided that: the infectivity of a single strain within concurrent infection is enhanced 2−7 times that within a single infection; cross-immunity as a result of past infection is 0.5–0.8 and lasts 2–9 years; while other parameters are within their widely accepted ranges (such as a 2–3 day infectious period and the basic reproductive number of 1.8–3.0). Moreover, the observed alternation of the dominant strain among epidemics emerges naturally from the best fit model. Alternative modelling that also includes seasonal forcing in transmissibility shows that both external mechanisms (i.e. seasonal forcing) and the intrinsic mechanisms (i.e., strain interactions) are equally able to generate the observed time-series in seasonal flu.

Conclusions

The intrinsic mechanism of strain interactions alone can generate the observed patterns of seasonal flu epidemics, but according to Kullback-Leibler information distance the importance of extrinsic mechanisms cannot be excluded. The intrinsic mechanism illustrated here to explain seasonal flu may also apply to other infectious diseases caused by polymorphic pathogens.

Influenza-associated mortality in Thailand, 2006-2011

Background

Influenza-associated mortality in subtropical or tropical regions, particularly in developing countries, remains poorly quantified and often underestimated. We analyzed data in Thailand, a middle-income tropical country with good vital statistics and influenza surveillance data.

Methods

We obtained weekly mortality data for all-cause and three underlying causes of death (circulatory and respiratory diseases, and pneumonia and influenza), and weekly influenza virus data, from 2006 to 2011. A negative binomial regression model was used to estimate deaths attributable to influenza in two age groups (<65 and ≥65 years) by incorporating influenza viral data as covariates in the model.

Results

From 2006 to 2011, the average annual influenza-associated mortality per 100 000 persons was 4·0 (95% CI: −18 to 26). Eighty-three percent of influenza-associated deaths occurred among persons aged > 65 years. The average annual rate of influenza-associated deaths was 0·7 (95% CI: −8·2 to 10) per 100 000 population for person aged <65 years and 42 (95% CI: −137 to 216) for person aged ≥ 65 years.

Discussion

In Thailand, estimated excess mortality associated with influenza was considerable even during non-pandemic years. These data provide support for Thailand's seasonal influenza vaccination campaign. Continued monitoring of mortality data is important to assess impact.

Disease Interventions Can Interfere with One Another through Disease-Behaviour Interactions

Theoretical models of disease dynamics on networks can aid our understanding of how infectious diseases spread through a population. Models that incorporate decision-making mechanisms can furthermore capture how behaviour-driven aspects of transmission such as vaccination choices and the use of non-pharmaceutical interventions (NPIs) interact with disease dynamics. However, these two interventions are usually modelled separately. Here, we construct a simulation model of influenza transmission through a contact network, where individuals can choose whether to become vaccinated and/or practice NPIs. These decisions are based on previous experience with the disease, the current state of infection amongst one's contacts, and the personal and social impacts of the choices they make. We find that the interventions interfere with one another: because of negative feedback between intervention uptake and infection prevalence, it is difficult to simultaneously increase uptake of all interventions by changing utilities or perceived risks. However, on account of vaccine efficacy being higher than NPI efficacy, measures to expand NPI practice have only a small net impact on influenza incidence due to strongly mitigating feedback from vaccinating behaviour, whereas expanding vaccine uptake causes a significant net reduction in influenza incidence, despite the reduction of NPI practice in response. As a result, measures that support expansion of only vaccination (such as reducing vaccine cost), or measures that simultaneously support vaccination and NPIs (such as emphasizing harms of influenza infection, or satisfaction from preventing infection in others through both interventions) can significantly reduce influenza incidence, whereas measures that only support expansion of NPI practice (such as making hand sanitizers more available) have little net impact on influenza incidence. (However, measures that improve NPI efficacy may fare better.) We conclude that the impact of interference on programs relying on multiple interventions should be more carefully studied, for both influenza and other infectious diseases.

Computational Characterization of Transient Strain-Transcending Immunity against Influenza A

The enigmatic observation that the rapidly evolving influenza A (H3N2) virus exhibits, at any given time, a limited standing genetic diversity has been an impetus for much research. One of the first generative computational models to successfully recapitulate this pattern of consistently constrained diversity posits the existence of a strong and short-lived strain-transcending immunity. Building on that model, we explored a much broader set of scenarios (parameterizations) of a transient strain-transcending immunity, ran long-term simulations of each such scenario, and assessed its plausibility with respect to a set of known or estimated influenza empirical measures. We evaluated simulated outcomes using a variety of measures, both epidemiological (annual attack rate, epidemic duration, reproductive number, and peak weekly incidence), and evolutionary (pairwise antigenic diversity, fixation rate, most recent common ancestor, and kappa, which quantifies the potential for antigenic evolution). Taking cumulative support from all these measures, we show which parameterizations of strain-transcending immunity are plausible with respect to the set of empirically derived target values. We conclude that strain-transcending immunity which is milder and longer lasting than previously suggested is more congruent with the observed short- and long-term behavior of influenza.

Influenza vaccine efficacy trials: a simulation approach to understand failures from the past

The success of a seasonal influenza vaccine efficacy trial depends not only upon the design but also upon the annual epidemic characteristics. In this context, simulation methods are an essential tool in evaluating the performances of study designs under various circumstances. However, traditional methods for simulating time-to-event data are not suitable for the simulation of influenza vaccine efficacy trials because of the seasonality and heterogeneity of influenza epidemics. Instead, we propose a mathematical model parameterized with historical surveillance data, heterogeneous frailty among the subjects, survey-based heterogeneous number of daily contact, and a mixed vaccine protection mechanism. We illustrate our methodology by generating multiple-trial data similar to a large phase III trial that failed to show additional relative vaccine efficacy of an experimental adjuvanted vaccine compared with the reference vaccine. We show that small departures from the designing assumptions, such as a smaller range of strain protection for the experimental vaccine or the chosen endpoint, could lead to smaller probabilities of success in showing significant relative vaccine efficacy.

Statistical identifiability and sample size calculations for serial seroepidemiology

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We investigate whether disease dynamics can be inferred by repeated serum collections.

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Measuring antibody waning is critical for inference in serological time series.

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Collecting 200 samples every 2 months allows for inference of transmission parameters.

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Low-level seasonality is difficult to detect statistically.

Inference on disease dynamics is typically performed using case reporting time series of symptomatic disease. The inferred dynamics will vary depending on the reporting patterns and surveillance system for the disease in question, and the inference will miss mild or underreported epidemics. To eliminate the variation introduced by differing reporting patterns and to capture asymptomatic or subclinical infection, inferential methods can be applied to serological data sets instead of case reporting data. To reconstruct complete disease dynamics, one would need to collect a serological time series. In the statistical analysis presented here, we consider a particular kind of serological time series with repeated, periodic collections of population-representative serum. We refer to this study design as a serial seroepidemiology (SSE) design, and we base the analysis on our epidemiological knowledge of influenza. We consider a study duration of three to four years, during which a single antigenic type of influenza would be circulating, and we evaluate our ability to reconstruct disease dynamics based on serological data alone. We show that the processes of reinfection, antibody generation, and antibody waning confound each other and are not always statistically identifiable, especially when dynamics resemble a non-oscillating endemic equilibrium behavior. We introduce some constraints to partially resolve this confounding, and we show that transmission rates and basic reproduction numbers can be accurately estimated in SSE study designs. Seasonal forcing is more difficult to identify as serology-based studies only detect oscillations in antibody titers of recovered individuals, and these oscillations are typically weaker than those observed for infected individuals. To accurately estimate the magnitude and timing of seasonal forcing, serum samples should be collected every two months and 200 or more samples should be included in each collection; this sample size estimate is sensitive to the antibody waning rate and the assumed level of seasonal forcing.

The Possible Impact of Vaccination for Seasonal Influenza on Emergence of Pandemic Influenza via Reassortment

BACKGROUND

One pathway through which pandemic influenza strains might emerge is reassortment from coinfection of different influenza A viruses. Seasonal influenza vaccines are designed to target the circulating strains, which intuitively decreases the prevalence of coinfection and the chance of pandemic emergence due to reassortment. However, individual-based analyses on 2009 pandemic influenza show that the previous seasonal vaccination may increase the risk of pandemic A(H1N1) pdm09 infection. In view of pandemic influenza preparedness, it is essential to understand the overall effect of seasonal vaccination on pandemic emergence via reassortment.

METHODS AND FINDINGS

In a previous study we applied a population dynamics approach to investigate the effect of infection-induced cross-immunity on reducing such a pandemic risk. Here the model was extended by incorporating vaccination for seasonal influenza to assess its potential role on the pandemic emergence via reassortment and its effect in protecting humans if a pandemic does emerge. The vaccination is assumed to protect against the target strains but only partially against other strains. We find that a universal seasonal vaccine that provides full-spectrum cross-immunity substantially reduces the opportunity of pandemic emergence. However, our results show that such effectiveness depends on the strength of infection-induced cross-immunity against any novel reassortant strain. If it is weak, the vaccine that induces cross-immunity strongly against non-target resident strains but weakly against novel reassortant strains, can further depress the pandemic emergence; if it is very strong, the same kind of vaccine increases the probability of pandemic emergence.

CONCLUSIONS

Two types of vaccines are available: inactivated and live attenuated, only live attenuated vaccines can induce heterosubtypic immunity. Current vaccines are effective in controlling circulating strains; they cannot always help restrain pandemic emergence because of the uncertainty of the oncoming reassortant strains, however. This urges the development of universal vaccines for prevention of pandemic influenza.

Evaluation of outbreak detection performance using multi-stream syndromic surveillance for influenza-like illness in rural Hubei Province, China: a temporal simulation model based on healthcare-seeking behaviors

BACKGROUND

Syndromic surveillance promotes the early detection of diseases outbreaks. Although syndromic surveillance has increased in developing countries, performance on outbreak detection, particularly in cases of multi-stream surveillance, has scarcely been evaluated in rural areas.

OBJECTIVE

This study introduces a temporal simulation model based on healthcare-seeking behaviors to evaluate the performance of multi-stream syndromic surveillance for influenza-like illness.

METHODS

Data were obtained in six towns of rural Hubei Province, China, from April 2012 to June 2013. A Susceptible-Exposed-Infectious-Recovered model generated 27 scenarios of simulated influenza A (H1N1) outbreaks, which were converted into corresponding simulated syndromic datasets through the healthcare-behaviors model. We then superimposed converted syndromic datasets onto the baselines obtained to create the testing datasets. Outbreak performance of single-stream surveillance of clinic visit, frequency of over the counter drug purchases, school absenteeism, and multi-stream surveillance of their combinations were evaluated using receiver operating characteristic curves and activity monitoring operation curves.

RESULTS

In the six towns examined, clinic visit surveillance and school absenteeism surveillance exhibited superior performances of outbreak detection than over the counter drug purchase frequency surveillance; the performance of multi-stream surveillance was preferable to signal-stream surveillance, particularly at low specificity (Sp <90%).

CONCLUSIONS

The temporal simulation model based on healthcare-seeking behaviors offers an accessible method for evaluating the performance of multi-stream surveillance.

Estimating the effectiveness of early control measures through school absenteeism surveillance in observed outbreaks at rural schools in Hubei, China

BACKGROUND

School absenteeism is a common data source in syndromic surveillance, which allows for the detection of outbreaks at an early stage. Previous studies focused on its correlation with other data sources. In this study, we evaluated the effectiveness of control measures based on early warning signals from school absenteeism surveillance in rural Chinese schools.

METHODS

A school absenteeism surveillance system was established in all 17 primary schools in 3 adjacent towns in the Chinese region of Hubei. Three outbreaks (varicella, mumps, and influenza-like illness) were detected and controlled successfully from April 1, 2012, to January 15, 2014. An impulse susceptible-exposed-infectious-recovered model was used to fit the epidemics of these three outbreaks. Moreover, it simulated the potential epidemics under interventions resulting from traditional surveillance signals. The effectiveness of the absenteeism-based control measures was evaluated by comparing the simulated datasets.

RESULTS

The school absenteeism system generated 52 signals. Three outbreaks were verified through epidemiological investigation. Compared to traditional surveillance, the school absenteeism system generated simultaneous signals for the varicella outbreak, but 3 days in advance for the mumps outbreak and 2-4 days in advance for the influenza-like illness outbreak. The estimated excess protection rates of control measures based on early signals were 0.0%, 19.0-44.1%, and 29.0-37.0% for the three outbreaks, respectively.

CONCLUSIONS

Although not all outbreak control measures can benefit from early signals through school absenteeism surveillance, the effectiveness of early signal-based interventions is obvious. School absenteeism surveillance plays an important role in reducing outbreak spread.

Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature

BACKGROUND

The potential impact of an influenza pandemic can be assessed by calculating a set of transmissibility parameters, the most important being the reproduction number (R), which is defined as the average number of secondary cases generated per typical infectious case.

METHODS

We conducted a systematic review to summarize published estimates of R for pandemic or seasonal influenza and for novel influenza viruses (e.g. H5N1). We retained and summarized papers that estimated R for pandemic or seasonal influenza or for human infections with novel influenza viruses.

RESULTS

The search yielded 567 papers. Ninety-one papers were retained, and an additional twenty papers were identified from the references of the retained papers. Twenty-four studies reported 51 R values for the 1918 pandemic. The median R value for 1918 was 1.80 (interquartile range [IQR]: 1.47-2.27). Six studies reported seven 1957 pandemic R values. The median R value for 1957 was 1.65 (IQR: 1.53-1.70). Four studies reported seven 1968 pandemic R values. The median R value for 1968 was 1.80 (IQR: 1.56-1.85). Fifty-seven studies reported 78 2009 pandemic R values. The median R value for 2009 was 1.46 (IQR: 1.30-1.70) and was similar across the two waves of illness: 1.46 for the first wave and 1.48 for the second wave. Twenty-four studies reported 47 seasonal epidemic R values. The median R value for seasonal influenza was 1.28 (IQR: 1.19-1.37). Four studies reported six novel influenza R values. Four out of six R values were <1.

CONCLUSIONS

These R values represent the difference between epidemics that are controllable and cause moderate illness and those causing a significant number of illnesses and requiring intensive mitigation strategies to control. Continued monitoring of R during seasonal and novel influenza outbreaks is needed to document its variation before the next pandemic.

Rate of decline of antibody titers to pandemic influenza A (H1N1-2009) by hemagglutination inhibition and virus microneutralization assays in a cohort of seroconverting adults in Singapore

Background

The rate of decline of antibody titers to influenza following infection can affect results of serological surveys, and may explain re-infection and recurrent epidemics by the same strain.

Methods

We followed up a cohort who seroconverted on hemagglutination inhibition (HI) antibody titers (≥4-fold increase) to pandemic influenza A(H1N1)pdm09 during a seroincidence study in 2009. Along with the pre-epidemic sample, and the sample from 2009 with the highest HI titer between August and October 2009 (A), two additional blood samples obtained in April 2010 and September 2010 (B and C) were assayed for antibodies to A(H1N1)pdm09 by both HI and virus microneutralization (MN) assays. We analyzed pair-wise mean-fold change in titers and the proportion with HI titers ≥ 40 and MN ≥ 160 (which correlated with a HI titer of 40 in our assays) at the 3 time-points following seroconversion.

Results

A total of 67 participants contributed 3 samples each. From the highest HI titer in 2009 to the last sample in 2010, 2 participants showed increase in titers (by HI and MN), while 63 (94%) and 49 (73%) had reduction in HI and MN titers, respectively. Titers by both assays decreased significantly; while 70.8% and 72.3% of subjects had titers of ≥ 40 and ≥ 160 by HI and MN in 2009, these percentages decreased to 13.9% and 36.9% by September 2010. In 6 participants aged 55 years and older, the decrease was significantly greater than in those aged below 55, so that none of the elderly had HI titers ≥ 40 nor MN titers ≥ 160 by the final sample. Due to this decline in titers, only 23 (35%) of the 65 participants who seroconverted on HI in sample A were found to seroconvert between the pre-epidemic sample and sample C, compared to 53 (90%) of the 59 who seroconverted on MN on Sample A.

Conclusions

We observed marked reduction in titers 1 year after seroconversion by HI, and to a lesser extent by MN. Our findings have implications for re-infections, recurrent epidemics, vaccination strategies, and for cohort studies measuring infection rates by seroconversion.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2334-14-414) contains supplementary material, which is available to authorized users.

4Flu - an individual based simulation tool to study the effects of quadrivalent vaccination on seasonal influenza in Germany

BACKGROUND

Influenza vaccines contain Influenza A and B antigens and are adjusted annually to match the characteristics of circulating viruses. In Germany, Influenza B viruses belonged to the B/Yamagata lineage, but since 2001, the antigenically distinct B/Victoria lineage has been co-circulating. Trivalent influenza vaccines (TIV) contain antigens of the two A subtypes A(H3N2) and A(H1N1), yet of only one B lineage, resulting in frequent vaccine mismatches. Since 2012, the WHO has been recommending vaccine strains from both B lineages, paving the way for quadrivalent influenza vaccines (QIV).

METHODS

Using an individual-based simulation tool, we simulate the concomitant transmission of four influenza strains, and compare the effects of TIV and QIV on the infection incidence. Individuals are connected in a dynamically evolving age-dependent contact network based on the POLYMOD matrix; their age-distribution reproduces German demographic data and predictions. The model considers maternal protection, boosting of existing immunity, loss of immunity, and cross-immunizing events between the B lineages. Calibration to the observed annual infection incidence of 10.6% among young adults yielded a basic reproduction number of 1.575. Vaccinations are performed annually in October and November, whereby coverage depends on the vaccinees' age, their risk status and previous vaccination status. New drift variants are introduced at random time points, leading to a sudden loss of protective immunity for part of the population and occasionally to reduced vaccine efficacy. Simulations run for 50 years, the first 30 of which are used for initialization. During the final 20 years, individuals receive TIV or QIV, using a mirrored simulation approach.

RESULTS

Using QIV, the mean annual infection incidence can be reduced from 8,943,000 to 8,548,000, i.e. by 395,000 infections, preventing 11.2% of all Influenza B infections which still occur with TIV (95% CI: 10.7-11.8%). Using a lower B lineage cross protection than the baseline 60%, the number of Influenza B infections increases and the number additionally prevented by QIV can be 5.5 times as high.

CONCLUSIONS

Vaccination with TIV substantially reduces the Influenza incidence compared to no vaccination. Depending on the assumed degree of B lineage cross protection, QIV further reduces Influenza B incidence by 11-33%.

Dynamically correlated mutations drive human Influenza A evolution

Human Influenza A virus undergoes recurrent changes in the hemagglutinin (HA) surface protein, primarily involved in the human antibody recognition. Relevant antigenic changes, enabling the virus to evade host immune response, have been recognized to occur in parallel to multiple mutations at antigenic sites in HA. Yet, the role of correlated mutations (epistasis) in driving the molecular evolution of the virus still represents a challenging puzzle. Further, though circulation at a global geographic level is key for the survival of Influenza A, its role in shaping the viral phylodynamics remains largely unexplored. Here we show, through a sequence based epidemiological model, that epistatic effects between amino acids substitutions, coupled with a reservoir that mimics worldwide circulating viruses, are key determinants that drive human Influenza A evolution. Our approach explains all the up-to-date observations characterizing the evolution of H3N2 subtype, including phylogenetic properties, nucleotide fixation patterns, and composition of antigenic clusters.

The impact of coinfections and their simultaneous transmission on antigenic diversity and epidemic cycling of infectious diseases

Epidemic cycling in human infectious diseases is common; however, its underlying mechanisms have been poorly understood. Much effort has been made to search for external mechanisms. Multiple strains of an infectious agent were usually observed and coinfections were frequent; further, empirical evidence indicates the simultaneous transmission of coinfections. To explore intrinsic mechanisms for epidemic cycling, in this study we consider a multistrain Susceptible-Infected-Recovered-Susceptible epidemic model by including coinfections and simultaneous transmission. We show that coinfections and their simultaneous transmission widen the parameter range for coexistence and coinfections become popular when strains enhance each other and the immunity wanes quickly. However, the total prevalence is nearly independent of these characteristics and approximated by that of one-strain model. With sufficient simultaneous transmission and antigenic diversity, cyclical epidemics can be generated even when strains interfere with each other by reducing infectivity. This indicates that strain interactions within coinfections and cross-immunity during subsequent infection provide a possible intrinsic mechanism for epidemic cycling.

Multiannual forecasting of seasonal influenza dynamics reveals climatic and evolutionary drivers

Human influenza occurs annually in most temperate climatic zones of the world, with epidemics peaking in the cold winter months. Considerable debate surrounds the relative role of epidemic dynamics, viral evolution, and climatic drivers in driving year-to-year variability of outbreaks. The ultimate test of understanding is prediction; however, existing influenza models rarely forecast beyond a single year at best. Here, we use a simple epidemiological model to reveal multiannual predictability based on high-quality influenza surveillance data for Israel; the model fit is corroborated by simple metapopulation comparisons within Israel. Successful forecasts are driven by temperature, humidity, antigenic drift, and immunity loss. Essentially, influenza dynamics are a balance between large perturbations following significant antigenic jumps, interspersed with nonlinear epidemic dynamics tuned by climatic forcing.

Estimated effects of projected climate change on the basic reproductive number of the Lyme disease vector Ixodes scapularis

BACKGROUND

The extent to which climate change may affect human health by increasing risk from vector-borne diseases has been under considerable debate.

OBJECTIVES

We quantified potential effects of future climate change on the basic reproduction number (R0) of the tick vector of Lyme disease, Ixodes scapularis, and explored their importance for Lyme disease risk, and for vector-borne diseases in general.

METHODS

We applied observed temperature data for North America and projected temperatures using regional climate models to drive an I. scapularis population model to hindcast recent, and project future, effects of climate warming on R0. Modeled R0 increases were compared with R0 ranges for pathogens and parasites associated with variations in key ecological and epidemiological factors (obtained by literature review) to assess their epidemiological importance.

RESULTS

R0 for I. scapularis in North America increased during the years 1971-2010 in spatio-temporal patterns consistent with observations. Increased temperatures due to projected climate change increased R0 by factors (2-5 times in Canada and 1.5-2 times in the United States), comparable to observed ranges of R0 for pathogens and parasites due to variations in strains, geographic locations, epidemics, host and vector densities, and control efforts.

CONCLUSIONS

Climate warming may have co-driven the emergence of Lyme disease in northeastern North America, and in the future may drive substantial disease spread into new geographic regions and increase tick-borne disease risk where climate is currently suitable. Our findings highlight the potential for climate change to have profound effects on vectors and vector-borne diseases, and the need to refocus efforts to understand these effects.

Spatio-temporal synchrony of influenza in cities across Israel: the "Israel is one city" hypothesis

We analysed an 11-year dataset (1998-2009) of Influenza-Like Illness (ILI) that was based on surveillance of ∽23% of Israel's population. We examined whether the level of synchrony of ILI epidemics in Israel's 12 largest cities is high enough to view Israel as a single epidemiological unit. Two methods were developed to assess the synchrony: (1) City-specific attack rates were fitted to a simple model in order to estimate the temporal differences in attack rates and spatial differences in reporting rates of ILI. The model showed good fit to the data (R2  =  0.76) and revealed considerable differences in reporting rates of ILI in different cities (up to a factor of 2.2). (2) A statistical test was developed to examine the null hypothesis (H0) that ILI incidence curves in two cities are essentially identical, and was tested using ILI data. Upon examining all possible pairs of incidence curves, 77.4% of pairs were found not to be different (H0 was not rejected). It was concluded that all cities generally have the same attack rate and follow the same epidemic curve each season, although the attack rate changes from season to season, providing strong support for the "Israel is one city" hypothesis. The cities which were the most out of synchronization were Bnei Brak, Beersheba and Haifa, the latter two being geographically remote from all other cities in the dataset and the former geographically very close to several other cities but socially separate due to being populated almost exclusively by ultra-orthodox Jews. Further evidence of assortative mixing of the ultra-orthodox population can be found in the 2001-2002 season, when ultra-orthodox cities and neighborhoods showed distinctly different incidence curves compared to the general population.

Effect of the one-child policy on influenza transmission in China: a stochastic transmission model

BACKGROUND

China's one-child-per-couple policy, introduced in 1979, led to profound demographic changes for nearly a quarter of the world's population. Several decades later, the consequences include decreased fertility rates, population aging, decreased household sizes, changes in family structure, and imbalanced sex ratios. The epidemiology of communicable diseases may have been affected by these changes since the transmission dynamics of infectious diseases depend on demographic characteristics of the population. Of particular interest is influenza because China and Southeast Asia lie at the center of a global transmission network of influenza. Moreover, changes in household structure may affect influenza transmission. Is it possible that the pronounced demographic changes that have occurred in China have affected influenza transmission?

METHODS AND FINDINGS

To address this question, we developed a continuous-time, stochastic, individual-based simulation model for influenza transmission. With this model, we simulated 30 years of influenza transmission and compared influenza transmission rates in populations with and without the one-child policy control. We found that the average annual attack rate is reduced by 6.08% (SD 2.21%) in the presence of the one-child policy compared to a population in which no demographic changes occurred. There was no discernible difference in the secondary attack rate, -0.15% (SD 1.85%), between the populations with and without a one-child policy. We also forecasted influenza transmission over a ten-year time period in a population with a two-child policy under a hypothesis that a two-child-per-couple policy will be carried out in 2015, and found a negligible difference in the average annual attack rate compared to the population with the one-child policy.

CONCLUSIONS

This study found that the average annual attack rate is slightly lowered in a population with a one-child policy, which may have resulted from a decrease in household size and the proportion of children in the population.

Guess who's not coming to dinner? Evaluating online restaurant reservations for disease surveillance

Background

Alternative data sources are used increasingly to augment traditional public health surveillance systems. Examples include over-the-counter medication sales and school absenteeism.

Objective

We sought to determine if an increase in restaurant table availabilities was associated with an increase in disease incidence, specifically influenza-like illness (ILI).

Methods

Restaurant table availability was monitored using OpenTable, an online restaurant table reservation site. A daily search was performed for restaurants with available tables for 2 at the hour and at half past the hour for 22 distinct times: between 11:00 am-3:30 pm for lunch and between 6:00-11:30 PM for dinner. In the United States, we examined table availability for restaurants in Boston, Atlanta, Baltimore, and Miami. For Mexico, we studied table availabilities in Cancun, Mexico City, Puebla, Monterrey, and Guadalajara. Time series of restaurant use was compared with Google Flu Trends and ILI at the state and national levels for the United States and Mexico using the cross-correlation function.

Results

Differences in restaurant use were observed across sampling times and regions. We also noted similarities in time series trends between data on influenza activity and restaurant use. In some settings, significant correlations greater than 70% were noted between data on restaurant use and ILI trends.

Conclusions

This study introduces and demonstrates the potential value of restaurant use data for event surveillance.

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.

Optimal strategies of social distancing and vaccination against seasonal influenza

Optimal control strategies for controlling seasonal influenza transmission in the US are of high interest, because of the significant epidemiological and economic burden of influenza. To evaluate optimal strategies of vaccination and social distancing, we used an age-structured dynamic model of seasonal influenza. We applied optimal control theory to identify the best way of reducing morbidity and mortality at a minimal cost. In combination with the Pontryagins maximum principle, we calculated time-dependent optimal policies of vaccination and social distancing to minimize the epidemiological and economic burden associated with seasonal influenza. We computed optimal age-specific intervention strategies and analyze them under various costs of interventions and disease transmissibility. Our results show that combined strategies have a stronger impact on the reduction of the final epidemic size. Our results also suggest that the optimal vaccination can be achieved by allocating most vaccines to preschool-age children (age under five) followed by young adults (age 20-39) and school age children (age 6-19). We find that the optimal vaccination rates for all age groups are highest at the beginning of the outbreak, requiring intense effort at the early phase of an epidemic. On the other hand, optimal social distancing of clinical cases tends to last the entire duration of an outbreak, and its intensity is relatively equal for all age groups. Furthermore, with higher transmissibility of the influenza virus (i.e. higher R0), the optimal control strategy needs to include more efforts to increase vaccination rates rather than efforts to encourage social distancing. Taken together, public health agencies need to consider both the transmissibility of the virus and ways to encourage early vaccination as well as voluntary social distancing of symptomatic cases in order to determine optimal intervention strategies against seasonal influenza.

Modelling seasonal influenza: the role of weather and punctuated antigenic drift

Seasonal influenza appears as annual oscillations in temperate regions of the world, yet little is known as to what drives these annual outbreaks and what factors are responsible for their inter-annual variability. Recent studies suggest that weather variables, such as absolute humidity, are the key drivers of annual influenza outbreaks. The rapid, punctuated, antigenic evolution of the influenza virus is another major factor. We present a new framework for modelling seasonal influenza based on a discrete-time, age-of-infection, epidemic model, which allows the calculation of the model's likelihood function in closed form. This framework may be used to perform model inference and parameter estimation rigorously. The modelling approach allows us to fit 11 years of Israeli influenza data, with the best models fitting the data with unusually high correlations in which r > 0.9. We show that using actual weather to modulate influenza transmission rate gives better results than using the inter-annual means of the weather variables, providing strong support for the role of weather in shaping the dynamics of influenza. This conclusion remains valid even when incorporating a more realistic depiction of the decay of immunity at the population level, which allows for discrete changes in immunity from year to year.

Forecasting peaks of seasonal influenza epidemics

We present a framework for near real-time forecast of influenza epidemics using a simulation optimization approach. The method combines an individual-based model and a simple root finding optimization method for parameter estimation and forecasting. In this study, retrospective forecasts were generated for seasonal influenza epidemics using web-based estimates of influenza activity from Google Flu Trends for 2004-2005, 2007-2008 and 2012-2013 flu seasons. In some cases, the peak could be forecasted 5-6 weeks ahead. This study adds to existing resources for influenza forecasting and the proposed method can be used in conjunction with other approaches in an ensemble framework.

Understanding the dynamics of seasonal influenza in Italy: incidence, transmissibility and population susceptibility in a 9-year period

OBJECTIVES

Influenza surveillance systems have been established in many countries in the world, yielding timely information about the intensity and features of seasonal outbreaks. Such data have also been used to estimate epidemiological parameters and to evaluate the effect of factors on infection dynamics. However, little is known about the extent of under-reporting in surveillance data, and thus of the true influenza incidence in the population.

DESIGN

Through mathematical and statistical modelling, we analysed Italian epidemiological and virological surveillance data collected together with serological data derived from influenza vaccine clinical trials performed in Italy.

RESULTS

Depending on the season, the reporting rate estimates ranged between 20% and 33% of the total incidence with higher reporting rates in seasons dominated by A/H3N2 virus. Despite a generally higher number of individuals immune against A/H3N2 viruses, effective reproduction ratios were quite similar in all seasons varying between 1·2 and 1·4. We observed an age-dependent transmissibility for different subtypes: susceptible children were more likely than susceptible adults and elderly to get infected when A/H1N1 or B strains were circulating, while no clear age-dependence was found for A/H3N2. We also perform sensitivity analysis under different assumptions for vaccine effectiveness, generation time (GT) and model variants; we found that the overall results in predicted patterns were extremely similar, with a slightly better fit obtained with shorter GTs.

CONCLUSIONS

Our results provide relevant information on the influenza dynamics to fine-tune intervention strategies and for data collection improvement.

Environmental predictors of seasonal influenza epidemics across temperate and tropical climates

Human influenza infections exhibit a strong seasonal cycle in temperate regions. Recent laboratory and epidemiological evidence suggests that low specific humidity conditions facilitate the airborne survival and transmission of the influenza virus in temperate regions, resulting in annual winter epidemics. However, this relationship is unlikely to account for the epidemiology of influenza in tropical and subtropical regions where epidemics often occur during the rainy season or transmit year-round without a well-defined season. We assessed the role of specific humidity and other local climatic variables on influenza virus seasonality by modeling epidemiological and climatic information from 78 study sites sampled globally. We substantiated that there are two types of environmental conditions associated with seasonal influenza epidemics: "cold-dry" and "humid-rainy". For sites where monthly average specific humidity or temperature decreases below thresholds of approximately 11-12 g/kg and 18-21°C during the year, influenza activity peaks during the cold-dry season (i.e., winter) when specific humidity and temperature are at minimal levels. For sites where specific humidity and temperature do not decrease below these thresholds, seasonal influenza activity is more likely to peak in months when average precipitation totals are maximal and greater than 150 mm per month. These findings provide a simple climate-based model rooted in empirical data that accounts for the diversity of seasonal influenza patterns observed across temperate, subtropical and tropical climates.

Policy resistance undermines superspreader vaccination strategies for influenza

Theoretical models of infection spread on networks predict that targeting vaccination at individuals with a very large number of contacts (superspreaders) can reduce infection incidence by a significant margin. These models generally assume that superspreaders will always agree to be vaccinated. Hence, they cannot capture unintended consequences such as policy resistance, where the behavioral response induced by a new vaccine policy tends to reduce the expected benefits of the policy. Here, we couple a model of influenza transmission on an empirically-based contact network with a psychologically structured model of influenza vaccinating behavior, where individual vaccinating decisions depend on social learning and past experiences of perceived infections, vaccine complications and vaccine failures. We find that policy resistance almost completely undermines the effectiveness of superspreader strategies: the most commonly explored approaches that target a randomly chosen neighbor of an individual, or that preferentially choose neighbors with many contacts, provide at best a 2% relative improvement over their non-targeted counterpart as compared to 12% when behavioral feedbacks are ignored. Increased vaccine coverage in super spreaders is offset by decreased coverage in non-superspreaders, and superspreaders also have a higher rate of perceived vaccine failures on account of being infected more often. Including incentives for vaccination provides modest improvements in outcomes. We conclude that the design of influenza vaccine strategies involving widespread incentive use and/or targeting of superspreaders should account for policy resistance, and mitigate it whenever possible.

Indirect transmission and the effect of seasonal pathogen inactivation on infectious disease periodicity

The annual occurrence of many infectious diseases remains a constant burden to public health systems. The seasonal patterns in respiratory disease incidence observed in temperate regions have been attributed to the impact of environmental conditions on pathogen survival. A model describing the transmission of an infectious disease by means of a pathogenic state capable of surviving in an environmental reservoir outside of its host organism is presented in this paper. The ratio of pathogen lifespan to the duration of the infectious disease state is found to be a critical parameter in determining disease dynamics. The introduction of a seasonally forced pathogen inactivation rate identifies a time delay between peak pathogen survival and peak disease incidence. The delay is dependent on specific disease parameters and, for influenza, decreases with increasing reproduction number. The observed seasonal oscillations are found to have a period identical to that of the seasonally forced inactivation rate and which is independent of the duration of infection acquired immunity.

Phylodynamic inference and model assessment with approximate bayesian computation: influenza as a case study

A key priority in infectious disease research is to understand the ecological and evolutionary drivers of viral diseases from data on disease incidence as well as viral genetic and antigenic variation. We propose using a simulation-based, Bayesian method known as Approximate Bayesian Computation (ABC) to fit and assess phylodynamic models that simulate pathogen evolution and ecology against summaries of these data. We illustrate the versatility of the method by analyzing two spatial models describing the phylodynamics of interpandemic human influenza virus subtype A(H3N2). The first model captures antigenic drift phenomenologically with continuously waning immunity, and the second epochal evolution model describes the replacement of major, relatively long-lived antigenic clusters. Combining features of long-term surveillance data from the Netherlands with features of influenza A (H3N2) hemagglutinin gene sequences sampled in northern Europe, key phylodynamic parameters can be estimated with ABC. Goodness-of-fit analyses reveal that the irregularity in interannual incidence and H3N2's ladder-like hemagglutinin phylogeny are quantitatively only reproduced under the epochal evolution model within a spatial context. However, the concomitant incidence dynamics result in a very large reproductive number and are not consistent with empirical estimates of H3N2's population level attack rate. These results demonstrate that the interactions between the evolutionary and ecological processes impose multiple quantitative constraints on the phylodynamic trajectories of influenza A(H3N2), so that sequence and surveillance data can be used synergistically. ABC, one of several data synthesis approaches, can easily interface a broad class of phylodynamic models with various types of data but requires careful calibration of the summaries and tolerance parameters.

The infectious disease dynamics of many viral pathogens like influenza, norovirus and coronavirus are inextricably tied to their evolution. This interaction between evolutionary and ecological processes complicates our ability to understand the infectious disease behavior of rapidly evolving pathogens. Most statistical methods for the analysis of these “phylodynamics” require that the likelihood of the data can be explicitly calculated. Currently, this is not possible for many phylodynamic models, so that questions on the interaction between viral variants cannot be well-addressed within this framework. Simulation-based statistical methods circumvent likelihood calculations. Considering interpandemic human influenza A virus subtype H3N2, we here illustrate the effectiveness of these methods to fit and assess complex phylodynamic models against both sequence and surveillance data. We find that combining molecular genetic and epidemiological data is key to estimate phylodynamic parameters reliably. Moreover, the information in the available data taken together is enough to expose quantitative model inconsistencies. Methods such as ABC which can combine sequence and surveillance data appear to be well-suited to fit and assess mechanistic hypotheses on the phylodynamics of RNA viruses.

Co-circulation of influenza A virus strains and emergence of pandemic via reassortment: the role of cross-immunity

Reassortment is an important evolutionary route for influenza A viruses to generate pandemic strains. The pre-requisite for reassortment to occur is co-infection of different influenza virus strains in the same host population. Empirical evidence suggests that co-circulation of influenza A virus strains is common and co-infection in patients has been reported. Whether a novel virus can successfully spread among a host population is determined by its life-history (infectivity and infectious period). It is also well known that different influenza A strains interfere through the immune response of human body cells. The reassortant virus strain generated from co-infections deviates dramatically in antigenic and genetic properties from its parental strains such that human populations have limited immunity against it. We consider a mathematical model which includes two strains of influenza virus within a standard SIR model and integrate life history and cross-immunity into the evolutionary dynamics of influenza virus. We assume that, following primary infection by one strain and recovery, individuals are susceptible to secondary infection by the other strain only but with reduced probability due to cross-immunity. Co-infection is included to examine how life-history and cross-immunity interplay to regulate the co-circulation and co-infection of different influenza A virus strains in human populations. Further, we introduce novel strains via reassortment and investigate how the opportunities of a reassortant strain developing into a pandemic are constrained by its life-history and the residual immunity within human populations. We find that though the probability of pandemic emergence via reassortment increases with transmissibility of reassortant strains and the rate of reassortment, the existence of cross-immunity acquired through previous infections or vaccination can greatly constrain pandemic emergence.

The role of social contacts and original antigenic sin in shaping the age pattern of immunity to seasonal influenza

Recent serological studies of seasonal influenza A in humans suggest a striking characteristic profile of immunity against age, which holds across different countries and against different subtypes of influenza. For both H1N1 and H3N2, the proportion of the population seropositive to recently circulated strains peaks in school-age children, reaches a minimum between ages 35–65, then rises again in the older ages. This pattern is little understood. Variable mixing between different age classes can have a profound effect on disease dynamics, and is hence the obvious candidate explanation for the profile, but using a mathematical model of multiple influenza strains, we see that age dependent transmission based on mixing data from social contact surveys cannot on its own explain the observed pattern. Instead, the number of seropositive individuals in a population may be a consequence of ‘original antigenic sin’; if the first infection of a lifetime dominates subsequent immune responses, we demonstrate that it is possible to reproduce the observed relationship between age and seroprevalence. We propose a candidate mechanism for this relationship, by which original antigenic sin, along with antigenic drift and vaccination, results in the age profile of immunity seen in empirical studies.

The way in which a population builds immunity to influenza affects outbreak size and the emergence of new strains. However, although age-specific immunity has been widely discussed for the 2009 influenza pandemic, the age profile of immunity to seasonal influenza remains little understood. In contrast to many infections, the proportion of people immune to recent strains peaks in school-age children then reaches a minimum between ages 35–65, before rising again in older age groups. Our results suggest that rather than variable mixing between different age groups being solely responsible, the pattern may be shaped by an effect known as ‘original antigenic sin’, by which the first infection of a lifetime dictates subsequent immune responses: instead of developing antibodies to every new virus that is encountered, the immune system may reuse the response to a similar virus it has already seen. The framework we describe, which extends theoretical models to allow for comparison with data, also opens the possibility of investigating the mechanisms behind patterns of immunity to other evolving pathogens.