Sensitivity Analysis of an Individual-Based Model for Simulation of Influenza Epidemics

Individual-based epidemiology models are increasingly used in the study of influenza epidemics. Several studies on influenza dynamics and evaluation of intervention measures have used the same incubation and infectious period distribution parameters based on the natural history of influenza. A sensitivity analysis evaluating the influence of slight changes to these parameters (in addition to the transmissibility) would be useful for future studies and real-time modeling during an influenza pandemic.In this study, we examined individual and joint effects of parameters and ranked parameters based on their influence on the dynamics of simulated epidemics. We also compared the sensitivity of the model across synthetic social networks for Montgomery County in Virginia and New York City (and surrounding metropolitan regions) with demographic and rural-urban differences. In addition, we studied the effects of changing the mean infectious period on age-specific epidemics. The research was performed from a public health standpoint using three relevant measures: time to peak, peak infected proportion and total attack rate. We also used statistical methods in the design and analysis of the experiments.The results showed that: (i) minute changes in the transmissibility and mean infectious period significantly influenced the attack rate; (ii) the mean of the incubation period distribution appeared to be sufficient for determining its effects on the dynamics of epidemics; (iii) the infectious period distribution had the strongest influence on the structure of the epidemic curves; (iv) the sensitivity of the individual-based model was consistent across social networks investigated in this study and (v) age-specific epidemics were sensitive to changes in the mean infectious period irrespective of the susceptibility of the other age groups. These findings suggest that small changes in some of the disease model parameters can significantly influence the uncertainty observed in real-time forecasting and predicting of the characteristics of an epidemic.     

Forecasting the 2013–2014 Influenza Season Using Wikipedia

Infectious diseases are one of the leading causes of morbidity and mortality around the world; thus, forecasting their impact is crucial for planning an effective response strategy. According to the Centers for Disease Control and Prevention (CDC), seasonal influenza affects 5% to 20% of the U.S. population and causes major economic impacts resulting from hospitalization and absenteeism. Understanding influenza dynamics and forecasting its impact is fundamental for developing prevention and mitigation strategies. We combine modern data assimilation methods with Wikipedia access logs and CDC influenza-like illness (ILI) reports to create a weekly forecast for seasonal influenza. The methods are applied to the 2013-2014 influenza season but are sufficiently general to forecast any disease outbreak, given incidence or case count data. We adjust the initialization and parametrization of a disease model and show that this allows us to determine systematic model bias. In addition, we provide a way to determine where the model diverges from observation and evaluate forecast accuracy. Wikipedia article access logs are shown to be highly correlated with historical ILI records and allow for accurate prediction of ILI data several weeks before it becomes available. The results show that prior to the peak of the flu season, our forecasting method produced 50% and 95% credible intervals for the 2013-2014 ILI observations that contained the actual observations for most weeks in the forecast. However, since our model does not account for re-infection or multiple strains of influenza, the tail of the epidemic is not predicted well after the peak of flu season has passed.     

Influenza A/H1N1 2009 Pandemic and Respiratory Virus Infections,Beijing, 2009–2010

To determine the role of the pandemic influenza A/H1N1 2009 (A/H1N1 2009pdm) in acute respiratory tract infections (ARTIs) and its impact on the epidemic of seasonal influenza viruses and other common respiratory viruses, nasal and throat swabs taken from 7,776 patients with suspected viral ARTIs from 2006 through 2010 in Beijing, China were screened by real-time PCR for influenza virus typing and subtyping and by multiplex or single PCR tests for other common respiratory viruses. We observed a distinctive dual peak pattern of influenza epidemic during the A/H1N1 2009pdm in Beijing, China, which was formed by the A/H1N1 2009pdm, and a subsequent influenza B epidemic in year 2009/2010. Our analysis also shows a small peak formed by a seasonal H3N2 epidemic prior to the A/H1N1 2009pdm peak. Parallel detection of multiple respiratory viruses shows that the epidemic of common respiratory viruses, except human rhinovirus, was delayed during the pandemic of the A/H1N1 2009pdm. The H1N1 2009pdm mainly caused upper respiratory tract infections in the sampled patients; patients infected with H1N1 2009pdm had a higher percentage of cough than those infected with seasonal influenza or other respiratory viruses. Our findings indicate that A/H1N1 2009pdm and other respiratory viruses except human rhinovirus could interfere with each other during their transmission between human beings. Understanding the mechanisms and effects of such interference is needed for effective control of future influenza epidemics.     

Predictive Validation of an Influenza Spread Model

Background

Modeling plays a critical role in mitigating impacts of seasonal influenza epidemics. Complex simulation models are currently at the forefront of evaluating optimal mitigation strategies at multiple scales and levels of organization. Given their evaluative role, these models remain limited in their ability to predict and forecast future epidemics leading some researchers and public-health practitioners to question their usefulness. The objective of this study is to evaluate the predictive ability of an existing complex simulation model of influenza spread.

Methods and Findings

We used extensive data on past epidemics to demonstrate the process of predictive validation. This involved generalizing an individual-based model for influenza spread and fitting it to laboratory-confirmed influenza infection data from a single observed epidemic (1998–1999). Next, we used the fitted model and modified two of its parameters based on data on real-world perturbations (vaccination coverage by age group and strain type). Simulating epidemics under these changes allowed us to estimate the deviation/error between the expected epidemic curve under perturbation and observed epidemics taking place from 1999 to 2006. Our model was able to forecast absolute intensity and epidemic peak week several weeks earlier with reasonable reliability and depended on the method of forecasting-static or dynamic.

Conclusions

Good predictive ability of influenza epidemics is critical for implementing mitigation strategies in an effective and timely manner. Through the process of predictive validation applied to a current complex simulation model of influenza spread, we provided users of the model (e.g. public-health officials and policy-makers) with quantitative metrics and practical recommendations on mitigating impacts of seasonal influenza epidemics. This methodology may be applied to other models of communicable infectious diseases to test and potentially improve their predictive ability.     

Predicting seasonal influenza using supermarket retail records

Increased availability of epidemiological data, novel digital data streams, and the rise of powerful machine learning approaches have generated a surge of research activity on real-time epidemic forecast systems. In this paper, we propose the use of a novel data source, namely retail market data to improve seasonal influenza forecasting. Specifically, we consider supermarket retail data as a proxy signal for influenza, through the identification of sentinel baskets, i.e., products bought together by a population of selected customers. We develop a nowcasting and forecasting framework that provides estimates for influenza incidence in Italy up to 4 weeks ahead. We make use of the Support Vector Regression (SVR) model to produce the predictions of seasonal flu incidence. Our predictions outperform both a baseline autoregressive model and a second baseline based on product purchases. The results show quantitatively the value of incorporating retail market data in forecasting models, acting as a proxy that can be used for the real-time analysis of epidemics.     

A Two-Year Surveillance of 2009 Pandemic Influenza A (H1N1) in Guangzhou,China: From Pandemic to Seasonal Influenza?

In this two-years surveillance of 2009 pandemic influenza A (H1N1) (pH1N1) in Guangzhou, China, we reported here that the scale and duration of pH1N1 outbreaks, severe disease and fatality rates of pH1N1 patients were significantly lower or shorter in the second epidemic year (May 2010-April 2011) than those in the first epidemic year (May 2009-April 2010) (P<0.05), but similar to those of seasonal influenza (P>0.05). Similar to seasonal influenza, pre-existing chronic pulmonary diseases was a risk factor associated with fatal cases of pH1N1 influenza. Different from seasonal influenza, which occurred in spring/summer seasons annually, pH1N1 influenza mainly occurred in autumn/winter seasons in the first epidemic year, but prolonged to winter/spring season in the second epidemic year. The information suggests a tendency that the epidemics of pH1N1 influenza may probably further shift to spring/summer seasons and become a predominant subtype of seasonal influenza in coming years in Guangzhou, China.     

Transmission of a 2009 pandemic influenza virus shows a sensitivity to temperature and humidity similar to that of an H3N2 seasonal strain

In temperate regions of the world, influenza epidemics follow a highly regular seasonal pattern, in which activity peaks in midwinter. Consistently with this epidemiology, we have shown previously that the aerosol transmission of a seasonal H3N2 influenza virus is most efficient under cold, dry conditions. With the 2009 H1N1 pandemic, an exception to the standard seasonality of influenza developed: during 2009 in the Northern Hemisphere, an unusually high level of influenza virus activity over the spring and summer months was followed by a widespread epidemic which peaked in late October, approximately 2.5 months earlier than usual. Herein we show that aerosol transmission of a 2009 pandemic strain shows a dependence on relative humidity and temperature very similar to that of a seasonal H3N2 influenza virus. Our data indicate that the observed differences in the timings of outbreaks with regard to the seasons are most likely not due to intrinsic differences in transmission between the pandemic H1N1 and seasonal H3N2 influenza viruses.     

Accurate influenza forecasts using type-specific incidence data for small geographic units

Influenza incidence forecasting is used to facilitate better health system planning and could potentially be used to allow at-risk individuals to modify their behavior during a severe seasonal influenza epidemic or a novel respiratory pandemic. For example, the US Centers for Disease Control and Prevention (CDC) runs an annual competition to forecast influenza-like illness (ILI) at the regional and national levels in the US, based on a standard discretized incidence scale. Here, we use a suite of forecasting models to analyze type-specific incidence at the smaller spatial scale of clusters of nearby counties. We used data from point-of-care (POC) diagnostic machines over three seasons, in 10 clusters, capturing: 57 counties; 1,061,891 total specimens; and 173,909 specimens positive for Influenza A. Total specimens were closely correlated with comparable CDC ILI data. Mechanistic models were substantially more accurate when forecasting influenza A positive POC data than total specimen POC data, especially at longer lead times. Also, models that fit subpopulations of the cluster (individual counties) separately were better able to forecast clusters than were models that directly fit to aggregated cluster data. Public health authorities may wish to consider developing forecasting pipelines for type-specific POC data in addition to ILI data. Simple mechanistic models will likely improve forecast accuracy when applied at small spatial scales to pathogen-specific data before being scaled to larger geographical units and broader syndromic data. Highly local forecasts may enable new public health messaging to encourage at-risk individuals to temporarily reduce their social mixing during seasonal peaks and guide public health intervention policy during potentially severe novel influenza pandemics.     

Epidemiologic and economic effectiveness of school closure during influenza epidemics and pandemics

Epidemiologic and economic effectiveness of school closure during influenza epidemics and pandemics is discussed. Optimal effect of school closure is observed when this measure is taken at the start of the epidemic or pandemic and for a sufficiently long time. School closure during high morbidity among schoolchildren, in the middle (at the peak) and by the end of epidemic or pandemic does not influence significantly the spread of influenza or morbidity. Significant economic losses and other negative consequences of school closure are noted. School closure may be the most appropriate during the emergence of influenza pandemic when the pandemic vaccine is not yet available, however timely mass immunization of schoolchildren against influenza may be a more appropriate measure than school closure for the reduction of influenza morbidity and spread during seasonal influenza epidemics.     

Comparing pandemic to seasonal influenza mortality: moderate impact overall but high mortality in young children

Background

We assessed the severity of the 2009 influenza pandemic by comparing pandemic mortality to seasonal influenza mortality. However, reported pandemic deaths were laboratory-confirmed – and thus an underestimation – whereas seasonal influenza mortality is often more inclusively estimated. For a valid comparison, our study used the same statistical methodology and data types to estimate pandemic and seasonal influenza mortality.

Methods and Findings

We used data on all-cause mortality (1999–2010, 100% coverage, 16.5 million Dutch population) and influenza-like-illness (ILI) incidence (0.8% coverage). Data was aggregated by week and age category. Using generalized estimating equation regression models, we attributed mortality to influenza by associating mortality with ILI-incidence, while adjusting for annual shifts in association. We also adjusted for respiratory syncytial virus, hot/cold weather, other seasonal factors and autocorrelation. For the 2009 pandemic season, we estimated 612 (range 266–958) influenza-attributed deaths; for seasonal influenza 1,956 (range 0–3,990). 15,845 years-of-life-lost were estimated for the pandemic; for an average seasonal epidemic 17,908. For 0–4 yrs of age the number of influenza-attributed deaths during the pandemic were higher than in any seasonal epidemic; 77 deaths (range 61–93) compared to 16 deaths (range 0–45). The ≥75 yrs of age showed a far below average number of deaths. Using pneumonia/influenza and respiratory/cardiovascular instead of all-cause deaths consistently resulted in relatively low total pandemic mortality, combined with high impact in the youngest age category.

Conclusion

The pandemic had an overall moderate impact on mortality compared to 10 preceding seasonal epidemics, with higher mortality in young children and low mortality in the elderly. This resulted in a total number of pandemic deaths far below the average for seasonal influenza, and a total number of years-of-life-lost somewhat below average. Comparing pandemic and seasonal influenza mortality as in our study will help assessing the worldwide impact of the 2009 pandemic.     

Key strategies for reducing spread of avian influenza among commercial poultry holdings: lessons for transmission to humans

Recent avian flu epidemics (A/H5N1) in Southeast Asia and case reports from around the world have led to fears of a human pandemic. Control of these outbreaks in birds would probably lead to reduced transmission of the avian virus to humans. This study presents a mathematical model based on stochastic farm-to-farm transmission that incorporates flock size and spatial contacts to evaluate the impact of control strategies. Fit to data from the recent epidemic in the Netherlands, we evaluate the efficacy of control strategies and forecast avian influenza dynamics. Our results identify high-risk areas of spread by mapping of the farm level reproductive number. Results suggest that an immediate depopulation of infected flocks following an accurate and quick diagnosis would have a greater impact than simply depopulating surrounding flocks. Understanding the relative importance of different control measures is essential for response planning.     

Impact of the 2009 H1N1 Pandemic on Age-Specific Epidemic Curves of Other Respiratory Viruses: A Comparison of Pre-Pandemic,Pandemic and Post-Pandemic Periods in a Subtropical City

Background

The 2009 H1N1 influenza pandemic caused offseason peaks in temperate regions but coincided with the summer epidemic of seasonal influenza and other common respiratory viruses in subtropical Hong Kong. This study was aimed to investigate the impact of the pandemic on age-specific epidemic curves of other respiratory viruses.

Methods

Weekly laboratory-confirmed cases of influenza A (subtypes seasonal A(H1N1), A(H3N2), pandemic virus A(H1N1)pdm09), influenza B, respiratory syncytial virus (RSV), adenovirus and parainfluenza were obtained from 2004 to 2013. Age-specific epidemic curves of viruses other than A(H1N1)pdm09 were compared between the pre-pandemic (May 2004 – April 2009), pandemic (May 2009 – April 2010) and post-pandemic periods (May 2010 – April 2013).

Results

There were two peaks of A(H1N1)pdm09 in Hong Kong, the first in September 2009 and the second in February 2011. The infection rate was found highest in young children in both waves, but markedly fewer cases in school children were recorded in the second wave than in the first wave. Positive proportions of viruses other than A(H1N1)pdm09 markedly decreased in all age groups during the first pandemic wave. After the first wave of the pandemic, the positive proportion of A(H3N2) increased, but those of B and RSV remained slightly lower than their pre-pandemic proportions. Changes in seasonal pattern and epidemic peak time were also observed, but inconsistent across virus-age groups.

Conclusion

Our findings provide some evidence that age distribution, seasonal pattern and peak time of other respiratory viruses have changed since the pandemic. These changes could be the result of immune interference and changing health seeking behavior, but the mechanism behind still needs further investigations.     

Comparison of Filtering Methods for the Modeling and Retrospective Forecasting of Influenza Epidemics

A variety of filtering methods enable the recursive estimation of system state variables and inference of model parameters. These methods have found application in a range of disciplines and settings, including engineering design and forecasting, and, over the last two decades, have been applied to infectious disease epidemiology. For any system of interest, the ideal filter depends on the nonlinearity and complexity of the model to which it is applied, the quality and abundance of observations being entrained, and the ultimate application (e.g. forecast, parameter estimation, etc.). Here, we compare the performance of six state-of-the-art filter methods when used to model and forecast influenza activity. Three particle filters—a basic particle filter (PF) with resampling and regularization, maximum likelihood estimation via iterated filtering (MIF), and particle Markov chain Monte Carlo (pMCMC)—and three ensemble filters—the ensemble Kalman filter (EnKF), the ensemble adjustment Kalman filter (EAKF), and the rank histogram filter (RHF)—were used in conjunction with a humidity-forced susceptible-infectious-recovered-susceptible (SIRS) model and weekly estimates of influenza incidence. The modeling frameworks, first validated with synthetic influenza epidemic data, were then applied to fit and retrospectively forecast the historical incidence time series of seven influenza epidemics during 2003–2012, for 115 cities in the United States. Results suggest that when using the SIRS model the ensemble filters and the basic PF are more capable of faithfully recreating historical influenza incidence time series, while the MIF and pMCMC do not perform as well for multimodal outbreaks. For forecast of the week with the highest influenza activity, the accuracies of the six model-filter frameworks are comparable; the three particle filters perform slightly better predicting peaks 1–5 weeks in the future; the ensemble filters are more accurate predicting peaks in the past.     

Use of Hangeul Twitter to Track and Predict Human Influenza Infection

Influenza epidemics arise through the accumulation of viral genetic changes. The emergence of new virus strains coincides with a higher level of influenza-like illness (ILI), which is seen as a peak of a normal season. Monitoring the spread of an epidemic influenza in populations is a difficult and important task. Twitter is a free social networking service whose messages can improve the accuracy of forecasting models by providing early warnings of influenza outbreaks. In this study, we have examined the use of information embedded in the Hangeul Twitter stream to detect rapidly evolving public awareness or concern with respect to influenza transmission and developed regression models that can track levels of actual disease activity and predict influenza epidemics in the real world. Our prediction model using a delay mode provides not only a real-time assessment of the current influenza epidemic activity but also a significant improvement in prediction performance at the initial phase of ILI peak when prediction is of most importance.     

Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: Assessing the effects of hypothetical interventions

Recurrent outbreaks of the avian H5N1 influenza virus in Asia represent a constant global pandemic threat. We characterize and evaluate hypothetical public health measures during the 1918 influenza pandemic in the Canton of Geneva, Switzerland. The transmission rate, the recovery rate, the diagnostic rate, the relative infectiousness of asymptomatic cases, and the proportion of clinical cases are estimated through least-squares fitting of the model to epidemic curve data of the cumulative number of hospital notifications. The latent period and the case fatality proportion are taken from published literature. We determine the variance and identifiability of model parameters via a simulation study. Our epidemic model agrees well with the observed epidemic data. We estimate the basic reproductive number for the spring wave R1;=1.49 (95% CI: 1.45-1.53) and the reproductive number for the fall wave R2;=3.75 (95% CI: 3.57-3.93). In addition, we estimate the clinical reporting for these two waves to be 59.7% (95% CI: 55.7-63.7) and 83% (95% CI: 79-87). We surmise that the lower reporting in the first wave can be explained by a lack of initial awareness of the epidemic and the relative higher severity of the symptoms experienced during the fall wave. We found that effective isolation measures in hospital clinics at best would only ensure control with probability 0.87 while reducing the transmission rate by >76.5% guarantees stopping an epidemic.     

Corporate preparedness for pandemic influenza: a survey of pharmaceutical and biotechnology companies in Montgomery County, Maryland

Objectives: We conducted a survey of corporate preparedness for pandemic influenza among biotechnology and pharmaceutical companies in Montgomery County, Maryland, to determine the level of preparedness for this industry and geographic region. Methods: The survey, based on the HHS Business Pandemic Influenza Planning Checklist, established whether a company had a preparedness plan specific to pandemic influenza, the contents of its plan, or its reasons for a lack of a plan. Results: A total of 50 companies participated in the survey. Of these, 40 did not have any type of preparedness plan, 3 were drafting plans, 6 had general preparedness plans that could be applied to an influenza pandemic, and only 1 company had a preparedness plan specifically designed to address pandemic influenza. Conclusions: Biotechnology and pharmaceutical companies in this geographic region are currently not well prepared for pandemic influenza. Public health officials should offer more help, possibly in the form of a model small business preparedness plan, and collaboration between companies should be encouraged to foster sharing of preparedness plans.     

The impact of seasonal and year-round transmission regimes on the evolution of influenza A virus

Punctuated antigenic change is believed to be a key element in the evolution of influenza A; clusters of antigenically similar strains predominate worldwide for several years until an antigenically distant mutant emerges and instigates a selective sweep. It is thought that a region of East-Southeast Asia with year-round transmission acts as a source of antigenic diversity for influenza A and seasonal epidemics in temperate regions make little contribution to antigenic evolution. We use a mathematical model to examine how different transmission regimes affect the evolutionary dynamics of influenza over the lifespan of an antigenic cluster. Our model indicates that, in non-seasonal regions, mutants that cause significant outbreaks appear before the peak of the wild-type epidemic. A relatively large proportion of these mutants spread globally. In seasonal regions, mutants that cause significant local outbreaks appear each year before the seasonal peak of the wild-type epidemic, but only a small proportion spread globally. The potential for global spread is strongly influenced by the intensity of non-seasonal circulation and coupling between non-seasonal and seasonal regions. Results are similar if mutations are neutral, or confer a weak to moderate antigenic advantage. However, there is a threshold antigenic advantage, depending on the non-seasonal transmission intensity, beyond which mutants can escape herd immunity in the non-seasonal region and there is a global explosion in diversity. We conclude that non-seasonal transmission regions are fundamental to the generation and maintenance of influenza diversity owing to their epidemiology. More extensive sampling of viral diversity in such regions could facilitate earlier identification of antigenically novel strains and extend the critical window for vaccine development.     

Mitigation strategies for pandemic influenza A: balancing conflicting policy objectives

Mitigation of a severe influenza pandemic can be achieved using a range of interventions to reduce transmission. Interventions can reduce the impact of an outbreak and buy time until vaccines are developed, but they may have high social and economic costs. The non-linear effect on the epidemic dynamics means that suitable strategies crucially depend on the precise aim of the intervention. National pandemic influenza plans rarely contain clear statements of policy objectives or prioritization of potentially conflicting aims, such as minimizing mortality (depending on the severity of a pandemic) or peak prevalence or limiting the socio-economic burden of contact-reducing interventions. We use epidemiological models of influenza A to investigate how contact-reducing interventions and availability of antiviral drugs or pre-pandemic vaccines contribute to achieving particular policy objectives. Our analyses show that the ideal strategy depends on the aim of an intervention and that the achievement of one policy objective may preclude success with others, e.g., constraining peak demand for public health resources may lengthen the duration of the epidemic and hence its economic and social impact. Constraining total case numbers can be achieved by a range of strategies, whereas strategies which additionally constrain peak demand for services require a more sophisticated intervention. If, for example, there are multiple objectives which must be achieved prior to the availability of a pandemic vaccine (i.e., a time-limited intervention), our analysis shows that interventions should be implemented several weeks into the epidemic, not at the very start. This observation is shown to be robust across a range of constraints and for uncertainty in estimates of both R(0) and the timing of vaccine availability. These analyses highlight the need for more precise statements of policy objectives and their assumed consequences when planning and implementing strategies to mitigate the impact of an influenza pandemic.     

Flexible Modeling of Epidemics with an Empirical Bayes Framework

Seasonal influenza epidemics cause consistent, considerable, widespread loss annually in terms of economic burden, morbidity, and mortality. With access to accurate and reliable forecasts of a current or upcoming influenza epidemic’s behavior, policy makers can design and implement more effective countermeasures. This past year, the Centers for Disease Control and Prevention hosted the “Predict the Influenza Season Challenge”, with the task of predicting key epidemiological measures for the 2013–2014 U.S. influenza season with the help of digital surveillance data. We developed a framework for in-season forecasts of epidemics using a semiparametric Empirical Bayes framework, and applied it to predict the weekly percentage of outpatient doctors visits for influenza-like illness, and the season onset, duration, peak time, and peak height, with and without using Google Flu Trends data. Previous work on epidemic modeling has focused on developing mechanistic models of disease behavior and applying time series tools to explain historical data. However, tailoring these models to certain types of surveillance data can be challenging, and overly complex models with many parameters can compromise forecasting ability. Our approach instead produces possibilities for the epidemic curve of the season of interest using modified versions of data from previous seasons, allowing for reasonable variations in the timing, pace, and intensity of the seasonal epidemics, as well as noise in observations. Since the framework does not make strict domain-specific assumptions, it can easily be applied to some other diseases with seasonal epidemics. This method produces a complete posterior distribution over epidemic curves, rather than, for example, solely point predictions of forecasting targets. We report prospective influenza-like-illness forecasts made for the 2013–2014 U.S. influenza season, and compare the framework’s cross-validated prediction error on historical data to that of a variety of simpler baseline predictors.