Variational data assimilation with epidemic models

Predicting the Behavior of Sparsely-Sampled Systems Across Neurobiology and Epidemiology

Inference is a term that encompasses many techniques including statistical data assimilation (SDA). Unlike machine learning, which is designed to harness predictive power from extremely large data sets, SDA is designed for sparsely-sampled systems. This is the realm of study of nonlinear dynamical systems in nature. Formulated as an optimization procedure, SDA can be considered a path-integral approach to state and parameter estimation. Within this formulation, we can use the physical principle of least action to identify optimal solutions: solutions that are consistent with both measurements and a dynamical model assumed to give rise to those measurements. I review examples from neurobiology and an epidemiological model tailored to the coronavirus SARS-CoV-2, to demonstrate the versatility of SDA across the sciences, and how these distinct applications possess commonalities that can inform one another.

Dynamic calibration with approximate Bayesian computation for a microsimulation of disease spread

The global COVID-19 pandemic brought considerable public and policy attention to the field of infectious disease modelling. A major hurdle that modellers must overcome, particularly when models are used to develop policy, is quantifying the uncertainty in a model's predictions. By including the most recent available data in a model, the quality of its predictions can be improved and uncertainties reduced. This paper adapts an existing, large-scale, individual-based COVID-19 model to explore the benefits of updating the model in pseudo-real time. We use Approximate Bayesian Computation (ABC) to dynamically recalibrate the model's parameter values as new data emerge. ABC offers advantages over alternative calibration methods by providing information about the uncertainty associated with particular parameter values and the resulting COVID-19 predictions through posterior distributions. Analysing such distributions is crucial in fully understanding a model and its outputs. We find that forecasts of future disease infection rates are improved substantially by incorporating up-to-date observations and that the uncertainty in forecasts drops considerably in later simulation windows (as the model is provided with additional data). This is an important outcome because the uncertainty in model predictions is often overlooked when models are used in policy.

Effectiveness analysis of multiple epidemic prevention measures in the context of COVID-19 using the SVIRD model and ensemble Kalman filter

The ability to accurately forecast the spread of coronavirus disease 2019 (COVID-19) is of great importance to the resumption of societal normality. Existing methods of epidemic forecasting often ignore the comprehensive analysis of multiple epidemic prevention measures. This paper aims to analyze various epidemic prevention measures through a compound framework. Here, a susceptible-vaccinated-infected-recovered-deceased (SVIRD) model is constructed to consider the effects of population mobility among origin and destination, vaccination, and positive retest populations. And we further use real-time observations to correct the model trajectory with the help of data assimilation. Seven prevention measures are used to analyze the short-term trend of active cases. The results of the synthetic scene recommended that four measures-improving the vaccination protection rate (IVPR), reducing the number of contacts per person per day (RNCP), selecting the region with less infected people as origin A (SES-O) and limiting population flow entering from A to B per day (LAIP-OD)-are the most effective in the short-term, with maximum reductions of 75%, 53%, 35% and 31%, respectively, in active cases after 150 days. The results of the real-world experiment with Hong Kong as the origin and Shenzhen as the destination indicate that when the daily vaccination rate increased from 5% to 9.5%, the number of active cases decreased by only 7.35%. The results demonstrate that reducing the number of contacts per person per day after productive life resumes is more effective than increasing vaccination rates.

Analysis of COVID-19 in Japan with extended SEIR model and ensemble Kalman filter

We introduce an extended SEIR infectious disease model with data assimilation for the study of the spread of COVID-19. In this framework, undetected asymptomatic and pre-symptomatic cases are taken into account, and the impact of their uncertain proportion is fully investigated. The standard SEIR model does not consider these populations, while their role in the propagation of the disease is acknowledged. An ensemble Kalman filter is implemented to assimilate reliable observations of three compartments in the model. The system tracks the evolution of the effective reproduction number and estimates the unobservable subpopulations. The analysis is carried out for three main prefectures of Japan and for the entire country of Japan. For these four communities, our estimated effective reproduction numbers are more stable than the corresponding ones estimated by a different method (Toyokeizai). We also perform sensitivity tests for different values of some uncertain medical parameters, like the relative infectivity of symptomatic/asymptomatic cases. The regional analysis results suggest the decreasing efficiency of the states of emergency.

Dynamic downscaling and daily nowcasting from influenza surveillance data

Real-time trends from surveillance data are important to assess and develop preparedness for influenza outbreaks. The overwhelming testing demand and limited capacity of testing laboratories for viral positivity render daily confirmed case data inaccurate and delay its availability in preparedness. Using Bayesian dynamic downscaling models, we obtained posterior estimates for daily influenza incidences from weekly estimates of the Centers for Disease Control and Prevention and daily reported constitutional and respiratory complaints during emergency department (ED) visits obtained from the state health departments. Our model provides one-day and seven-day lead forecasts along with 95 % $$ \% $$ prediction intervals. Our hybrid Markov Chain Monte Carlo and Kalman filter algorithms facilitate faster computation and enable us to update our estimates as new data become available. Our method is tested and validated using the State of Michigan data over the years 2009-2013. Reported constitutional and respiratory complaints at the EDs showed strong correlations of 0.81 and 0.68 respectively, with influenza rates. In general, our forecast model can be adapted to track an outbreak with only one respiratory virus as a causative agent.

Analysis of COVID-19 Spread in Tokyo through an Agent-Based Model with Data Assimilation

In this paper, we introduce an agent-based model together with a particle filter approach to study the spread of COVID-19. Investigations are mainly performed on the metropolis of Tokyo, but other prefectures of Japan are also briefly surveyed. A novel method for evaluating the effective reproduction number is one of the main outcomes of our approach. Other unknown parameters are also evaluated. Uncertain quantities, such as, for example, the probability that an infected agent develops symptoms, are tested and discussed, and the stability of our computations is examined. Detailed explanations are provided for the model and for the assimilation process.

Analyzing the effects of observation function selection in ensemble Kalman filtering for epidemic models

The Ensemble Kalman Filter (EnKF) is a popular sequential data assimilation method that has been increasingly used for parameter estimation and forecast prediction in epidemiological studies. The observation function plays a critical role in the EnKF framework, connecting the unknown system variables with the observed data. Key differences in observed data and modeling assumptions have led to the use of different observation functions in the epidemic modeling literature. In this work, we present a novel computational analysis demonstrating the effects of observation function selection when using the EnKF for state and parameter estimation in this setting. In examining the use of four epidemiologically-inspired observation functions of different forms in connection with the classic Susceptible-Infectious-Recovered (SIR) model, we show how incorrect observation modeling assumptions (i.e., fitting incidence data with a prevalence model, or neglecting under-reporting) can lead to inaccurate filtering estimates and forecast predictions. Results demonstrate the importance of choosing an observation function that well interprets the available data on the corresponding EnKF estimates in several filtering scenarios, including state estimation with known parameters, and combined state and parameter estimation with both constant and time-varying parameters. Numerical experiments further illustrate how modifying the observation noise covariance matrix in the filter can help to account for uncertainty in the observation function in certain cases.

Effectiveness of isolation policies in schools: evidence from a mathematical model of influenza and COVID-19

Background

Non-pharmaceutical interventions such as social distancing, school closures and travel restrictions are often implemented to control outbreaks of infectious diseases. For influenza in schools, the Center of Disease Control (CDC) recommends that febrile students remain isolated at home until they have been fever-free for at least one day and a related policy is recommended for SARS-CoV-2 (COVID-19). Other authors proposed using a school week of four or fewer days of in-person instruction for all students to reduce transmission. However, there is limited evidence supporting the effectiveness of these interventions.

Methods

We introduced a mathematical model of school outbreaks that considers both intervention methods. Our model accounts for the school structure and schedule, as well as the time-progression of fever symptoms and viral shedding. The model was validated on outbreaks of seasonal and pandemic influenza and COVID-19 in schools. It was then used to estimate the outbreak curves and the proportion of the population infected (attack rate) under the proposed interventions.

Results

For influenza, the CDC-recommended one day of post-fever isolation can reduce the attack rate by a median (interquartile range) of 29 (13–59)%. With 2 days of post-fever isolation the attack rate could be reduced by 70 (55–85)%. Alternatively, shortening the school week to 4 and 3 days reduces the attack rate by 73 (64–88)% and 93 (91–97)%, respectively. For COVID-19, application of post-fever isolation policy was found to be less effective and reduced the attack rate by 10 (5–17)% for a 2-day isolation policy and by 14 (5–26)% for 14 days. A 4-day school week would reduce the median attack rate in a COVID-19 outbreak by 57 (52–64)%, while a 3-day school week would reduce it by 81 (79–83)%. In both infections, shortening the school week significantly reduced the duration of outbreaks.

Conclusions

Shortening the school week could be an important tool for controlling influenza and COVID-19 in schools and similar settings. Additionally, the CDC-recommended post-fever isolation policy for influenza could be enhanced by requiring two days of isolation instead of one.

An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter

In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), and vaccinated (V). Initially, a mathematical analysis is carried out to illustrate the non-negativity, boundedness, epidemic equilibrium, existence, and uniqueness of the endemic equilibrium, and the basic reproduction number of the proposed model. Such numerical models can be, however, subject to various sources of uncertainties, due to an imperfect description of the biological processes governing the disease spread, which may strongly limit their forecasting skills. A data assimilation method, mainly, the ensemble Kalman filter (EnKF), is then used to constrain the model outputs and its parameters with available data. We conduct joint state-parameters estimation experiments assimilating daily data into the proposed model using the EnKF in order to enhance the model’s forecasting skills. Starting from the estimated set of model parameters, we then conduct short-term predictions in order to assess the predicability range of the model. We apply the proposed assimilation system on real data sets from Saudi Arabia. The numerical results demonstrate the capability of the proposed model in achieving accurate prediction of the epidemic development up to two-week time scales. Finally, we investigate the effect of vaccination on the spread of the pandemic.

'Dark matter', second waves and epidemiological modelling

Recent reports using conventional Susceptible, Exposed, Infected and Removed models suggest that the next wave of the COVID-19 pandemic in the UK could overwhelm health services, with fatalities exceeding the first wave. We used Bayesian model comparison to revisit these conclusions, allowing for heterogeneity of exposure, susceptibility and transmission. We used dynamic causal modelling to estimate the evidence for alternative models of daily cases and deaths from the USA, the UK, Brazil, Italy, France, Spain, Mexico, Belgium, Germany and Canada over the period 25 January 2020 to 15 June 2020. These data were used to estimate the proportions of people (i) not exposed to the virus, (ii) not susceptible to infection when exposed and (iii) not infectious when susceptible to infection. Bayesian model comparison furnished overwhelming evidence for heterogeneity of exposure, susceptibility and transmission. Furthermore, both lockdown and the build-up of population immunity contributed to viral transmission in all but one country. Small variations in heterogeneity were sufficient to explain large differences in mortality rates. The best model of UK data predicts a second surge of fatalities will be much less than the first peak. The size of the second wave depends sensitively on the loss of immunity and the efficacy of Find-Test-Trace-Isolate-Support programmes. In summary, accounting for heterogeneity of exposure, susceptibility and transmission suggests that the next wave of the SARS-CoV-2 pandemic will be much smaller than conventional models predict, with less economic and health disruption. This heterogeneity means that seroprevalence underestimates effective herd immunity and, crucially, the potential of public health programmes.

Effectiveness of Isolation Policies in Schools: Evidence from a Mathematical Model of Influenza and COVID-19

Background

Non-pharmaceutical interventions such as social distancing, school closures and travel restrictions are often implemented to control outbreaks of infectious diseases. For influenza in schools, the Center of Disease Control (CDC) recommends that febrile students remain isolated at home until they have been fever-free for at least one day and a related policy is recommended for SARS-CoV2 (COVID-19). Other authors proposed using a school week of four or fewer days of in-person instruction for all students to reduce transmission. However, there is limited evidence supporting the effectiveness of these interventions.

Methods

We introduced a mathematical model of school outbreaks that considers both intervention methods. Our model accounts for the school structure and schedule, as well as the time-progression of fever symptoms and viral shedding. The model was validated on outbreaks of seasonal and pandemic influenza and COVID-19 in schools. It was then used to estimate the outbreak curves and the proportion of the population infected (attack rate) under the proposed interventions.

Results

For influenza, the CDC-recommended one day of post-fever isolation can reduce the attack rate by a median (interquartile range) of 29 (13 - 59)%. With two days of post-fever isolation the attack rate could be reduced by 70 (55 - 85)%. Alternatively, shortening the school week to four and three days reduces the attack rate by 73 (64 - 88)% and 93 (91 - 97)%, respectively. For COVID-19, application of post-fever isolation policy was found to be less effective and reduced the attack rate by 10 (5 - 17)% for a two-day isolation policy and by 14 (5 - 26)% for 14 days. A four-day school week would reduce the median attack rate in a COVID-19 outbreak by 57 (52 - 64)%, while a three-day school week would reduce it by 81 (79 - 83)%. In both infections, shortening the school week significantly reduced the duration of outbreaks.

Conclusions

Shortening the school week could be an important tool for controlling influenza and COVID-19 in schools and similar settings. Additionally, the CDC-recommended post-fever isolation policy for influenza could be enhanced by requiring two days of isolation instead of one.

Identifying the measurements required to estimate rates of COVID-19 transmission, infection, and detection, using variational data assimilation

We demonstrate the ability of statistical data assimilation (SDA) to identify the measurements required for accurate state and parameter estimation in an epidemiological model for the novel coronavirus disease COVID-19. Our context is an effort to inform policy regarding social behavior, to mitigate strain on hospital capacity. The model unknowns are taken to be: the time-varying transmission rate, the fraction of exposed cases that require hospitalization, and the time-varying detection probabilities of new asymptomatic and symptomatic cases. In simulations, we obtain estimates of undetected (that is, unmeasured) infectious populations, by measuring the detected cases together with the recovered and dead - and without assumed knowledge of the detection rates. Given a noiseless measurement of the recovered population, excellent estimates of all quantities are obtained using a temporal baseline of 101 days, with the exception of the time-varying transmission rate at times prior to the implementation of social distancing. With low noise added to the recovered population, accurate state estimates require a lengthening of the temporal baseline of measurements. Estimates of all parameters are sensitive to the contamination, highlighting the need for accurate and uniform methods of reporting. The aim of this paper is to exemplify the power of SDA to determine what properties of measurements will yield estimates of unknown parameters to a desired precision, in a model with the complexity required to capture important features of the COVID-19 pandemic.

Effective immunity and second waves: a dynamic causal modelling study

This technical report addresses a pressing issue in the trajectory of the coronavirus outbreak; namely, the rate at which effective immunity is lost following the first wave of the pandemic. This is a crucial epidemiological parameter that speaks to both the consequences of relaxing lockdown and the propensity for a second wave of infections. Using a dynamic causal model of reported cases and deaths from multiple countries, we evaluated the evidence models of progressively longer periods of immunity. The results speak to an effective population immunity of about three months that, under the model, defers any second wave for approximately six months in most countries. This may have implications for the window of opportunity for tracking and tracing, as well as for developing vaccination programmes, and other therapeutic interventions.

Effective immunity and second waves: a dynamic causal modelling study

This technical report addresses a pressing issue in the trajectory of the coronavirus outbreak; namely, the rate at which effective immunity is lost following the first wave of the pandemic. This is a crucial epidemiological parameter that speaks to both the consequences of relaxing lockdown and the propensity for a second wave of infections. Using a dynamic causal model of reported cases and deaths from multiple countries, we evaluated the evidence models of progressively longer periods of immunity. The results speak to an effective population immunity of about three months that, under the model, defers any second wave for approximately six months in most countries. This may have implications for the window of opportunity for tracking and tracing, as well as for developing vaccination programmes, and other therapeutic interventions.

Simulation of the COVID-19 epidemic on the social network of Slovenia: Estimating the intrinsic forecast uncertainty

In the article a virus transmission model is constructed on a simplified social network. The social network consists of more than 2 million nodes, each representing an inhabitant of Slovenia. The nodes are organised and interconnected according to the real household and elderly-care center distribution, while their connections outside these clusters are semi-randomly distributed and undirected. The virus spread model is coupled to the disease progression model. The ensemble approach with the perturbed transmission and disease parameters is used to quantify the ensemble spread, a proxy for the forecast uncertainty. The presented ongoing forecasts of COVID-19 epidemic in Slovenia are compared with the collected Slovenian data. Results show that at the end of the first epidemic wave, the infection was twice more likely to transmit within households/elderly care centers than outside them. We use an ensemble of simulations (N = 1000) and data assimilation approach to estimate the COVID-19 forecast uncertainty and to inversely obtain posterior distributions of model parameters. We found that in the uncontrolled epidemic, the intrinsic uncertainty mostly originates from the uncertainty of the virus biology, i.e. its reproduction number. In the controlled epidemic with low ratio of infected population, the randomness of the social network becomes the major source of forecast uncertainty, particularly for the short-range forecasts. Virus transmission models with accurate social network models are thus essential for improving epidemics forecasting.

An epidemiological modelling approach for COVID-19 via data assimilation

The global pandemic of the 2019-nCov requires the evaluation of policy interventions to mitigate future social and economic costs of quarantine measures worldwide. We propose an epidemiological model for forecasting and policy evaluation which incorporates new data in real-time through variational data assimilation. We analyze and discuss infection rates in the UK, US and Italy. We furthermore develop a custom compartmental SIR model fit to variables related to the available data of the pandemic, named SITR model, which allows for more granular inference on infection numbers. We compare and discuss model results which conducts updates as new observations become available. A hybrid data assimilation approach is applied to make results robust to initial conditions and measurement errors in the data. We use the model to conduct inference on infection numbers as well as parameters such as the disease transmissibility rate or the rate of recovery. The parameterisation of the model is parsimonious and extendable, allowing for the incorporation of additional data and parameters of interest. This allows for scalability and the extension of the model to other locations or the adaption of novel data sources.

Use of daily Internet search query data improves real-time projections of influenza epidemics

Seasonal influenza causes millions of illnesses and tens of thousands of deaths per year in the USA alone. While the morbidity and mortality associated with influenza is substantial each year, the timing and magnitude of epidemics are highly variable which complicates efforts to anticipate demands on the healthcare system. Better methods to forecast influenza activity would help policymakers anticipate such stressors. The US Centers for Disease Control and Prevention (CDC) has recognized the importance of improving influenza forecasting and hosts an annual challenge for predicting influenza-like illness (ILI) activity in the USA. The CDC data serve as the reference for ILI in the USA, but this information is aggregated by epidemiological week and reported after a one-week delay (and may be subject to correction even after this reporting lag). Therefore, there has been substantial interest in whether real-time Internet search data, such as Google, Twitter or Wikipedia could be used to improve influenza forecasting. In this study, we combine a previously developed calibration and prediction framework with an established humidity-based transmission dynamic model to forecast influenza. We then compare predictions based on only CDC ILI data with predictions that leverage the earlier availability and finer temporal resolution of Wikipedia search data. We find that both the earlier availability and the finer temporal resolution are important for increasing forecasting performance. Using daily Wikipedia search data leads to a marked improvement in prediction performance compared to weekly data especially for a three- to four-week forecasting horizon.

Early and Real-Time Detection of Seasonal Influenza Onset

Every year, influenza epidemics affect millions of people and place a strong burden on health care services. A timely knowledge of the onset of the epidemic could allow these services to prepare for the peak. We present a method that can reliably identify and signal the influenza outbreak. By combining official Influenza-Like Illness (ILI) incidence rates, searches for ILI-related terms on Google, and an on-call triage phone service, Saúde 24, we were able to identify the beginning of the flu season in 8 European countries, anticipating current official alerts by several weeks. This work shows that it is possible to detect and consistently anticipate the onset of the flu season, in real-time, regardless of the amplitude of the epidemic, with obvious advantages for health care authorities. We also show that the method is not limited to one country, specific region or language, and that it provides a simple and reliable signal that can be used in early detection of other seasonal diseases.

Influenza, generally referred to as the flu, is a common infectious disease that affects millions of people. Every year, we expect this seasonal disease to occur during the Winter, but exactly when it will start and how severe it will be is not known. This places a strong burden on health services, as often the spread can be felt as very fast and emergency rooms become flooded with patients. With this work, we propose a new method that identifies the beginning of the yearly flu season. This is done by using several different data sources, including searches for flu-related symptoms on Google and phone call logs to a specialized medical phone service. These data sources, together with our method, can provide a daily or weekly report, making it much faster than current methods, which require lab testing or centralized medical reports. Our method was applied to different European countries and can anticipate current official alerts by several weeks.

Data-driven outbreak forecasting with a simple nonlinear growth model

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We present EpiGro, a simple data-driven method to forecast the scope of an ongoing outbreak.

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We provide general hypotheses for expected model validity and also discuss model limitations.

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We propose an automated parameter estimation method that can be used for forecasting.

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We test our approach on 9 different outbreaks and show robustness over multiple systems and over noisy data sets.

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In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders.

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders.

The Impact of Population, Contact, and Spatial Heterogeneity on Epidemic Model Predictions

Our objective was to evaluate the effect that complexity in the form of different levels of spatial, population, and contact heterogeneity has in the predictions of a mechanistic epidemic model. A model that simulates the spatiotemporal spread of infectious diseases between animal populations was developed. Sixteen scenarios of foot-and-mouth disease infection in cattle were analyzed, involving combinations of the following factors: multiple production-types (PT) with heterogeneous contact and population structure versus single PT, random versus actual spatial distribution of population units, high versus low infectivity, and no vaccination versus preemptive vaccination. The epidemic size and duration was larger for scenarios with multiple PT versus single PT. Ignoring the actual unit locations did not affect the epidemic size in scenarios with multiple PT/high infectivity, but resulted in smaller epidemic sizes in scenarios using multiple PT/low infectivity. In conclusion, when modeling fast-spreading epidemics, knowing the actual locations of population units may not be as relevant as collecting information on population and contact heterogeneity. In contrast, both population and spatial heterogeneity might be important to model slower spreading epidemic diseases. Our findings can be used to inform data collection and modeling efforts to inform health policy and planning.

Dynamic calibration of agent-based models using data assimilation

A widespread approach to investigating the dynamical behaviour of complex social systems is via agent-based models (ABMs). In this paper, we describe how such models can be dynamically calibrated using the ensemble Kalman filter (EnKF), a standard method of data assimilation. Our goal is twofold. First, we want to present the EnKF in a simple setting for the benefit of ABM practitioners who are unfamiliar with it. Second, we want to illustrate to data assimilation experts the value of using such methods in the context of ABMs of complex social systems and the new challenges these types of model present. We work towards these goals within the context of a simple question of practical value: how many people are there in Leeds (or any other major city) right now? We build a hierarchy of exemplar models that we use to demonstrate how to apply the EnKF and calibrate these using open data of footfall counts in Leeds.

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.

Triggering interventions for influenza: the ALERT algorithm

BACKGROUND

Early, accurate predictions of the onset of influenza season enable targeted implementation of control efforts. Our objective was to develop a tool to assist public health practitioners, researchers, and clinicians in defining the community-level onset of seasonal influenza epidemics.

METHODS

Using recent surveillance data on virologically confirmed infections of influenza, we developed the Above Local Elevated Respiratory Illness Threshold (ALERT) algorithm, a method to identify the period of highest seasonal influenza activity. We used data from 2 large hospitals that serve Baltimore, Maryland and Denver, Colorado, and the surrounding geographic areas. The data used by ALERT are routinely collected surveillance data: weekly case counts of laboratory-confirmed influenza A virus. The main outcome is the percentage of prospective seasonal influenza cases identified by the ALERT algorithm.

RESULTS

When ALERT thresholds designed to capture 90% of all cases were applied prospectively to the 2011-2012 and 2012-2013 influenza seasons in both hospitals, 71%-91% of all reported cases fell within the ALERT period.

CONCLUSIONS

The ALERT algorithm provides a simple, robust, and accurate metric for determining the onset of elevated influenza activity at the community level. This new algorithm provides valuable information that can impact infection prevention recommendations, public health practice, and healthcare delivery.

Bayesian tracking of emerging epidemics using ensemble optimal statistical interpolation

We present a preliminary test of the Ensemble Optimal Statistical Interpolation (EnOSI) method for the statistical tracking of an emerging epidemic, with a comparison to its popular relative for Bayesian data assimilation, the Ensemble Kalman Filter (EnKF). The spatial data for this test was generated by a spatial susceptible-infectious-removed (S-I-R) epidemic model of an airborne infectious disease. Both tracking methods in this test employed Poisson rather than Gaussian noise, so as to handle epidemic data more accurately. The EnOSI and EnKF tracking methods worked well on the main body of the simulated spatial epidemic, but the EnOSI was able to detect and track a distant secondary focus of infection that the EnKF missed entirely.

Influenza forecasting in human populations: a scoping review

Forecasts of influenza activity in human populations could help guide key preparedness tasks. We conducted a scoping review to characterize these methodological approaches and identify research gaps. Adapting the PRISMA methodology for systematic reviews, we searched PubMed, CINAHL, Project Euclid, and Cochrane Database of Systematic Reviews for publications in English since January 1, 2000 using the terms “influenza AND (forecast* OR predict*)”, excluding studies that did not validate forecasts against independent data or incorporate influenza-related surveillance data from the season or pandemic for which the forecasts were applied. We included 35 publications describing population-based (N = 27), medical facility-based (N = 4), and regional or global pandemic spread (N = 4) forecasts. They included areas of North America (N = 15), Europe (N = 14), and/or Asia-Pacific region (N = 4), or had global scope (N = 3). Forecasting models were statistical (N = 18) or epidemiological (N = 17). Five studies used data assimilation methods to update forecasts with new surveillance data. Models used virological (N = 14), syndromic (N = 13), meteorological (N = 6), internet search query (N = 4), and/or other surveillance data as inputs. Forecasting outcomes and validation metrics varied widely. Two studies compared distinct modeling approaches using common data, 2 assessed model calibration, and 1 systematically incorporated expert input. Of the 17 studies using epidemiological models, 8 included sensitivity analysis. This review suggests need for use of good practices in influenza forecasting (e.g., sensitivity analysis); direct comparisons of diverse approaches; assessment of model calibration; integration of subjective expert input; operational research in pilot, real-world applications; and improved mutual understanding among modelers and public health officials.

Forecasting seasonal outbreaks of influenza

Influenza recurs seasonally in temperate regions of the world; however, our ability to predict the timing, duration, and magnitude of local seasonal outbreaks of influenza remains limited. Here we develop a framework for initializing real-time forecasts of seasonal influenza outbreaks, using a data assimilation technique commonly applied in numerical weather prediction. The availability of real-time, web-based estimates of local influenza infection rates makes this type of quantitative forecasting possible. Retrospective ensemble forecasts are generated on a weekly basis following assimilation of these web-based estimates for the 2003-2008 influenza seasons in New York City. The findings indicate that real-time skillful predictions of peak timing can be made more than 7 wk in advance of the actual peak. In addition, confidence in those predictions can be inferred from the spread of the forecast ensemble. This work represents an initial step in the development of a statistically rigorous system for real-time forecast of seasonal influenza.

Innovative Approaches Helpful to Enhance Knowledge on Weather-Related Stroke Events Over a Wide Geographical Area and a Large Population

Background and Purpose—

Results on the effect of weather on stroke occurrences are still confusing and controversial. The aim of this study was to retrospectively investigate in Tuscany (central Italy) the weather-related stroke events through the use of an innovative source of weather data (Reanalysis) together with an original statistical approach to quantify the prompt/delayed health effects of both cold and heat exposures.

Methods—

Daily stroke hospitalizations and meteorologic data from the Reanalysis 2 Achieve were obtained for the period 1997 to 2007. Generalized linear and additive models and an innovative modeling approach, the constrained segmented distributed lag model, were applied.

Results—

Both daily averages and day-to-day changes of air temperature and geopotential height (a measure that approximates the mean surface pressure) were selected as independent predictors of all stroke occurrences. In particular, a 5°C temperature decrease was associated with 16.5% increase of primary intracerebral hemorrhage of people ≥65 years of age. A general short-term cold effect on hospitalizations limited to 1 week after exposure was observed and, for the first time, a clear harvesting effect (deficit of hospitalization) for cold-related primary intracerebral hemorrhage was described. Day-to-day changes of meteorologic parameters disclosed characteristic U- and J-shaped relationships with stroke occurrences.

Conclusions—

Thanks to the intrinsic characteristic of Reanalysis, these results might simply be implemented in an operative forecast system regarding weather-related stroke events with the aim to develop preventive health plans.

Data driven computing by the morphing fast Fourier transform ensemble Kalman filter in epidemic spread simulations

The FFT EnKF data assimilation method is proposed and applied to a stochastic cell simulation of an epidemic, based on the S-I-R spread model. The FFT EnKF combines spatial statistics and ensemble filtering methodologies into a localized and computationally inexpensive version of EnKF with a very small ensemble, and it is further combined with the morphing EnKF to assimilate changes in the position of the epidemic.