Real-time numerical forecast of global epidemic spreading: case study of 2009 A/H1N1pdm
© Tizzoni et al; licensee BioMed Central Ltd. 2012
Received: 12 April 2012
Accepted: 13 December 2012
Published: 13 December 2012
Mathematical and computational models for infectious diseases are increasingly used to support public-health decisions; however, their reliability is currently under debate. Real-time forecasts of epidemic spread using data-driven models have been hindered by the technical challenges posed by parameter estimation and validation. Data gathered for the 2009 H1N1 influenza crisis represent an unprecedented opportunity to validate real-time model predictions and define the main success criteria for different approaches.
We used the Global Epidemic and Mobility Model to generate stochastic simulations of epidemic spread worldwide, yielding (among other measures) the incidence and seeding events at a daily resolution for 3,362 subpopulations in 220 countries. Using a Monte Carlo Maximum Likelihood analysis, the model provided an estimate of the seasonal transmission potential during the early phase of the H1N1 pandemic and generated ensemble forecasts for the activity peaks in the northern hemisphere in the fall/winter wave. These results were validated against the real-life surveillance data collected in 48 countries, and their robustness assessed by focusing on 1) the peak timing of the pandemic; 2) the level of spatial resolution allowed by the model; and 3) the clinical attack rate and the effectiveness of the vaccine. In addition, we studied the effect of data incompleteness on the prediction reliability.
Real-time predictions of the peak timing are found to be in good agreement with the empirical data, showing strong robustness to data that may not be accessible in real time (such as pre-exposure immunity and adherence to vaccination campaigns), but that affect the predictions for the attack rates. The timing and spatial unfolding of the pandemic are critically sensitive to the level of mobility data integrated into the model.
Our results show that large-scale models can be used to provide valuable real-time forecasts of influenza spreading, but they require high-performance computing. The quality of the forecast depends on the level of data integration, thus stressing the need for high-quality data in population-based models, and of progressive updates of validated available empirical knowledge to inform these models.
Keywordscomputational epidemiology H1N1 influenza pandemic prediction validation.
Over the past 10 years, the real-world accuracy of mathematical and computational models (MCMs) used in epidemiology has been considerably improved by the integration of large-scale datasets and explicit simulations of entire populations down to the scale of single individuals [1–9]. MCMs have gained in importance in the public-health domain, especially in infectious disease epidemiology, by providing rationales and quantitative analysis to support decision-making and policy-making processes [5, 6, 10–15]. Although there are contrasting opinions among modelers about the value of MCMs in epidemiology , many researchers advocate the use of these models as predictive tools .
With regard to modeling, it is important to distinguish between two different types of predictions . The first class of predictions, or projections, offered by models is the classic scenario and 'what if' analysis. In this case, prototypical values for the basic disease parameters and other key parameters, such as time of implementation of specific policies, are assumed in the MCM to produce plausible scenarios for the epidemics and to evaluate containment/mitigation procedures as a function of the explored parameter space. Over the past few years, a large body of work has been published, aimed at informing contingency plans for pandemic preparedness [19–24].
A more difficult challenge compared with scenario analysis is the use of MCMs for the real-time forecasting of unfolding epidemics. It must also be said that forecasting approaches contain a number of assumptions, such as those introduced by the model structure, scale, and implementation techniques. However, in forecasting approaches, the model has to be calibrated by using statistical estimates based on the analysis of epidemic outbreak data for as many key parameters as possible, and possibly by matching less crucial parameters with published historical data. One major technical problem for real-time forecasting is that some parameters, such as the basic reproduction number, are not absolute quantities, and are very dependent on the choice of the model and model parameterization. Two models with different assumptions may reproduce an epidemic profile equally well by using slightly different values of the basic reproduction number, because of the different modeling assumptions used . Thus, within each modeling framework, it is important to have techniques for parameter estimation that are self-consistent with the model assumptions, and cannot be generally imported from other studies. In data-driven MCMs, the self-consistent calibration of the model represents a real challenge because of the number of estimated parameters and the computational costs needed in the case of stochastic individual-based models. Finally, another major problem hindering the advance of real-time forecasting with MCMs is model validation. Real-time forecasting has to be validated using datasets that are independent from those used for the model calibration. Only a few events in recent times have offered the possibility of a posteriori validation of the real-time forecasting of MCMs, using rich and high-quality datasets .
The 2009 H1N1 influenza pandemic indicated an important role for MCMs in the real-time analysis of disease dynamics and propagation [2, 27–39]. Given the uncertainty associated with the emergence of a new virus, such models allowed estimation of unknown epidemiological parameters, description of the observed epidemic propagation, interpretation of surveillance data, exploration of possible scenarios, estimation of the efficacy of intervention measures, and predictions of future influenza activity. The data gathered during the course of the pandemic can now be used to compare with the estimates calculated by the models, and thus these represent an unprecedented opportunity to validate and assess the results obtained by MCM approaches.
In this study, we assessed results obtained using the Global Epidemic and Mobility (GLEAM) computational model [2, 3]. This model integrates high-resolution data on human demography and mobility on a worldwide scale in a metapopulation stochastic epidemic framework. With the emergence of the novel H1N1 virus in 2009, the model offered the opportunity to study the spread of the pandemic in real time, and thus evaluate specific public-health actions and provide stochastic forecasts of its future unfolding. The basic model parameters (transmissibility and seasonality) were obtained with a Monte Carlo Maximum Likelihood (MCML)-based approach using the chronological data on the pandemic invasion up to 18 June 2009 . This procedure, although extremely costly in terms of computational time (more than 106 simulations were generated), can be performed in real time using a supercomputer. The obtained estimates were used to generate a large number of nominally identically initialized numerical stochastic simulations of the global progression of the H1N1 pandemic after 18 June 2009. The simulations provide, for each point in space and time allowed by the resolution of the model, the set of possible epidemic evolution by statistically defining the median, mean, and reference range of a number of epidemic parameters, including newly generated cases, seeding events, and time of arrival of the infection. For the model, we used 3,362 subpopulations in 220 countries worldwide, with a geographical resolution of 15 × 15 minutes of arc, and the time scale of a single day. Based on the early data of the H1N1 pandemic up to June 2009, the model allowed the stochastic forecasting of the activity peak of the fall/winter wave in the northern hemisphere, along with other quantities of interest. The forecasts were published in September 2009 , well before the peak weeks of epidemic activity in the northern hemisphere.
The aim of this study was to validate the model's predictions by comparing them with real-life data collected from surveillance and virologic sources in 48 countries in the northern hemisphere during the course of the pandemic. These data allowed independent validation of the obtained results and also allowed the accuracy of the model to be tested. Specifically, we considered the validity of the predicted peak time of the fall wave in the northern hemisphere, the clinical attack rate, and the effectiveness of vaccination. Furthermore, we analyzed results at a finer spatial resolution to ascertain the validity of the model on scales smaller than country level. Using the surveillance data, the timing of the pandemic activity peak was found to fall within the prediction interval for 87% of the countries. In the 13% of the cases falling outside the 95% reference range, the offset with respect to the confidence interval was, at most, 2 weeks at the country level. Because the activity peak in each country is defined as an average over regions composed of many different subpopulations, where data were available we have provided the analysis broken down into smaller surveillance regions, obtaining very good agreement between the model results and data. We also integrated into the model all available data on the vaccination campaigns in 27 countries, and compared the predicted incidence intervals with official estimates such as those produced by the Center for Disease Control and Prevention in the USA. In addition, we analyzed the effect of introducing into the model predictions a number of additional factors that were only known at the end of the pandemic, such as pre-existing immunity, and found that the epidemic timing results were sufficiently robust to cope with changes in these parameters.
Finally, we explored the robustness of the stochastic forecast as a function of the completeness of the data integrated into the model. In particular, one subject of debate has been the level of detail about the international aviation transportation network that would be required to reliably simulate the spreading of infectious diseases worldwide. Whereas the GLEAM model used the full international aviation database, many previous studies have focused only on partial datasets that comprise the top 30% or less of the full dataset [4, 6, 9, 14, 29, 40, 41]. We show that working with partial datasets considerably reduces the accuracy of the predictions at both the local and the global level.
This study shows that although supercomputing capabilities are required, data-driven MCM allows real-time forecasting of emerging influenza-like illnesses (ILIs) with an accuracy that can provide valuable information to inform public-health decision-making. The GLEAM computational tool also allows the introduction of further details in the population structure, such as age classes, and it has been aligned with an agent-based model , thus providing avenues for the development of hybrid computational approaches that are able to use different levels of data integration in different subpopulations, with an appropriate compromise between computational requirements and resolution scale of the results.
We used a data-driven global stochastic epidemic model, which is based on the metapopulation approach [4–6, 9, 14, 22, 43–48]. The model has been extensively described previously, and all the technical details and the algorithms underpinning the model results reported [2, 3, 49]. By integrating real demographic and mobility data, the model divides the world population into geographic census areas that are defined around transportation hubs and connected by mobility fluxes, which then defines a subpopulation network. Within each subpopulation, a compartmental structure models the disease spread between individuals. Individuals can move from one subpopulation to another along the mobility network; in this way, an outbreak originating in a seed subpopulation can lead to a global-scale epidemic. The GLEAM model can simulate the global spread of ILIs, and also allows study of the implementation of a wide range of intervention strategies, including vaccinations, antiviral treatment, and travel restrictions (which can be temporally and geographically dependent), to model the different measures adopted by countries in response to an ongoing pandemic. The GLEAM model architecture integrates three different data layers: 1) the population layer, 2) the transportation mobility layer, and 3) the epidemic layer.
The population layer is based on the high-resolution population database of the 'Gridded Population of the World' project of the Socioeconomic Data and Application Center at Columbia University (SEDAC) . This database provides a population estimate by using a grid of cells covering the whole planet, with a resolution of 15 × 15 minutes of arc. The subpopulations of the metapopulation structure correspond to geographic census areas defined around transportation hubs, which are represented by the world airports, as provided by international databases of air travel. The census areas are obtained using a Voronoi-like tessellation of the Earth's surface by assigning each cell of the grid to the closest airport, taking into account distance constraints . The resulting network of subpopulations counts 3,362 census areas in 220 different countries.
The mobility layer takes into account the multiscale nature of human mobility. The GLEAM model integrates the mobility by global air travel (obtained from the International Air Transport Association  and Official Airline Guide  databases) and the short-scale mobility between adjacent subpopulations, which represents the daily commuting patterns of individuals. We obtained the commuting fluxes by collecting and integrating the data of 30 countries in 5 continents across the world  (see Additional file 1A). The model simulates the number of passengers traveling daily worldwide by using the real data obtained from the airline transportation databases, which contain the number of available seats on each airline connection in the world. The commuting short-range couplings between subpopulations are accounted for by defining the effective force of infections in subpopulations connected by commuting flows [3, 53, 54].
However, in a metapopulation framework in which space is explicitly considered, the reproductive number is dependent on space and time, and it is more appropriate to define an effective reproduction number R(t). In more detail, to take into account seasonal effects in the transmission of influenza, we considered a seasonal forcing of the reproduction number, dependent on the calendar time and the region considered. We assumed the world is divided into three regions, delimited by the two Tropics: the northern hemisphere, the southern hemisphere, and the tropical region. We denoted by R 0 the reference value of the reproduction number in the Tropics that needed to be estimated from empirical data of the epidemic. The model reproduces seasonality by means of a sinusoidal rescaling of R 0, by a factor ranging from α min (during the summer season) to α max (during the winter season) .
where the time of year for the minimum and maximum is fixed and is based on historical data and previous models set at 15 July and 15 January, in opposition in the northern and southern hemispheres. Values of α min are typically very small for seasonal influenza, so that during the summer season, the effective reproduction number is rescaled to values of less than 1, which are below the threshold for transmission. We set α max to 1.1, corresponding to a mild increase in disease transmissibility during winter compared with the reference value. Thus, α min is one of the key parameters to be calibrated from the empirical data of the initial invasion of H1N1 pandemic in order to assess the seasonal variation of the transmissibility of the pandemic virus (see the subsection entitled 'Monte Carlo Maximum Likelihood parameter estimate').
The average running time depends on the number of simulated stochastic realizations of the model and the number of transitions between the epidemic compartments to be modeled. In a cluster with 20 central processing units (Xeon 2 Ghz; Intel Corp., Santa Clara, CA, USA), simulating 2,000 realizations of the model with 365 time steps takes between 3 and 5 hours, depending on the complexity of the compartmentalization and the simulated interventions. Simulating one full pandemic scenario, corresponding to 2,000 realizations for three different seasonality values, on the same cluster took an average of 12 hours.
In July 2010, we released the GLEAMviz Simulator, a software system based on GLEAM, which is publicly available , and is based on a client-server system. The GLEAMviz client provides access to all the basic GLEAM features through an interactive graphical user interface. The user can configure freely the compartmental model and simulation scenario by setting compartment-specific variables, transitions, and initial conditions. The user's settings are sent to the GLEAMviz server, which performs the simulations and sends back the analyzed results to the user's client application. Finally, the user can export the results or visualize them in terms of dynamic maps and charts. A full description of the software has been reported previously .
Monte Carlo Maximum Likelihood parameter estimate
Sensitivity analysis range
Reference reproduction number in the Tropics
Minimal seasonality rescaling
Generation time, days3
3.6 (2.2 to 5.1)
Mean infectious period, days3
2.5 (1.1 to 4.0)
Average latency period, days
1.1 to 2.5
Relative infectiousness of asymptomatic individuals
0.1 to 0.8
Probability of becoming an asymptomatic individual
0.33 and 0.5
Probability of traveling of a symptomatic individual
0.4 to 0.6
μ -1 R 0/(1-p a -r β p t )
As calculated from the reference range of R 0
Maximal seasonality rescaling
1.0 and 1.1
For the set of key parameters, we used a two-step process that first estimated the reproductive number R 0 in the Tropics region, where seasonality is assumed not to occur, and then estimated the degree of seasonal damping factor by examining a longer time period for international spread to allow for seasonal variations. As reported previously , estimation of the reference value of the reproduction number was performed using an MCML technique based on the early chronology of the H1N1 epidemic. We began the model with initial conditions set near La Gloria (in the state of Veracruz, Mexico) on 18 February 2009, as detailed previously [3, 27] and according to official Mexican sources . The arrival time of infected individuals in the countries seeded by Mexico is clearly a combination of the number of cases present in the originating country (Mexico) and the mobility network, both within Mexico and connecting Mexico with other countries. By relying on the explicit modeling of the travel behavior of individuals based on the real data, it was possible to shift the estimation of R 0 from the incidence data in the seed country to the timing of the early invasion pattern, with the aim of reducing the errors induced by possible underestimation of cases by surveillance sources. Indeed, the number of cases reported by the surveillance systems was found to be dramatically underestimated, as a result of underdetection and different sampling techniques, as well as changes in surveillance requirements and capacities over time [27, 31, 65, 66]. For this reason, we opted to use as the calibration dataset the first reported case in countries not yet reached by the epidemic. A similar approach was used by Fraser et al. , and a full sensitivity analysis on the accuracy of this data for the GLEAM model was performed by Balcan et al. . Furthermore, the data on the first case were not limited to the arrival date of the person, but usually included additional information about the date of the onset of symptoms, the travel history of the individual, and the supposed source of infection .
Full calibration of the transmission scenario of the model requires an estimate of the seasonality factor (α min) to assess the degree of seasonality of the pandemic virus. As previously described for the reproduction number, we based our estimation on the infection arrival times. We used a larger dataset of 93 countries seeded before 18 June, regardless of the origin of the first case, to explore the evolution of the pandemic on a longer time span, over which seasonality effects could be appreciable. Finally, we analyzed the correlation between the empirically observed arrival times and those provided by the model's simulations, by exploring the possible values of α min. Importantly, we did not fit or calibrate the timing of the seasonal forcing.
Each calibration of the model is computationally expensive, as millions of stochastic simulations are needed to generate the appropriate ensemble describing the spatiotemporal statistical properties that define the likelihood function. Thus, real-time calibrations require supercomputing resources, which in June 2009 were provided to us by the Big Red supercomputer facility . The calibration must be repeated if any new information on the disease is introduced or if specific data that are not initially available will affect the initial conditions or the early phase of the outbreak. Furthermore, each calibration produces different stochastic forecast outputs, as described in the Results section.
Modeling pandemic management
The GLEAM model allows the implementation of different intervention strategies, including pharmaceutical measures (such as vaccinations and the use of antiviral drugs), and non-pharmaceutical measures (such as travel restrictions and social distancing).
Mass vaccination aims at reducing 1) the susceptibility to infection; 2) the infectiousness if infection occurs; and 3) the probability of developing clinical symptoms . The efficacy of the vaccine with respect to these effects is quantified by the parameters VES, VEI, and VED, respectively. We incorporated additional compartments in the disease structure to model mass vaccination  (see Additional file 1C), and, based on preliminary studies indicating a similar efficacy to that for the vaccine against seasonal influenza A(H1N1), we referred to previous estimates available in the literature for vaccine efficacy , which are similar to those adopted to provide predictions for the H1N1 pandemic . We assumed that a susceptible individual, after vaccination, has a reduced probability of becoming infected by a factor VES = 70%. Then, if infection occurs, his infectiousness is reduced by VEI = 30%, while the probability of becoming symptomatic is reduced by VED = 50%. A sensitivity analysis of these values and of the vaccination scheme of the model has been reported previously . The efficacy of vaccines is not instantaneous, and thus we assumed that a single dose of vaccine would be administered, providing protection after a delay of 2 weeks, based on available data from adult clinical studies on the H1N1 influenza vaccine . Given that GLEAM does not consider any additional social or age structure of the population within each geographical census area, the prioritized distribution of vaccines to risk groups cannot be implemented in the model, thus we assumed uniform distribution of the vaccines to a given fraction of the population.
Mass vaccination campaigns in the northern hemisphere.1,2
Mass vaccination starting date
Final vaccine uptake, %
Daily administration rate, %3
September 14, 2009
October 1, 2009
October 5, 2009
October 12, 2009
October 12, 2009
October 19, 2009
October 19, 2009
October 20, 2009
October 21, 2009
October 26, 2009
October 26, 2009
October 26, 2009
October 26, 2009
October 26, 2009
October 31, 2009
November 2, 2009
November 2, 2009
November 2, 2009
November 2, 2009
November 2, 2009
November 9, 2009
November 15, 2009
November 16, 2009
November 16, 2009
November 16, 2009
November 23, 2009
December 1, 2009
Although the treatment of clinical cases with antiviral drugs (neuraminidase inhibitors) aimed at reducing the severity of the disease and the transmissibility while infectious [5, 11, 13, 21–23, 70–72], were not implemented systematically during the A/H1N1 pandemic, we considered this possibility in the model in order to investigate any possible modifications to the overall spatiotemporal pattern of the pandemic. In particular, we studied a scenario assuming the prompt detection of symptomatic cases and the rapid administration of the drug to 30% of the clinical cases who would be treated within the first day from the onset of symptoms [2, 5]. Moreover, we assumed the efficacy of the drug in reducing transmission to be equal to 62%, and a reduction of 1 day in the total infectious period, as available from the existing literature [22, 23], although the evidence of the efficacy of neuraminidase inhibitors in relation to transmission is still under debate . To guarantee a realistic description of the antiviral distribution, we modeled the drug availability in each country by using actual data, collected from the study of Singer et al.  and from national agencies. Thus, treatment with antiviral drugs was simulated only for those countries that had drug stockpiles available at the beginning of the pandemic. The intervention at the national level was assumed to start with a delay of 3 days after the appearance of the first symptomatic individual in the country, but not before the international pandemic alert released on 25 April. Administration of the drugs was assumed to occur at a constant rate until depletion of the country's stockpile. Figure S1 (see Additional file 1C) displays the compartmental structure in each subpopulation when pharmaceutical measures were considered.
In addition to pharmaceutical measures, we also considered interventions aimed at limiting the mobility of individuals and applied in terms of travel restrictions. The explicit inclusion of the mobility network in the GLEAM model allowed us to apply modifications to individual mobility by air in a variety of forms to take into account real-life behaviors. More specifically, interruption of specific travel routes or airports for an arbitrary period can be considered in the model, and the traffic flows to and from given locations (for example, the outbreak seed) can be reduced and modulated in time, based on real data. Some countries did in fact adopt travel-related measures in an attempt to contain or slow down the international spread of the A/H1N1 virus. In a few extreme cases, the authorities banned all the flights directed to/from Mexico, in order to prevent infected individuals from crossing international borders. These measures, along with self-imposed travel limitations, contributed to a decline of about 40% in international air traffic to and from Mexico after the international alert, which was slowly reduced after June 2009 and had returned back to normal in about 3 months (see references [75, 76] for analysis of the data). Thus, simulations with travel-related measures considered the variation over time of the reduction of traffic flows to and from Mexico, as observed in the data.
Finally, control strategies implemented at the level of social groups of single individuals, such as social distancing measures or school closure, can be introduced into the model only by an effective rescaling of the reproduction number for a given time period and in a specific geographic region. Applying this approach, we simulated the interventions that took place in Mexico starting on 24 April and ending on 10 May, using a time-dependent modification of the reproductive number in the country as reported previously . During the period when social distancing was effective in Mexico, we assumed that the reproductive number in Mexico, R Mex, changed its value to R Mex = 0.9, resulting in about a 50% reduction from the reference value. Different reduction rates of R Mex have been tested previously , and no significant changes were found.
Modeling population immunity profile
Taking into account the recent results of serological analyses [78–81], we also considered simulations in which the population had an initial degree of immunity before exposure, and assessed the change in the predictions provided by the model when full susceptibility in the population is taken into account. Measurements of antibodies in serum samples can be used to identify cross-reactivity between antibodies elicited by seasonal influenza viruses circulating before the pandemic, thus providing estimates of pre-exposure immunity to the H1N1 pandemic virus in the population [17, 82]. Serological surveys reported evidence of substantial pre-exposure immunity to the 2009 A/H1N1 pandemic virus among older sections of the population. The detected levels of pre-exposure cross-reactive antibodies ranged from 23% of individuals aged 65 years or over in the UK , to 30% and 34% for those born before 1950 (that is, those aged 60 years or over in 2009) in Finland  and the USA , respectively, and 37% in Germany for the same age group . To explore the effects of pre-exposure immunity, we assumed that 33% of individuals older than 60 years would be immune and completely protected against the H1N1 pandemic virus. We used the data from the International Database of the US Census Bureau  to estimate the corresponding fraction of each country's total population with pre-exposure immunity, relying on the different national age profiles, given that in this work we did not consider age structure in the GLEAM modeling of the population.
To compare our numerical results with the observed temporal and geographic pattern of the pandemic fall/winter wave, we collected data from the monitoring systems of 48 countries in the northern hemisphere, accessing their official websites on a regular weekly basis, and also downloading their final reports at the end of the wave with an assessment of the influenza activity using the most relevant indicators (for the full list of our data sources, see Additional file 1E).
Surveillance systems in the countries under study use different operative methods and a wide range of influenza case definitions to monitor influenza activity within the country. Our data sources reported at least one or more of the following indicators on a weekly basis: ILI incidence, acute respiratory infection (ARI) incidence, fraction of ILI visits or fraction of ILI patients per sentinel doctor, and number of H1N1pdm laboratory-confirmed cases. All of the indicators are generally based on the number of individuals that seek health care and who have respiratory symptoms that can be specifically diagnosed as ILI or, with a broader set of possible causes, as ARIs. Specific virologic analyses are typically conducted on a subset of patients to monitor the activity per strain. Worldwide surveillance networks adopt a large variety of clinical case definitions, and there is currently no international consensus on a 'gold standard' for the case definition of influenza (see, for instance, the UK Health Protection Agency  and the US Centers for Disease Control  definitions for H1N1 cases). Nevertheless, most surveillance networks share common symptoms or common generic terms in their definitions , and both the ILI and ARI case definitions were found to be good indicators of influenza activity in Europe . The harmonization of influenza monitoring across countries with a single ILI case definition is currently being tested in Europe, using online surveillance systems .
Depending on the system, indicators may need to be adjusted to specific normalization factors or consultation rates to extrapolate numbers of cases with respect to the whole population. In particular, healthcare-seeking behavior is a parameter that is difficult to estimate. Moreover, it may vary across age groups and it may also change over time, especially during a health emergency such as a pandemic influenza, as a result of government advice, media coverage, and resulting public anxiety . Given that we were interested in the fall/winter wave of the 2009 H1N1 pandemic, we assumed a constant surveillance effort and consultation rate across time in the countries under study (the same assumption would not be true when comparing the first and the second waves, as, for example, in the UK [89–91]). In addition, because surveillance data were used in this work only to provide a comparison with the timing of our predictions, we disregarded normalization factors and consultation rates, and assumed that surveillance data provided a reliable estimate of the timing of the influenza activity peak using the various available indicators . Finally, to account for the uncertainty intrinsic to empirical data, we used a color gradient to indicate the observed peak weeks, with the limits corresponding to the time interval in which an incidence of greater than 80% of the maximum was observed.
Results and Discussion
Stochastic forecast output sets
As discussed in the Methods section, the GLEAM model generates a large number of nominally identically initialized numerical stochastic simulations of an epidemic's global progression. The simulations provide, for each point in space and time as given by the resolution of the model, an ensemble of possible epidemic evolutions. It gives median, mean, and reference ranges for epidemic observables, such as newly generated cases, seeding events, time of arrival of the infection, and number of drugs used. The ensemble forecast and the statistical quantities depend on the key parameters determined by the MCML calibration of the model. Each calibration thus defines a different stochastic forecast output (SFO) set that can be validated against real data.
Each MCML calibration and the corresponding SFO set corresponded to the numerical generation of more than 106 global simulations, and the manipulation and storage of about 1 terabyte of data.
We considered the following SFO sets and their corresponding calibrations:
Baseline SFO set. This is the set corresponding to the numerical analysis presented previously . This set was generated in June 2009, and owing to lack of data, it did not include change in traveling behavior and/or pre-exposure immunity. This set was particularly relevant in the validation process because it is the SFO achieved in real time before the unfolding of the winter wave of influenza in the northern hemisphere.
Reference SFO set. This SFO set was obtained by a calibration that considered the observed drop in travel flow during the early stage of the outbreak, as reported by the Mexican authorities . These data became available in December 2009, and for this reason, could not be considered in our initial work. The reference SFO was then coupled with a series of intervention options (outside Mexico), considered one at a time (described in the Methods section), to assess the effect of the following: travel restrictions of increased magnitude; vaccination campaigns as deployed in reality (obtained from data available after the pandemic); and antiviral treatment and pre-vaccination as hypothetical scenarios. Those interventions, which were implemented well after the start of the pandemic, did not affect the model calibration.
Pre-exposure immunity SFO set. Based on the recent results of serological analyses [78–81], this set assumed that a fraction of the total population of each country would have pre-exposure immunity to the pandemic virus. This fraction was calculated by relying on the different national age profiles to match the observed pre-exposure immunity in individuals older than 60 years (see Methods). Unlike the other SFO sets, in which interventions starting at a later stage of the epidemic were considered, the pre-exposure immunity SFO set requires performance of a full MCML calibration, given that the initial conditions of the population's immunity profile have changed. The pre-exposure immunity SFO set is also analyzed by including vaccination campaigns.
Summary of the A/H1N1pdm Monte Carlo Maximum Likelihood (MCML) calibrations and best parameter estimates.
MCML and interventions1,2
Pre-exposure immunity SFO
Social distancing in Mexico, April 24-May 10, 2009
Traffic reduction after April 25, 2009
Vaccinations campaigns (data-driven)
Antiviral treatment (hypothetical scenario)
Pre-vaccination (hypothetical scenario)
MCML estimates 3
Minimal seasonal rescaling factor, α min 4
(0.60 - 0.70)
(0.60 - 0.70)
(0.65 - 0.75)
Reference reproduction number in the Tropics, R 0 5
1.75 (1.64 - 1.88)
1.75 (1.64 - 1.88)
1.8 (1.69 - 1.91)
Finally, we explored additional SFO sets to perform a sensitivity analysis of the conditions and assumptions considered in the simulations, in which we assessed the role of the following: consideration of a sample of the airline transportation network; the winter and summer rescaling values of the seasonal sinusoidal function (α max and α min, respectively); the parameters related to asymptomatic infections; and the initial geographic conditions of the seed outbreak location in Mexico. In all of these cases, a new estimate of the seasonal transmission scenario was performed because the initial conditions had changed. All of the SFO sets explored the evolution of the pandemic over a time span of 1 year, and the results shown in the following sections were obtained from at least 2,000 stochastic simulations.
We report in Table 3 the values of the parameters obtained by the MCML estimate for each of the SFO sets. Generally, the parameter values were not particularly sensitive to the progressive integration of data on reduction of travel to and from Mexico. A rationale for this result is provided in the next section. The values obtained in the different MCML estimates for R 0 ranged from 1.64 to 1.91. It should be noted that this number refers to the reference value, and the effective reproduction number is determined at each time step of the simulation by considering the seasonal effects. This seasonal scaling provides an effective reproduction number in the northern hemisphere, ranging from 1.05 to 1.5 in the spring/summer months, in agreement with published estimates of the reproduction number [27, 28]. The time dependence of the seasonally effective reproduction number R(t) in the northern and southern hemispheres, for the estimated values of R 0 and α min in the A/H1N1 pandemic baseline SFO set, was calculated (see Additional file 1D, Figure S2).
Early stage, first-case importations, and travel restrictions
In the early stage of the A/H1N1 2009 pandemic, the worldwide air-transportation network was the main dissemination mechanism from Mexico to the rest of the world. We first assessed the role of the observed travel decline on the MCML estimates and the SFO set for the early stage of the epidemic by using the data on travel to and from Mexico that became available at the end of 2009. We compared the results of the baseline SFO with those of the reference SFO in which the observed travel decline was considered. The discrete stochastic structure of the model allowed tracking of the arrival of each detectable (that is, symptomatic) and non-detectable (that is, latent or asymptomatic) infected individual in any given country. By defining the arrival time as the date on which the first symptomatic case arrived in a given country, it was possible to quantify the delay in the spreading of the epidemic from country to country that was achieved by traffic reduction. The decline of 40% in the travel flows to and from Mexico reported for the month of May 2009 (which was then followed by lowered reductions until a return to normality 3 months later) led to an average delay in the importation of the first case in seeded countries of less than 3 days , without altering the MCML estimate of the seasonal transmission. This is consistent with the results we previously obtained in a sensitivity analysis investigating the robustness of the estimation procedure to variations in the chronological data of the first imported case, assuming possible inaccuracies in the reporting .
Furthermore, the numerical simulations allowed us to test whether a decrease in travel flows of magnitudes larger than the observed 40% would have provided any additional benefit in slowing down the propagation of the A/H1N1 virus across the world. We considered reductions ranging from 50% to 90% in the air travel flows connecting Mexico with the rest of the world, starting on 25 April, after the international alert, and optimistically assumed prompt implementation of the intervention by the authorities, with no further delays. We also assumed that the reduction would be kept constant across time and would never reduce nor return to normality, which is different from the situation revealed by the real data.
Confirming previous modeling and theoretical works on travel restrictions in pandemic planning [5, 9, 12–14, 20, 92] and empirical studies on entry screening , these results suggest that the observed travel drop did not lead to substantial delays in the arrival of the H1N1 epidemic to non-affected areas. In addition, the simulations showed that it would not be possible to contain the pandemic by the sole implementation of travel restrictions, even if these were unfeasibly strict. These results can be rationalized in a theoretical framework characterizing the invasion dynamics of the epidemics at the metapopulation level, and are related to the heterogeneity of the mobility patterns of humans [76, 94].
Pandemic activity peaks in the northern hemisphere
Correlation of population variables and epidemic statistics as seen and predicted by the model.
Correlation observed in real dataa
Correlation predicted by the modela
Air traffic to/from North America
Attack rate reduction, %
European countries only
Intra-EU air traffic
Air traffic to/from North America
Attack rate reduction, %
The empirical data were compared with the results of the numerical simulations performed for the baseline SFO set (Figure 5). In light of the results presented in the previous subsection, we checked whether the timing of the simulated epidemic activity showed any differences between the reference SFO set (in which the observed travel drop during the early stage was incorporated into the model) and the baseline SFO set (in which that aspect was not considered because the data were not yet available), for which predictions were reported previously . We found that 95% of the reference range of the simulated peak week was obtained from the minimal seasonality rescaling, α min, in the range of 0.6 to 0.7, estimated from the calibration. The SFO sets therefore seemed to be in very good agreement with the empirical data, showing that the latter fell within the confidence interval of numerical results in most of the countries under study. Only for 13% of the countries did our predictions differ from the observed timing of the influenza activity, and in these, the early arrival (France, Switzerland, Hungary) or the delay (Ukraine, Mongolia, Uzbekistan) compared with the simulations was 2 weeks at most, measured from peak week to the closest end value of the reference range of the numerical results.
It should be noted that the obtained results are highly non-trivial because of the anticipated peak of the pandemic in the northern hemisphere. The GLEAM model does not alter the timing of the seasonal forcing that would intuitively generate an activity peak in mid-January. The anticipated peaks are thus a genuine result originating from the initial condition of the pandemic, the transmissibility estimate, and the spreading pattern generated by the human mobility integrated into the model. In this sense, the offset of 1 or 2 weeks observed for a limited number of countries can still be considered a good result, compared with the several months for dispersion allowed in principle by the seasonal forcing only.
An offset of 2 or 3 weeks for the forecast may be due not only to the model approximations and components but also to other factors that were not considered in the GLEAM model because of lack of data at the time of the predictions or because they would require country-specific implementation in the model. An example is provided by the case of France, where the beginning of the exponential increase of the incidence curve in fall 2009 was interrupted by a sudden drop , corresponding to a countrywide school break of 2 weeks (during weeks 43 and 44), consistent with the results observed from the analysis of the timing of holidays and from 21 years of French surveillance data of ILI . The fact that the peak appeared 2 weeks later than predicted by the model may thus be explained by the delaying effect produced by the school holiday. This and other effects, although they could be implemented in the model through explicit or effective means, would require the collection of country-specific data worldwide for a large spectrum of events. Although we performed simulations with explicit travel drops and vaccination campaigns at the country level as they took place in reality (see previous and next subsection), the inclusion of country-specific additional factors, such as school holidays, were beyond the scope of this study.
Calibration of GLEAM based on the chronological data of the H1N1 invasion up to 18 June 2009 was able to provide accurate predictions (2 to 4 months in advance) of the timing of the peak activity in countries in the northern hemisphere (Figure 5, Figure 6). This information provided additional support for the evaluation of real-time interventions aimed at mitigating the pandemic , and was made available to public-health policymakers to provide guidance for strategic planning. In addition, the large-scale extent of this approach enabled predictions for countries not usually considered by other modeling approaches that require large detailed datasets to build synthetic populations, and described their behavior at the individual level. Other than the USA [7, 13, 22, 24, 98], specific European countries [12, 15], or the European continent as a whole , other developed countries do not appear in modeling studies, and underdeveloped countries have been considered in agent-based models in only a few cases, such as in pandemic preparedness studies that focused on Thailand with regard to the possible emergence of a pandemic from the H5N1 avian flu virus [11, 24].
Spatial resolution analysis
To test the reliability of the GLEAM model on a smaller geographical scale and in countries with heterogeneous climatic structures, we validated the baseline SFO for two countries, India and Canada, for which there are no specific models available and which are characterized by their large geographical extension. Furthermore, the coupling between the different regions of those countries is complicated by the presence of different seasonal areas within the same country (in the case of India) and by a highly structured population with a large extension of inhabited areas (in the case of Canada). We expected this to have a strong effect on the timing of the pandemic activity peak .
By contrast, Canada falls completely within the northern hemisphere, where the seasonal rescaling function modulates the value of R 0, leading to higher transmissibility rates during wintertime. The Canadian case is of interest because the country has one of the lowest population densities in the world, and is characterized by a largely heterogeneous geographical distribution, with cities mainly scattered along the border with the USA, and varying densities from west to east. Despite the synchronization effect of epidemic waves produced by seasonal rescaling, the heterogeneous population distribution in a vast area leaves room for an important role of the mobility pattern in shaping the timing of the arrival of the epidemic and its peak activity in different regions. We collected the weekly incidence data reported by the surveillance systems of seven Canadian provinces (Alberta, British Columbia, Manitoba, New Brunswick, Nova Scotia, Quebec, and Ontario, which account for more than 94% of the Canadian population), and compared the observed activity peak with the simulated peak in our baseline SFO. The pandemic activity peaked between the end of October and the end of November (weeks 43 to 47), with the timing over all regions spanning an entire month, and with the presence of narrow to broad peaks in the incidence profiles, as shown, for instance, by the cases of New Brunswick and Manitoba, respectively (Figure 7B). The 95% reference ranges of the peak week in our reference SFO simulations were in good agreement with the surveillance data, and were able to reproduce a variation in the timing of the peak occurrence across the country. This is a result of the interplay of the region's connection to the rest of the world where the epidemic was unfolding, and the intra-country connections and population distribution that drove the local epidemic propagation and internal coupling across regions due to local mobility. As expected, those regions that are better connected to the rest of the world through international travel flows of passengers experienced the peak earlier, with the exception of New Brunswick, which synchronized with the early timing of the peak; this may be explained by the large commuting flows from New Brunswick to the neighboring regions . For the sake of completeness, we also provide a validation of the model results for Mexico, with a breakdown by Mexican region (see Additional file 1G).
The effect of vaccination on peak timing
The real data and the model output provided similar results, as expressed in terms of a negative correlation, which was not significant, between the peak week and the vaccine uptake (Table 4), indicating a larger uptake in those countries that experienced an earlier pandemic wave, such as Canada and the USA.
Clinical attack rate and the effects of vaccination and pre-exposure immunity
The comparison of the absolute values of predicted attack rates with real data was hampered by the limited availability of accurate data on the total number of people infected by the 2009 H1N1 pandemic worldwide . Surveillance data usually rely on the measure of the number of individuals with ILI symptoms who seek medical care, which leads to underestimation of the number of clinical cases because it does not account for those individuals with influenza who do not seek medical attention. By adjusting for consultation rates, current estimates of the epidemic size range from 1.8% for symptomatic cases in the UK , to 18% in France for the overall proportion of the infected population , to about 14% to 29% of the illness attack rate in the USA . The large variation in these estimates is related to the intrinsic under-ascertainment of surveillance systems and to different healthcare-seeking behaviors, which may vary from country to country and may also change in time within the same population [89–91]. Additional estimates of the extent of the infection in a population were provided by serological analyses conducted during and immediately after the pandemic wave. Available studies measured overall attack rates of 19% in the UK during the first wave  and 36% after the second wave ; 21.5% in the USA, from data collected till early December 2009 ; and 11% in Hong Kong, from a survey running to the end of December 2009 . However, these results are difficult to interpret given the sampling and timing biases of the serological analyses. However, the available evidence suggests that the incidence figures originally provided during and immediately after the outbreak dramatically underestimated the true number of overall infections [38, 78, 102].
In our model, the value of the attack rate depends on parameters that were prospectively unavailable for real-time forecast. The final epidemic size is non-trivially affected by the time and type of implementation of vaccination campaigns, by the level of pre-exposure immunity in the population, and by the proportions of asymptomatic infections, all information that became available only after the pandemic wave ended.
If we consider that a portion of the population had an initial degree of immunity, provided by cross-reacting antibodies elicited by previously circulating seasonal strains (see Methods section), the relative reduction in the final size of the epidemic increases considerably. We assessed the relative reduction obtained by comparing the pre-exposure immunity SFO set in which vaccination had also been implemented (that is, pre-exposure immunity + vaccination) with the reference SFO set (Figure 11C; also considered as a benchmark for the results shown in Figure 11B). A new MCML calibration that integrated data on pre-exposure immunity had to be performed to generate the corresponding set of SFO, because the initial conditions of the immunity profile of the population were changed with respect to the other SFO sets. Although this change did not affect the timing of the pandemic wave (Figure S5), the presence of pre-exposure immunity in older age groups reduced the effect of the disease in that population, in agreement with other modeling studies [100, 106]. The values of the relative reduction increased by a factor of approximately 2 with respect to the reference + vaccination case for those countries experiencing the largest benefit from the massive vaccination campaigns (for example, USA, Hungary, and Sweden), and were considerably (about one order of magnitude) higher for the countries in which this benefit was extremely limited in the absence of pre-exposure immunity (for example, Czech Republic, Italy, and Norway). The relative variation is an overall result of the effects related to the start of the vaccination campaigns, peak timing, and the population distribution by age for each country owing to the pre-exposure immunity in older age groups. For instance, smaller reductions were seen in countries characterized by relatively young age profiles, such as Turkey and Tunisia.
Antiviral treatment and pre-vaccination
During the 2009 A/H1N1 pandemic, only a few countries adopted the systematic use of antiviral drugs as a mitigation strategy: Canada, Germany, Hong Kong SAR, Japan, the UK, and the USA . Furthermore, in those countries, the antiviral treatment was limited to the early stage of the outbreak, and the effort was not sustained in the later stages of the pandemic.
In the model, we considered the intervention applied to all countries having drug stockpiles available at the beginning of the outbreak , and for each country, we assumed this would occur until the country's stockpile was depleted. Antiviral treatment was considered in isolation on top of the reference SFO, and no vaccination was implemented. It should be noted that this is a 'what if' scenario informed by the data on antiviral stockpiles around the world.
Moreover, the trade-off between the severity of the infection and the risk of inducing antiviral resistance has to be factored into the final decision considering the implementation of systematic treatment policies. In this hypothetical scenario, we considered the antiviral efficacy for transmission and reduction of the infectious period as that available in the modeling literature. As discussed in the Methods section, we acknowledge that there is an ongoing debate on the availability of the empirical evidence supporting these estimates .
Effects of pre-vaccination.
Relative reduction in epidemic size, %a
27.3 to 28.2
46.3 to 48.2
98.9 to 99.3
23.2 to 24.4
38.6 to 39.2
87.9 to 90.0
20.5 to 21.8
35.2 to 36.2
92.4 to 95.5
21.5 to 22.6
37.5 to 38.3
93.4 to 95.6
23.0 to 24.4
38.3 to 39.0
90.2 to 91.8
23.4 to 26.8
38.1 to 40.1
85.5 to 89.8
22.9 to 24.8
37.8 to 38.8
84.3 to 86.4
22.0 to 24.2
36.6 to 38.1
84.4 to 86.8
23.1 to 24.8
38.2 to 39.0
86.3 to 88.6
22.2 to 24.6
36.6 to 38.4
84.7 to 88.4
22.6 to 24.2
37.7 to 38.6
88.9 to 90.6
22.7 to 24.5
37.1 to 38.6
88.3 to 92.4
22.9 to 24.7
37.7 to 38.7
84.5 to 87.3
21.6 to 23.5
35.8 to 37.1
81.7 to 84.1
22.0 to 24.0
36.2 to 37.6
83.0 to 86.6
21.5 to 23.5
35.6 to 37.1
81.7 to 85.0
26.5 to 27.0
46.4 to 49.6
95.4 to 95.8
20.6 to 24.8
33.9 to 38.6
78.8 to 87.8
23.2 to 24.8
38.6 to 39.4
89.1 to 91.1
21.5 to 23.3
35.3 to 36.8
76.4 to 81.1
21.7 to 24.7
36.3 to 38.4
85.5 to 89.5
21.0 to 24.0
34.4 to 36.8
77.5 to 81.9
22.4 to 23.7
37.7 to 39.0
91.7 to 93.7
23.2 to 24.8
38.6 to 39.5
86.1 to 87.7
24.5 to 25.7
41.0 to 42.1
90.9 to 92.0
24.8 to 25.6
42.0 to 44.9
89.7 to 90.6
23.1 to 24.7
37.9 to 38.9
85.9 to 88.7
Sensitivity analysis on the epidemiological parameters
In this analysis, we explored the effects induced by changes in the values of the epidemiological parameters considered in the model, including assumptions and estimated values. First, we focused on the sinusoidal rescaling of the reproductive number to account for seasonal effects. We assumed a different setting in which the maximum value of the rescaling function, α max, was set to 1 [4, 9] instead of 1.1 [2, 108] thus, the maximum value reached by α(t)R 0 in the temperate regions during wintertime is equal to the reference value of the reproductive number in the Tropics, R 0.
Second, we investigated the role of our estimate of the seasonal effects from the initial pandemic international invasion. Instead of estimating the value of α min in the range of 0.6 to 0.7 from the correlation procedure described in the calibration subsection, we assumed α min = 0.1, as in the case of seasonal influenza . In this case, the simulations predicted an epidemic peak at the beginning of 2010 for almost all countries in the northern hemisphere, thus resulting in a delay of about 1.5 months with respect to the initial predictions of the baseline case (Figure S7). These results highlight the importance of obtaining a correct estimate of the strength of seasonal effects in order to provide accurate predictions.
Finally, we also investigated the effect of changes in the assumed parameters concerning asymptomatic infections, that is, the relative fraction of asymptomatic cases, p a and their relative transmissibility, r β . A broad exploration of parameters and a thorough sensitivity analysis has been provided in a previous study . For the sake of completeness, we provide an enlarged sensitivity analysis of the parameter r β (see Additional file 1K), which is generally assumed in modeling studies to be equal to 50% [23, 24, 27]. We found that the predictions obtained in the baseline SFO set for the timing of the pandemic influenza peak and the illness attack rate were very robust against changes of r β , even in the extreme case of r β = 10% (Figure S8).
Sensitivity analysis of data knowledge and integration
The sensitivity analysis of most epidemic models focuses only on the parameters describing the disease. However, in a large-scale computational model, the integration and assimilation of data on census, mobility, and other demographic factors has to deal with issues related to the quality and completeness of the data. The sensitivity analysis of the model results with regard to the incompleteness or poor quality of those 'structural' data is thus extremely important. We tested this aspect by assessing whether the full complexity of the real mobility data considered in GLEAM would be essential to obtain the SFO presented in the previous subsection, or if a simplified version of the model would allow similar results.
Other approaches have considered only one transportation mode (air travel) and included a limited number of airports, ranging from 52 to 500 [4, 6, 9, 14, 29, 43]. A recent study compared the spread of influenza at the global level by considering different samples obtained from the full OAG (Official Airline Guide)  database of 2000 . Its results have shown that samples of the 200 to 300 largest airports in the world would reproduce fairly well the backbone of spreading at the global and regional scales. Although we agree with previous studies which state that considering partial datasets is informative for the overall theoretical analysis of general spreading features, we tested the performance of partial datasets in providing reliable SFO sets at the country or city scale.
Geographic resolution of GLEAM with the full database and with the top 500 airports.
Countries in the full database, n
Countries in the top 500 database, n
Relative reduction, %
Because this analysis modified the structure of the model, we performed a new calibration, using a new estimate of the reproductive number (R 0) of 1.5, and a value of α min in the range 0.8 to 0.9. The calibration procedure was still based on the same dataset of arrival times used in the reference SFO set, because the corresponding countries were covered by the sampled mobility network.
Although the top 500 airports gather about 80% of the worldwide air traffic, the differences in the median peak times are clearly non-negligible (Figure 14). A specific application to a real-world epidemic is thus able to show how the global backbone of invasion can be strongly affected by the partial sampling of the mobility network, owing to the interplay of different parameters, such as the presence of loops, local connectivity, seasonal effects, and the real and effective (that is, measured on the sampled network) distance of the location from the seed of the outbreak. In addition, a limited version of the model may not be applicable to a specific real epidemic, given its partial coverage of the locations and countries in the world, as would be the case where the initial seed of the outbreak belongs to a region not included in the data integrated into the model. Indeed, in the top 500 airports, the sampling of the mobility network restricts the choice of the seed location to Mexico City, which is the major airport found close to the original outbreak location. Therefore, the results (Figure 14) are affected by the following two effects, which occur because of the restriction of the analysis to the top 500 airports: the change in the mobility network structure and the change in the seed location, as forced by the lack of resolution in the sampled mobility network. For this reason, we analyzed the change in peak time as a function of the initial condition in Mexico City in the case of the full mobility network (see Additional file 1L). The results showed how the reduction of the full mobility dataset has considerable consequences on the timing of the pandemic in the various locations discounted of the effects induced by the initial condition resolution. Overall, the peak time shift between the full database scenario and the sampled database scenario, which both had the seed in Mexico City, ranged from 69 days earlier up to 20 days later (Figure S9).
In this study, we examined the application of GLEAM, a global stochastic simulation model of epidemic spread based on real data of human population distribution and mobility, to the 2009 A/H1N1 pandemic. We analyzed, in real time, the pandemic emergency that led to the publication in summer 2009 of the predicted timing for the pandemic wave in the countries in the northern hemisphere for the fall/winter period. Using surveillance data from various monitoring and virologic sources, we have provided a validation of the SFO of the GLEAM model for the unfolding of the A/H1N1 pandemic in 2009. Our findings indicate very good agreement in the predicted timing for a large variety of countries, including those with underdeveloped surveillance schemes, and for intra-country spatial scales. The results are encouraging in advocating the use of large-scale computational approaches in providing real-time forecast and scenarios of epidemic outbreaks. If the appropriate MCML calibration is performed, the SFOs are very stable against changes in epidemiological parameters that are difficult to estimate for an emerging virus, such as the asymptomatic proportion of the population and its relative infectiousness. Changes in those parameters are generally absorbed by the rescaling of the key disease parameters in a self-consistent way. However, the model output shows strong dependence on the accuracy of the initial conditions and the mobility network considered. This highlights the need for a detailed level of description of human mobility and population distribution in the world in order to achieve reliable predictions at a high-resolution scale. We also considered additional scenarios to allow more realistic simulation of the pandemic event worldwide, based on detailed data of country-based interventions and population initial immunity profiles, which became available throughout and after the outbreak. Consequently, accurate data should be rapidly available during the initial phase of the outbreak in order to allow careful calibration of the model, and close collaboration with public-health officials should allow careful consideration of possible intervention scenarios to support policy decisions for contingency planning at both country and global levels.
Acute respiratory infection
Global Epidemic and Mobility
Monte Carlo Maximum Likelihood
Mathematical and Computational Model
Stochastic Forecast Output.
We thank IATA and OAG for providing their databases. MT thanks the Center for Complex Networks and Systems Research of Indiana University, Bloomington, for their hospitality and support during his visit. This work was partially funded by the National Institutes of Health (R21-DA024259 award), a Lilly Endowment Grant 2008 (number 1639-000) and a DTRA-1-0910039 Award to AV; an EC-ICT contract (number 231807; EPIWORK) to AV and VC; an EC-FET contract (number 233847; DYNANETS) to AV, VC, and JJR; and an ERC Ideas contract (number ERC-2007-Stg204863; EPIFOR) to VC, PB, CP, and MT. The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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