Physics World, February 2010 issue.

The Flu Fighters.

A special feature is dedicated to infectious diseases, how they rapidly spread in our modern society, and what weapons we have nowadays to fight them.  The article titled The Flu Fighters by Vittoria Colizza and Alessandro Vespignani describes the contribution of physicists to an interdisciplinary area where complex systems are the main ingredients, and modeling human behavior and biological contagion is the ultimate challenge. The cover of the special issue shows an illustration by B. Goncalves et al. of the multiscale worldwide mobility networks used in the GLEaM model.

PNAS cover image.

In the issue of December the 22nd of the Proceedings of the National Academy of Sciences, we publish a paper that discusses the interplay of human mobility patterns like those between local metropolitan commuters and long-range airline travelers during a global epidemic. The image of the worldwide mobility network constructed in our paper has been featured in the cover of the journal.

Multiscale mobility networks and the spatial spreading of infectious diseases.
D.Balcan, V. Colizza, B. Gonçalves, H. Hu, J. J. Ramasco, A. Vespignani
Proc Natl Acad Sci U S A 106, 21484-21489 (2009).

In the paper we detail the definition of the worldwide multiscale mobility network at the core of the Global Epidemic and Mobility (GLEaM) model and discuss the data integration process and the statistical analysis that allow its construction.

Have a look at this video presenting an overview of the GLEaM model.

We also tackle some general theoretical questions that concerns the basic understanding of the spatial spread of infectious diseases on the large scale:
i)    Is there a most relevant mobility scale in the definition of the global epidemic pattern?
ii)    At which level of resolution of the epidemic behavior a given mobility scale starts to be relevant and to which extent?

In order to fully consider the effect of multiscale mobility processes we first integrate data of commuting patterns in five different continents with the airline transportation database and then develop a time-scale separation technique for evaluating the force of infection due to different mobility couplings and simulate global pandemics with tunable reproductive ratios. The results obtained from the full multiscale mobility network are compared to the simulations in which only the large scale coupling of the airline transportation network is included. Our analysis shows that while commuting flows are, on average, one order of magnitude larger than the long-range airline traffic, the global spatio-temporal patterns of disease spreading are mainly determined by the airline network. Short-range commuting interactions have on the other hand a role in defining a larger degree of synchronization of nearby subpopulations and specific regions which can be considered weakly connected by the airline transportation system.

It also is possible to show that short-range mobility has an impact in the definition of the subpopulation infection hierarchy. In other words, global disease outbreaks tend to touch down at major travel hubs, generally major airport locations and spread out like a wave that follow local commuting patterns. The findings of the paper open the path to quantitative approximation schemes that calibrate the level of data resolution and the needed computational resources with respect to the accuracy in the description of the epidemics.

The techniques developed here allow for an understanding of the level of data integration required to obtain reliable results in large scale modeling of infectious diseases and have already have contributed to the improvement of the computational model we use to provide estimates and projections of the H1N1 pandemic.

Modeling the critical care demand and antibiotics resources needed during the Fall 2009 wave of influenza A(H1N1) pandemic
D Balcan, V Colizza, AC Singer, C Chouaid, H Hu, B Gonçalves, P Bajardi, C Poletto, JJ Ramasco, N Perra, M Tizzoni, D Paolotti, W Van den Broeck, A-J Valleron and A Vespignani.
PLoS Currents: Influenza. 2009 Dec 4, RRN1133.

The most common symptoms of influenza are generally mild for the majority of people infected. However, in a small portion of clinical cases infected with influenza, the disease can lead to complications of increasing severity requiring medical attention, antibiotics, and, in more serious situations, hospitalization and intensive care. Given the limited capacity of health care providers and hospitals and the limited supplies of antibiotics, it is important to predict the potential demand on critical care to assist planning for the management of resources and plan for additional stockpiling.

In the knol, we introduce a model that considers the development of influenza-associated complications and incorporate it into a GLEaM to assess the expected surge in critical care demands due to viral and bacterial pneumonia. More specifically, the new compartmentalization adds to the basic structure of the influenza dynamics a set of compartments and transitions taking into account the possible evolution of the complications associated to an influenza infection, including viral and bacterial pneumonia, and different speed of progression and stages of severity of the disease. It includes home treatment, hospitalizations, and admission to intensive care unit (ICU). Patients in each stage of pneumonia complications are assumed to be treated with antibiotics, with a preferred empirical antibiotic regimens based on the guidelines issued by the British Thoracic Society. A sketch of the complete compartmental model can be seen in the figure below (click on the left panel to zoom in).

Sketch of the compartment relations for the new epidemic model

Time evolution of the ICU occupancy in a set of countries, measured as the predicted need of ICU beds per 100,000 persons.

Based on the most recent estimates of complication rates, we predict the expected peak number of intensive care unit beds and the stockpile of antibiotic courses needed for the current pandemic wave. The effects of dynamic vaccination campaigns (see this post), and of different length of staying in the intensive care unit are also explored. The right panel of the figure (click on it to expand it) shows the predicted ICU occupancy as a function of time for four countries of the Northern Hemisphere. The three profiles per each country refer to the predicted ICU occupancy in the baseline case when no intervention is implemented, and in case dynamic vaccination campaigns with distribution rates rv=0.1% and rv=1% are considered. Solid curves correspond to the median profiles and the shaded areas to the 95% reference range obtained from 2,000 stochastic simulations. The average ICU length of staying is assumed equal to 7 days.

Tables 1 displays further details on these ICU predictions for a baseline situation and when a vaccination campaign with distribution rates rv=0.1% is considered. The predicted need of ICU beds at peak are typically moderate even when the baseline scenario without intervention is considered, ranging approximately from 5 to 7 ICU beds per 100 000 inhabitants, well below the average national capacity of ICU beds per 100,000 inhabitants. Such numbers can be reduced if measures as vaccination campaigns are taken into account.

Table 1: Predicted need of ICU beds in a scenario with a vaccination campaign covering 0.1% of the population per day until end of vaccine stockpile. The 95% reference range (RR) of the daily number of occupied ICU beds per 100,000 is reported at its peak for several countries in the Northern Hemisphere.

Table 2 reports the number of antibiotics courses needed daily at the peak of the requests, and the total size predicted to be used at the end of the pandemic wave, based on the empirical guidelines of the British Thoracic Society and broken down by the stage of severity of pneumonia. A single course of antibiotics is defined as the combination of antimicrobial drugs considered in the treatment regimen for the suggested duration (see the knol for additional details). The total size of antibiotics courses predicted to be used in the current Fall 2009 pandemic is in the range of [6,337-7,149] per 100,000 for the set of countries explored, which needs to be compared with the available stockpiles of antibiotics courses to cover high-risk groups. Many countries however do not possess nation-wide antibiotic supplies, as antibiotics are generally available through short supply chains able to fulfill average just-in-time requests. The estimates contained in Table 2 can therefore be considered as guidelines to assess the expected needs during the remaining evolution of the pandemic wave with respect to the present usage pattern and available resources.

Table 2: Predicted usage pattern of antibiotics in the scenario with the previous vaccination campaign. The 95% RR of the daily number of administered antibiotics courses per 100,000 at its peak is reported, along with the total amount predicted to be administered by the end of the pandemic wave. Results are shown for several countries in the Northern Hemisphere, broken down for different stages of influenza-associated complications. Pneumonia stages I, II and III corresponds to home-treatment (or supervised outpatient treatment), hospital wards and ICU, respectively.

Estimate of Novel Influenza A/H1N1 cases in Mexico at the early stage of the pandemic with a spatially structured epidemic model
V Colizza, A Vespignani, N Perra, C Poletto, B Gonçalves, H Hu, D Balcan, D Paolotti, W Van den Broeck, M Tizzoni, P Bajardi, JJ Ramasco. PLoS Currents: Influenza. 2009 Nov 11:RRN1129.

Determining the number of cases in an influenza epidemic represents a great challenge. Reliable figures for the actual number of cases are key to properly assess several parameters, such as mortality, morbidity or hospitalization rates. This is particularly relevant during the early phase of an outbreak, in order to better inform decision making process. Surveillance of cases inevitably suffers of several biases overall leading to an underascertainment of influenza cases. For example, many cases showing mild symptoms might not seek for medical attention, and would therefore not be included in the counting of cases. Moreover, the monitoring of cases is expected to change with time. After the initial alert at the beginning of an outbreak, an enhanced surveillance system is expected to have a large monitoring capacity. However, this situation changes with time, due to the large increase in the number of cases and the majority of resources being dedicated to the severe patients. This leads to an ascertainment mainly focused on the most severe cases, with the number of confirmed cases being a gross underestimation of the actual number of people infected by influenza. A significant example is provided by the time evolution of the monitored cases in Mexico during the first months of the epidemic: two studies [1] [2] have assessed the size of the epidemic in the country and both of them found a significant underascertainment of the confirmed cases as reported by the mexican authorities. [3]

In order to address this point we use GLEaM to simulate the epidemic spreading and compute the number of cases in Mexico at the end of April and the beginning of May. We calibrate our model with a maximum likelihood estimate of the infection parameters, fitting the empirical arrival dates of the first infected in the countries seeded from Mexico (a detailed description of the estimate procedure is reported here). This allows us to provide an ab-initio calculation of the number of cases in Mexico independently by the estimation precedure. In the Table below the number of infectious individuals obtained in our simulations is reported, comparing it with the same number obtained in Refs [1][2] and with the confirmed cases reported by mexican authorities.

	Number of symptomatic cases in Mexico (Apr. the 30th)
Simulation Results	[121,000 - 1,394,000]
Lower bound range of Ref. [2]	113,000-375,000
Estimate of Ref. [1]*	2,000 – 280,000
Mexican official report [3] (confirmed cases)	3,350

Predictions of GLEaM for the size of the epidemic in Mexico on April 30 in thousands of cases and comparison with other approaches and with empirical data. The simulations are obtained with our infectious parameter estimates (a detailed description of the estimate procedure is reported here) and show the 95% reference range over 2,000 stochastic realizations. The results are compared with the lower bound estimate range in [2], the estimate provided in Ref. [1] and the number of confirmed cases given by official reports [3]. *The interval provided for Ref.[1] is obtained by merging the results reported in the paper under different assumptions and including the 95% CI.

Despite the different approximations used here and in Refs. [1][2], the three approaches are providing support to the possibility of a reporting ratio of infected cases in Mexico as low as 1 in 100. This finding is important when evaluating the massive amount of data which are now being collected in a large number of countries around the world. We can easily imagine that the reporting rate as well as the estimate of the cumulative attack rate in most of the countries could be easily underestimated in similar cases.

[1] Fraser C, Donnelly CA, Cauchemez S, Hanage WP, Van Kerkhove MD, et al. Pandemic Potential of a Strain of Influenza A (H1N1): Early Findings. Science 2009, 324: 1557-1561.

[2] Lipsitch M, La jous M, O’Hagan JJ, Cohen T, Miller JC, et al. Use of Cumulative Incidence of Novel Influenza A/H1N1 in Foreign Travelers to Estimate Lower Bounds on Cumulative Incidence in Mexico. PLoS ONE , 2009 4: e6895.

[3] Secretaria de Salud, Mexico. Situation actual de la epidemia, Oct 12, 2009. http://portal.salud.gob.mx/sites/salud/descargas/pdf/influenza/situacion_actual_epidemia_121009.pdf

Modeling vaccination campaigns and the Fall/Winter 2009 activity of the new A(H1N1) influenza in the Northern Hemisphere
P Bajardi, C Poletto, D Balcan, H Hu, B Goncalves, JJ Ramasco, D Paolotti, N Perra, M Tizzoni, W Van den Broeck, V Colizza, A Vespignani
Emerging Health Threats Journal 2009, 2:e11.

The paper discusses the effectiveness of the vaccination campaign in mitigating the epidemic in the northern hemisphere, according to the predicted epidemic unfolding. The relative reduction of the epidemic peak activity with respect to the baseline (no-interventions) scenario is measured. Mitigating effects are explored depending on the interplay between the predicted pandemic evolution and the expected delivery and distribution rate of vaccines.

The incidence curves, reported below, show the impact of an incremental vaccination with 1% daily distribution starting on October 15. US and Spain are considered as examples. The model is calibrated using the latest estimates on the transmissibility of the new A(N1H1) influenza, considering as reference the late peak case (the details are reported here). The effect of the vaccination campaign is compared with a combined strategy that includes the systematic treatment of clinical cases with antiviral drugs, where different antiviral distribution rates are considered.

Incidence curves for US and Spain for different intervention scenarios. The gray bar indicates the time period during which the immunization takes effect.

The results show that if additional intervention strategies were not used to delay the time of pandemic peak, vaccination campaigns may not roll out before the pandemic peak is already reached. In the US it is likely that the vaccination campaign will not be able to substantially reduce the epidemic activity, vaccination however will be crucial for the protection of risk groups and healthcare workers. In Europe the activity peak is shifted of a few weeks and the modeling shows that timely vaccination campaigns able to cover 30% of the populations by the second half of November might be effective in mitigating the pandemic. Unfortunately reports of delays in the production and distribution of vaccine have fuelled concern that supplies will arrive too late to make a difference in the number of people that get infected with the new virus. This is again a strong rationale for the prioritized vaccine distribution programs focusing on high-risk groups, healthcare and social infrastructure workers.

The coupled animations show the geotemporal evolution of the swine flu epidemic in the United States, by comparing the observed pattern (left) with the simulated one (right). Simulations refer to the baseline scenario obtained from the maximum likelihood analysis used to estimate the transmission potential of the new influenza A(H1N1) (see this post for more details) [1]. Simulations are not iteratively calibrated, and containment or mitigation interventions are not considered in the model. The maps represent the geographic distribution of the cumulative number of cases at a resolution level of ¼°. Both maps adopt the same color code ranging from a minimum of 1 case per cell (pink) to the maximum number of cases per cell reached in the time frame explored (red). This allows a one-to-one comparison of the two epidemics at each date, highlighting analogies and differences of the geographic spread and of the epidemic activity in terms of number of cases. The data reported on the ‘Real map’ is obtained from official sources and projected at this level of resolution, accessible by the model in the simulations. The data reported on the ‘Simulated map’ is obtained from the average value calculated on 2,000 stochastic realizations of the model. The timeline shown is from May 1, 2009 to July 6, 2009, after which date it was no longer possible to track confirmed cases at this level of resolution.

In a special issue Airneth Column, titled  “People interact. They travel. And diseases might travel with them”, Vittoria Colizza discusses the effects of travel flows on epidemic phenomena.

In the figure below the arrows represent the seeding of countries by infected travelers, during the early outbreak of the new H1N1 influenza, and the color code indicates the time of seeding.

Global invasion of the H1N1 influenza by air travel during the early outbreak.

The animation shows the predicted geotemporal evolution of the H1N1 flu epidemic in Europe for the next fall, comparing the no intervention scenario (left map) with a scenario in which mitigation strategies are considered (right map). Simulations for the no-intervention scenario are obtained from the maximum likelihood analysis used to estimate the transmission potential of the new influenza A(H1N1) (see this post for more details) [1]. The antiviral treatment scenario foresees the use of antiviral drugs administered to 30% of the clinical cases within one day from the onset of symptoms.

The maps display the daily new number of cases at a resolution level of ¼° with a color code ranging from yellow (low activity) to dark red (peak activity). The data mapped is obtained from the average value of the daily new number of cases calculated on 2,000 stochastic realizations of the model, for each of the two scenarios.

The animation shows the predicted geotemporal evolution of the H1N1 flu epidemic in the United States for the next fall, comparing the no intervention scenario (left map) with a scenario in which mitigation strategies are considered (right map). Simulations for the no intervention scenario are obtained from the maximum likelihood analysis used to estimate the transmission potential of the new influenza A(H1N1) (see this post for more details) [1]. The antiviral treatment scenario foresees the use of antiviral drugs administered to 30% of the clinical cases within one day from the onset of symptoms.

The maps display the daily new number of cases at a resolution level of ¼° with a color code ranging from yellow (low activity) to dark red (peak activity). The data mapped is obtained from the average value of the daily new number of cases calculated on 2,000 stochastic realizations of the model, for each of the two scenarios.

Seasonal transmission potential and activity peaks of the new influenza A(H1N1): a Monte Carlo likelihood analysis based on human mobility
D Balcan, H Hu, B Goncalves, P Bajardi, C Poletto, JJ Ramasco, D Paolotti, N Perra, M Tizzoni, W Van den Broeck, V Colizza, A Vespignani
BMC Medicine 2009, 7:45 .

A description of the Monte Carlo procedure used in the work to estimate the seasonal transmission potential and the results obtained for the projections of the winter activity peaks in the Northern hemisphere is reported here. The map below shows the 12 countries infected by travelers from Mexico used in the Monte Carlo likelihood analysis to estimate the H1N1 transmission potential. The color code of the arrows from red to yellow indicates the time ordering of the epidemic invasion.

12 countries seeded from Mexico used in the Monte Carlo likelihood analysis to estimate the H1N1 transmission potential.

Additional posts showing the comparison of simulations vs real data, and the visualizations of the projected evolution of the pandemic will be posted in the next few days.