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. 2007 Nov 21:5:34.
doi: 10.1186/1741-7015-5-34.

Predictability and epidemic pathways in global outbreaks of infectious diseases: the SARS case study

Affiliations

Predictability and epidemic pathways in global outbreaks of infectious diseases: the SARS case study

Vittoria Colizza et al. BMC Med. .

Abstract

Background: The global spread of the severe acute respiratory syndrome (SARS) epidemic has clearly shown the importance of considering the long-range transportation networks in the understanding of emerging diseases outbreaks. The introduction of extensive transportation data sets is therefore an important step in order to develop epidemic models endowed with realism.

Methods: We develop a general stochastic meta-population model that incorporates actual travel and census data among 3 100 urban areas in 220 countries. The model allows probabilistic predictions on the likelihood of country outbreaks and their magnitude. The level of predictability offered by the model can be quantitatively analyzed and related to the appearance of robust epidemic pathways that represent the most probable routes for the spread of the disease.

Results: In order to assess the predictive power of the model, the case study of the global spread of SARS is considered. The disease parameter values and initial conditions used in the model are evaluated from empirical data for Hong Kong. The outbreak likelihood for specific countries is evaluated along with the emerging epidemic pathways. Simulation results are in agreement with the empirical data of the SARS worldwide epidemic.

Conclusion: The presented computational approach shows that the integration of long-range mobility and demographic data provides epidemic models with a predictive power that can be consistently tested and theoretically motivated. This computational strategy can be therefore considered as a general tool in the analysis and forecast of the global spreading of emerging diseases and in the definition of containment policies aimed at reducing the effects of potentially catastrophic outbreaks.

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Figures

Figure 1
Figure 1
Flow diagram of the transmission model. The population of each city is classified into seven different compartments, namely susceptible (S), latent (L), infectious (I), hospitalized who either recover (HR) or die (HD), dead (D) and recovered (R) individuals. We assume that hospitalized as well as infectious individuals are able to transmit the infection, given the large percentage of the cases among health care workers [37-39]. The actual efficiency of hospital isolation procedures is modeled through a reduction of the transmission rate β by a factor rβ for hospitalized patients, with rβ = 20% as estimated for the early stage of the epidemic in Hong Kong [9]. The infectiousness of patients in the compartments HR and HD are assumed to be equal (although this assumption can easily be changed in the model). Susceptible individuals exposed to SARS enter the latent class. Latents represent infected who are not yet contagious and are assumed to be asymptomatic, as suggested by results based on epidemiologic, clinical and diagnostic data in Canada [40]. They become infectious after an average time ε-1 (mean latency period). The individual is classified as infectious during an average time equal to μ-1 from the onset of clinical symptoms to his admission to the hospital where he eventually dies or recovers. Patients admitted to the hospital are not allowed to travel. The average periods spent in the hospital from admission to death or recovery are equal to μD-1 and μR-1, respectively. The average death rate is denoted by d.
Figure 2
Figure 2
Worldwide map representation of the outbreak likelihood as predicted by the stochastic model. Countries are represented according to the color code, ranging from gray for low outbreak probability to red for high outbreak probability.
Figure 3
Figure 3
Map representation of the outbreak likelihood within Canada at the urban area resolution scale. Urban areas are represented according to the color code, ranging from gray for low outbreak probability to red for high outbreak probability. Airports within Canada are also shown.
Figure 4
Figure 4
Map representation of the comparison between numerical results and WHO reported cases. Countries are considered at risk if the probability of reporting an outbreak – computed on n = 103 different realizations of the stochastic noise – is larger than 20%. In red we represent countries for which model forecasts are in agreement with WHO official reports, distinguishing between correct predictions of outbreak (filled red) and correct predictions of no outbreak (striped red). Forecasts that deviate from observed data are represented in green. Results shown refer to the date of 11 July 2003.
Figure 5
Figure 5
Number of cases by country: comparison with WHO official reports. Quantitative comparison of forecasted number of cases (conditional of the occurrence of an outbreak) with observed data. Simulated results are represented with a box plot in which lowest and highest values represent the 90% CI and the box is delimited by lower and upper quartile and reports the value of the median. Red symbols represent WHO official reports and are accompanied by the value of the number of cases for sake of clarity. (A) Agreement of model predictions with observed data: symbols are compatible with the model predictions. Broken scale and inset are used for sake of visualization. (B,C) Disagreement of model predictions with observed data: WHO data lie outside the 90% CI obtained from n = 103 numerical simulations. Results are reported in two different plots characterized by two different scales for a better visualization.
Figure 6
Figure 6
Overlap profile. The value of the overlap is shown as a function of time, from the initial day of the simulations (21 February 2003) to 11 July 2003. Details on relevant events occurring during SARS epidemics are shown for reference.
Figure 7
Figure 7
Map representation of epidemic pathways. Arrows show the paths followed by the virus in the transmission of the infection from Hong Kong to the other countries. The thickness of the arrows represents the probability associated to a given path, where all paths with probability less than 10% have been filtered out for sake of simplicity. Two different colors are used: black for paths that transmit the virus directly from the seed – Hong Kong – to the first level of infected countries; gray for paths that start from the first level of infected countries.

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