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Sequential detection of influenza epidemics by the Kolmogorov-Smirnov test

Pau Closas1*, Ermengol Coma2 and Leonardo Méndez2

Author affiliations

1 Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Av. Carl Friedrich Gauss 7, 08860 Castelldefels, Barcelona, Spain

2 Institut Català de la Salut (ICS), Sistema d’Informació dels Serveis d’Atenció Primària (SISAP), Gran Via de les Corts Catalanes, 587-589, 08007 Barcelona, Spain

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Citation and License

BMC Medical Informatics and Decision Making 2012, 12:112  doi:10.1186/1472-6947-12-112

Published: 3 October 2012



Influenza is a well known and common human respiratory infection, causing significant morbidity and mortality every year. Despite Influenza variability, fast and reliable outbreak detection is required for health resource planning. Clinical health records, as published by the Diagnosticat database in Catalonia, host useful data for probabilistic detection of influenza outbreaks.


This paper proposes a statistical method to detect influenza epidemic activity. Non-epidemic incidence rates are modeled against the exponential distribution, and the maximum likelihood estimate for the decaying factor λ is calculated. The sequential detection algorithm updates the parameter as new data becomes available. Binary epidemic detection of weekly incidence rates is assessed by Kolmogorov-Smirnov test on the absolute difference between the empirical and the cumulative density function of the estimated exponential distribution with significance level 0 ≤ α ≤ 1.


The main advantage with respect to other approaches is the adoption of a statistically meaningful test, which provides an indicator of epidemic activity with an associated probability. The detection algorithm was initiated with parameter λ0 = 3.8617 estimated from the training sequence (corresponding to non-epidemic incidence rates of the 2008-2009 influenza season) and sequentially updated. Kolmogorov-Smirnov test detected the following weeks as epidemic for each influenza season: 50−10 (2008-2009 season), 38−50 (2009-2010 season), weeks 50−9 (2010-2011 season) and weeks 3 to 12 for the current 2011-2012 season.


Real medical data was used to assess the validity of the approach, as well as to construct a realistic statistical model of weekly influenza incidence rates in non-epidemic periods. For the tested data, the results confirmed the ability of the algorithm to detect the start and the end of epidemic periods. In general, the proposed test could be applied to other data sets to quickly detect influenza outbreaks. The sequential structure of the test makes it suitable for implementation in many platforms at a low computational cost without requiring to store large data sets.

Influenza; Sequential methods; Statistical test; Detection theory