Using Extreme Value Theory Approaches to Forecast the Probability of Outbreak of Highly Pathogenic Influenza in Zhejiang, China

Background: Influenza is a contagious disease with high transmissibility to spread around the world with considerable morbidity and mortality and presents an enormous burden on worldwide public health. Few mathematical models can be used because influenza incidence data are generally not normally distributed. We developed a mathematical model using Extreme Value Theory (EVT) to forecast the probability of outbreak of highly pathogenic influenza. Methods: The incidence data of highly pathogenic influenza in Zhejiang province from April 2009 to November 2013 were retrieved from the website of Health and Family Planning Commission of Zhejiang Province. MATLAB “VIEM” toolbox was used to analyze data and modelling. In the present work, we used the Peak Over Threshold (POT) model, assuming the frequency as a Poisson process and the intensity to be Pareto distributed, to characterize the temporal variability of the long-term extreme incidence of highly pathogenic influenza in Zhejiang, China. Results: The skewness and kurtosis of the incidence of highly pathogenic influenza in Zhejiang between April 2009 and November 2013 were 4.49 and 21.12, which indicated a “fat tail” distribution. A QQ plot and a mean excess plot were used to further validate the features of the distribution. After determining the threshold, we modeled the extremes and estimated the shape parameter and scale parameter by the maximum likelihood method. The results showed that months in which the incidence of highly pathogenic influenza is about 4462/2286/1311/487 are predicted to occur once every five/three/two/one year, respectively. Conclusions: Despite the simplicity, the present study successfully offers the sound modeling strategy and a methodological avenue to implement forecasting of an epidemic in the midst of its course.