Application of Extreme Value Analysis in Epidemiology: Modeling Dengue Prevalence Extremes

Abstract

This study explores the application of Extreme Value Theory (EVT) to epidemiology, demonstrating its capability to model rare but impactful disease prevalence events. Using monthly dengue prevalence in Bangladesh (January 2008–September 2023) as a case study, the objectives are to: evaluate the suitability of the Generalized Pareto Distribution (GPD) for capturing upper-tail behavior in epidemiological data, assess an automated threshold selection method based on the Anderson–Darling statistic and L-moments estimation (AD-L), and examine the impact of dataset extension on model performance and uncertainty. Non-stationarity is addressed by fitting a Seasonal ARIMA (SARIMA) model, with residuals used for GPD modeling. Return levels for 5-, 10-, and 20-year periods are estimated and expressed on the original prevalence scale, with 95% confidence intervals obtained via bootstrap resampling. A hybrid simulation framework generates synthetic series (N = 500) replicating observed trend, seasonality, and tail features to assess the effect of increased sample size. Results show that the GPD, combined with the AD-L method, effectively models heavy-tailed residual extremes, while simulated data improve goodness-of-fit metrics substantially. However, the scarcity of exceedances limits reductions in return level uncertainty. This work demonstrates a novel, data-driven application of EVT to infectious disease prevalence, offering a transferable framework for epidemiological risk assessment.