Modeling and Forecasting Influenza Outbreaks: A Robust Laplace-ARDL Framework vs. Deep Learning LSTM for Epidemiological Surveillance

Abstract

Accurate forecasts of seasonal influenza are imperative to successfully manage public health resources. However, epidemiological time series data often show significant spiky volatility along with heavy-tailed distributions that do not satisfy the normality assumption required by traditional linear models. This paper proposes a new model called Robust Laplace-ARDL, which uses a Double Exponential (Laplace) distribution instead of the standard normal distribution to accommodate heavy-tailed distributions. Using 792 weekly observations (2005–2020) and benchmarking against a Long Short-term Memory (LSTM) model, the Laplace-ARDL <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>5</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> model reduces the mean square error (MSE) by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mn>33.5</mml:mn> <mml:mtext>\%</mml:mtext> </mml:math> compared to the LSTM model. This paper provides empirical evidence that it is vital to solve the leptokurtic distribution in infection data for obtaining stable forecasts.