Epidemiological Modeling of Seasonal Influenza Through Periodic Mean-Reverting Stochastic Processes

Seasonal influenza follows annual cycles, but variation in epidemic magnitude and timing complicates preparedness. We applied periodic mean reverting stochastic differential equations (SDEs) to seven seasons of weekly Texas influenza surveillance data. Missing observations were imputed using MissForest and compared with four alternative methods. Stochastic variability was modeled using {sigma}X(t) dW(t), with p = 1/2,2/3,5/6, and 1, representing square root, intermediate sublinear, and multiplicative diffusion. Each specification was evaluated for direct influenza modeling and within a suscept

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