Stochastic Modelling of Seasonal Influenza Dynamics: Integrating Random Perturbations and Behavioural Factors

Abstract

The study proposes a stochastic model to investigate the seasonality of influenza in Saudi Arabia. In contrast to the classical deterministic model, we incorporate internal stochastic ambient noise through white noise perturbations in order to present a more realistic portrayal of the oscillation of sick individuals. The model correctly reproduces the empirical seasonal peak in
the number of influenza cases, which is most strongly expressed in epidemiologic week 30, also showing the seasonal outbreak periodicity. Sensitivity analysis demonstrates that the magnitudes of stochastic fluctuations play a crucial role in the prediction uncertainty and the outbreak variability. Transmission rates and the recovery parameter are the main determinants of the magnitude, timing, and impact on hospitalization of the epidemic wave. A greater transmission rate is consistently associated with more intense and prolonged breakouts, whereas a larger transmission rate facilitates a more rapid ascent and descent of the peak. These findings underscore the significance of stochastic factors and pinpoint essential parameters for enhancing public health interventions and resource allocation strategies. Our results provide practical recommendations for enhancing influenza preparation using data-driven stochastic modelling.