Abstract
Influenza remains a global challenge, imposing a significant burden on society and the economy. Many influenza cases are asymptomatic, leading to greater uncertainty and the under-reporting of cases in influenza transmission and preventing authorities from taking effective control measures. In this study, we propose a Bayesian hierarchical approach to model and correct under-reporting of influenza cases in Hong Kong, incorporating a discrete-time stochastic, Susceptible-Infected-Recovered-Susceptible (DT-SIRS) model that allows transmission rate to vary over time. The incidence of influenza exhibits seasonality. To examine the relationship between meteorological factors and seasonal influenza activity in subtropical areas, five meteorological factors are included in the model. The proposed model explores the effects of meteorological factors on transmission rates and disease detection covariates on under-reporting, and the inclusion of the DT-SIRS model enables more accurate inference regarding true disease counts. The results demonstrate that under-reporting rates of influenza cases vary significantly in different years and epidemic seasons. In conclusion, our method effectively captures the dynamic behavior of the disease, and we can accurately estimate under-reporting and provide new possibilities for early warning of influenza based on meteorological data and routine surveillance data.