Bayesian inference for modeling seasonal influenza transmission under control measures

Influenza-like infections, also known as influenza, remain a major public health and economic problem, especially in Saudi Arabia, where periodic epidemics cause a significant strain on public health resources. To assess the influence of vaccine interventions in the spread of the disease, we used a Bayesian inference technique to model and forecast influenza-like illness (influenza) transmission dynamics. We employed the SVEIHR model and used Markov Chain Monte Carlo (MCMC) simulations, along with a No-U-Turn Sampler (NUTS), to estimate the parameters from weekly confirmed cases of influenza in Saudi Arabia (2020–2022). The parameters were estimated along with 95% credible intervals (CrI), thus providing a sound statistical basis for assessing the efficacy of interventions. To determine the most influential parameters in disease transmission, we also conducted sensitivity analysis using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCC). The results reveal that the effective contact rate and initial exposure level are the most influential parameters in disease transmission, while the vaccination rate had a mild negative correlation.