Bayesian flexible multilevel nonlinear models in infectious disease modeling using non-informative priors

Accurate modeling of infectious diseases is essential for understanding and predicting pandemic trajectories and informing effective public health interventions. The complex and heterogeneous nature of epidemic data often pose challenges for traditional modeling approaches. This study introduces a novel approach using Bayesian flexible multilevel nonlinear models (SMSN-NLMMs: scale mixtures of skew-normal and SNP-NLMMs: semi-nonparametric approaches), to address these challenges. To evaluate the model performance, we conducted rigorous simulations in various epidemic scenarios and applied the models to real-world COVID-19 data from seven West-African countries. The results demonstrate that both SMSN-NLMMs and SNP-NLMMs significantly out-perform standard nonlinear mixed models (NLMMs) in accurately recovering key epidemic parameters. While both models exhibit similar performance with large sample sizes, SMSN-NLMM and SNP-NLMM with expansion order K = 1 demonstrates greater flexibility for daily reported data. Conversely, SNP-NLMM with K = 2 achieved a better fit for weekly simulated epidemic data. When applied to the COVID-19 data, the models produced results that align with the true estimated transmission parameters, including the turning point, the final size of the outbreak, and the basic reproduction number (R0). The paper also explores the convergence of the Hamiltonian Monte-Carlo (HMC) method in Stan and model sensitivity to prior distributions.