A Reproducible Bayesian–Mechanistic Framework for Reproduction-Number Estimation and Early Warning in Resource-Limited Surveillance: An Illustrative Simulation Study

Advanced epidemic-modelling methods are often difficult to deploy in resource-limited settings, where surveillance is weekly, delayed, and substantially under-reported. We present the Hybrid Bayesian–Mechanistic Framework (HBMF), coupling a mechanistic Erlang–SEIR model with a penalised B-spline representation of the time-varying transmission rate, a delayed time-varying reporting model, and a negative-binomial likelihood, with fully-marginalised uncertainty via Markov chain Monte Carlo (MCMC). The core of the paper is a declared synthetic identifiability and calibration study in which every figure and quantity is produced by the released code from data with a known ground truth. On synthetic weekly, delayed, under-reported data (mean reporting fraction 0.42), HBMF recovers the reproduction-number trajectory (posterior median RMSE 0.15; 95% credible band covering the true R_t at 100% of days on the reference dataset) and yields well-calibrated posterior-predictive intervals across 44 replicate datasets (coverage 0.52/0.82/0.97 at nominal 0.50/0.80/0.95; maximum split-R̂=1.06). The method's limits are equally clear: the level of R_t and the reporting trend are only partially identified from a single series, and a fast Laplace approximation under-covers latent R_t. Against EpiEstim given the most favourable treatment of its generation-time input (the true generation-time distribution) on the same data, HBMF attains both lower error (0.149 vs. 0.338) and higher 95% coverage (0.813 vs. 0.069). A supplementary application to real dengue surveillance (Rio de Janeiro, 2021; InfoDengue), not a validation since no true R_t exists, shows good in-sample fit and moderate agreement with an independent operational estimate (r=0.43); a held-out forecast was outperformed by a naive baseline, and replacing random-walk Metropolis with a Laplace-preconditioned Hamiltonian Monte Carlo sampler (maximum split-R̂ from 1.57 to 1.18) revealed that the under-converged chain had understated forecast uncertainty by roughly an order of magnitude—evidence that convergence diagnostics carry real operational consequences. All code and the exact real-data query are released for reproduction.