Theoretical and Computational Advances in Sequential Monte Carlo Methods for Online State Estimation in Nigerian Epidemiological Surveillance Systems

Real-time epidemiological surveillance in Nigeria requires statistical state estimation methods that update disease burden estimates sequentially as new data arrive from surveillance networks, without requiring full data re-analysis, and for which rigorous theoretical guarantees in the non-Gaussian, non-linear epidemiological model settings characterising Nigerian outbreak data remain underdeveloped. This dissertation develops theoretical and computational advances in sequential Monte Carlo (SMC) methods for online state estimation applicable to Nigerian epidemiological surveillance systems. New convergence rate theorems for SMC samplers under non-stationary transition kernels corresponding to epidemic phase transitions are derived, extending existing theoretical results. A computationally efficient resample-move SMC algorithm with adaptive tempering calibrated to Nigerian outbreak reporting delay distributions is introduced. Theoretical variance reduction bounds relative to bootstrap particle filter benchmarks are established. The methodology is applied to real-time estimation of effective reproduction numbers and disease burden in three Nigerian surveillance contexts: cholera in Borno State, Lassa fever in Edo State, and meningococcal meningitis in Sokoto State, using NCDC weekly surveillance data. The adaptive SMC algorithm achieved 41 percent variance reduction over bootstrap particle filters for effective reproduction number estimation during outbreak acceleration phases. Real-time burden estimates derived from the SMC system were available within 4 hours of weekly data upload, compared to 72-hour delays for batch analysis. The dissertation provides NCDC with a theoretically validated and computationally deployable online surveillance estimation system. Keywords: sequential Monte Carlo, particle filter, epidemiological surveillance, Nigeria NCDC, online state estimation