A Unified Theoretical Framework for Non-Stationary Spatial-Temporal Statistical Modelling of Infectious Disease Dynamics in Nigeria

Infectious disease dynamics in Nigeria operate across both geographic space and time in ways that existing statistical models address separately but rarely jointly within a unified theoretical framework adapted to Sub-Saharan African data structures. This dissertation develops a unified theoretical framework for non-stationary spatial-temporal statistical modelling of infectious disease dynamics in Nigeria, making original contributions to the methodology of space-time disease surveillance. The framework integrates non-stationary spatial covariance functions with temporally varying coefficient models within a Bayesian hierarchical structure. Three disease case studies were used for framework development and validation: cholera in the North East, meningitis in the North West, and malaria in the South South, using weekly LGA-level case count data from NCDC. Non-stationarity in spatial dependence was captured by spatially adaptive kernel convolution covariance structures estimated via Markov chain Monte Carlo. Temporal non-stationarity was addressed by time-varying spatial regression coefficients allowing covariate effects to change across epidemic phases. The unified model achieved superior predictive performance over separate spatial and temporal models by 23 percent RMSE reduction across all three diseases. The framework identified disease-specific spatial clustering radii and temporal regime shifts not detectable by conventional models. Formal theoretical properties including identifiability and posterior consistency conditions are derived. The dissertation provides a generalisable methodological contribution to African disease surveillance statistics. Keywords: spatial-temporal modelling, non-stationary covariance, Bayesian hierarchical model, infectious disease, Nigeria