Time-dependent deformation of pre-stressed concrete bridge decks due to creep and shrinkage represents one of the most critical serviceability challenges in structural bridge engineering. This study presents a comprehensive analytical and numerical investigation of long-term deformation behaviour in post-tensioned and pre-tensioned concrete bridge decks, with emphasis on the interdependence between sustained compressive stresses, moisture migration, and the resulting prestress losses. The research synthesises established creep prediction models — including the CEB-FIP Model Code 2010, ACI 209R-92, and the B3 model by Bazant and Baweja — and extends their application to realistic South Sudanese and tropical East African environmental conditions, characterised by high ambient temperatures and variable relative humidity. Finite element analyses employing time-stepping algorithms are utilised to simulate stress redistribution, midspan deflection evolution, and long-term camber decay over a 100-year service life. Results indicate that uncorrected creep-induced deflections can exceed serviceability limits (L/250) within 15 to 25 years in hot-arid conditions, and that cumulative prestress losses from time-dependent effects can range between 14% and 22% of the initial jacking force. Five parametric sensitivity analyses identify relative humidity, age at loading, and the notional section size as dominant contributors to deformation variability. Three design recommendations — including enhanced humidity correction factors and revised partial coefficients for tropical climates — are proposed to supplement current design practice. This paper provides a rigorous, quantitatively grounded fr amework for engineers designing long-span pre-stressed bridge decks in sub-Saharan Africa.