Asian Journal of Probability and Statistics

Epidemic modelling increasingly combines routine surveillance, mechanistic transmission theory and data-intensive learning, yet the resulting approaches are often compared as though they estimate the same quantities and serve the same decisions. This critical narrative review evaluates statistical, mathematical, machine-learning and hybrid approaches to infectious disease dynamics, with emphasis on inferential purpose, data-generating and observation processes, uncertainty, validation, interpretability and public-health use. Peer-reviewed literature published from January 2000 to 31 May 2026 was identified through biomedical, multidisciplinary and computing-oriented scholarly sources, supplemented by citation searching and verification against authoritative bibliographic records. Foundational earlier papers were retained when necessary. The synthesis indicates that no model class is uniformly superior. Statistical surveillance and time-series models are often efficient for anomaly detection, nowcasting and short-horizon forecasting, but their parameters rarely support intervention counterfactuals without additional causal structure. Mechanistic compartmental, network, spatial and agent-based models make transmission assumptions explicit and can represent intervention pathways, although structural misspecification, weak identifiability and mismatch between latent infections and observed reports can dominate their uncertainty. Machine-learning models can extract nonlinear and high-dimensional patterns from heterogeneous data, but apparent accuracy is vulnerable to temporal or spatial leakage, changing surveillance systems, distribution shift, weak probabilistic calibration and limited causal meaning. Hybrid models can combine epidemiological constraints with flexible learning and data assimilation; their interpretability nevertheless depends on identifiable parameters, biologically coherent architecture and validation beyond the setting used for training. Across paradigms, the observation process, target definition and decision horizon are as consequential as model form. Credible use therefore requires question-first model selection, explicit separation of forecasts from scenarios, rolling and geographically external validation, calibrated uncertainty, versioned data and code, and transparent communication of assumptions. Progress will depend less on greater complexity alone than on prospective benchmarking, identifiable hybridisation, behaviour-aware causal designs, multimodal surveillance, equitable data systems and operational model governance.