Advances in Statistical Modelling of Epidemics: Estimation and Innovations

Abstract

Statistical modelling plays a central role in understanding, forecasting, and mitigating infectious disease epidemics. This systematic review synthesizes major statistical frameworks used in epidemic modelling, including deterministic and stochastic models, Bayesian inference, machine learning techniques, and intervention analysis. A structured search strategy was employed using combinations of key terms such as “epidemic modelling”, “statistical estimation”, “infectious disease forecasting”, “Bayesian inference”, “machine learning”, “R₀ estimation”, “intervention impact”, and “stochastic epidemic models”. To ensure methodological rigor and contextual relevance, only studies meeting predefined quality and applicability criteria were included. Out of 285 unique records screened, 75 high-quality studies were selected for final analysis. The review begins by comparing deterministic models—based on differential equations and fixed population assumptions—with stochastic models that incorporate randomness to better capture real-world variability. Bayesian approaches are discussed for their strengths in uncertainty quantification, real-time updating, and parameter estimation using methods such as Markov Chain Monte Carlo (MCMC) and Gaussian processes. The review also examines sub-epidemic decomposition models that capture overlapping waves, and network-based models that reflect spatial structure and contact heterogeneity. Forecasting approaches—both mechanistic and data-driven—are critically assessed, alongside methods for estimating key epidemiological parameters such as the basic reproduction number (R0) and time-varying transmission rates. The integration of machine learning and hybrid models is highlighted for their growing potential in real-time surveillance and scenario analysis. The review concludes with an overview of intervention modelling, optimization strategies, and visualization tools, offering practical guidance for researchers and decision-makers while outlining challenges and future directions in epidemic modelling.