A Scoping Review on Mathematical Modelling Techniques Used in Non-communicable Disease (NCD) Research

Abstract

Aims: Non-communicable diseases (NCDs) now account for almost three-quarters of global mortality and impose an escalating burden on health systems. Their initiation and progression arise from interdependent mechanisms that arise from various angles. Mathematical and computational modelling affords an integrative framework for unifying evidence across these levels, therefore we aimed to synthesize how deterministic, stochastic, Markov, agent-based and related approaches, have been applied to NCD research, and to identify current strengths, gaps and future priorities. Study Design: Scoping review conducted in accordance with PRISMA-ScR guidelines. Place and Duration of Study: Electronic searches of PubMed, Web of Science, Scopus and Google Scholar were performed remotely for articles published between 2004 and 2024. Methodology: Titles and abstracts were screened against predefined inclusion criteria; full texts were assessed independently by two reviewers, with disagreements resolved by consensus. Eligible studies were charted and synthesised narratively with attention to modelling class, disease domain, data sources and analytic purpose. Results: Deterministic ordinary- and partial-differential-equation systems dominated mechanistic work, illuminating cellular and organ-level processes in myocardial infarction, tumour growth and glycaemic regulation. Stochastic and agent-based models captured intrinsic noise and population heterogeneity, clarifying clonal evolution in cancer, β-cell attrition in diabetes and ventilation defects in chronic lung disease. Markov and microsimulation frameworks traced long-term disease trajectories and underpinned most health-economic evaluations, typically wrapped in Monte Carlo procedures for probabilistic sensitivity analysis. Machine-learning algorithms and regression techniques unlocked high-dimensional clinical and omics data, supplying parameter estimates, risk scores and fast emulators that augment mechanistic cores. Across methods we observed two persistent gaps: (i) fragmented, non-interoperable datasets that hinder cross-disease learning, and (ii) limited incorporation of equity metrics when projecting intervention benefits. Conclusion: Integrated modelling provides a powerful route to deeper biological insight, more accurate burden projections and rigorous appraisal of interventions across NCDs. Nevertheless, there is an urgent need for harmonised, open-access longitudinal data pipelines, hybrid multiscale architectures that blend mechanistic transparency with machine-learning speed, statistically principled calibration, and equity-centred reporting so that next-generation models inform policies that are not only effective but also fair.