JMIR Publications

ABSTRACT

Background:

Mathematical models have become the intellectual infrastructure of modern infectious disease epidemiology. However, the literature on this topic is highly fragmented across different model families, specific pathogens, and methodological niches, lacking a comprehensive and integrative synthesis.

Objective:

This systematic scoping review aims to synthesize the theoretical foundations, structural typology, and public health applications of mathematical models in infectious disease epidemiology, while identifying critical methodological gaps to guide future research and practice.

Methods:

We conducted a systematic scoping review following the Arksey and O'Malley framework, updated by Levac et al. and the Joanna Briggs Institute guidelines, reported according to the PRISMA extension for Scoping Reviews (PRISMA-ScR). We searched six electronic databases (PubMed/MEDLINE, Embase, Web of Science, Scopus, MathSciNet, and Google Scholar) for literature published between January 1991 and December 2025. From 4,217 initially identified records, 228 were assessed in full text, and 50 studies were included in the final synthesis.

Results:

The review identified and systematically compared six structural model families: deterministic compartmental, stochastic, network-based, agent-based, statistical/hybrid, and fractional-order. Key epidemiological parameters synthesized included the basic reproduction number (R₀), the effective reproduction number R(t), the case fatality ratio (CFR), and the latent and incubation periods. Documented R₀ estimates ranged from 1.4-1.6 for pandemic influenza H1N1 (2009) to 12-18 for measles in unvaccinated populations. Applications spanned tuberculosis, HIV/AIDS, SARS, MERS-CoV, pandemic influenza, dengue fever, and COVID-19. While 96% of studies transparently described their model structure, only 28% provided code or data for reproducibility. To address a critical gap in behavioral modeling, we propose a parsimonious bio-behavioral dynamic transmission rate (β(t) = max(0, β₀ + αt - θI)) that incorporates adherence fatigue and prevalence-elastic risk awareness. The review identified three critical methodological gaps: validation during early outbreak phases, integration of human behavior, and systematic comparisons between model families.

Conclusions:

Mathematical models are indispensable tools for infectious disease epidemiology, yet their maximum utility depends on robust validation, methodological transparency, and high-quality data. This review provides a comprehensive typological comparison and synthesis of documented parameters while articulating an actionable research agenda prioritizing standardized validation platforms, behavioral integration, and multidisciplinary collaboration for future global health emergencies.