COVID-19 Mathematical Modeling During the First Five Years: A Comprehensive Review of Classical, Stochastic, and Fractional Approaches

Abstract

Mathematical modeling has played a crucial role in epidemiological research, its importance amplified during the COVID-19 pandemic. This comprehensive review provides a five-year analysis of mathematical models developed to understand and control COVID-19 transmission. The reviewed studies include deterministic models such as SIR and SEIR frameworks, stochastic models incorporating random effects, age-structured models accounting for demographic heterogeneity, within-host models describing viral dynamics and immune responses, and hybrid, multi-strain, agent-based, and network-based approaches. A literature search was conducted across major databases, and studies were categorized by model structure, analytical methods, and data integration strategies. The review examines the predictive capabilities of deterministic models, the role of stochasticity in capturing uncertainty, and the importance of demographic structure in explaining transmission and mortality patterns. The effectiveness of non-pharmaceutical interventions and vaccination strategies is also assessed. The integration of real-time epidemiological data into modeling efforts is discussed, highlighting insights into hospitalization demand, ICU utilization, and mortality trends across pandemic waves. By analyzing the strengths and limitations of each approach, this review aims to inform future pandemic management, concluding with emerging trends, including the integration of genomic data, and future directions for the field.