A systematic and critical review of fractional order models in infectious disease dynamics

Abstract Fractional-order models have become increasingly relevant in infectious disease epidemiology for characterizing transmission dynamics, capturing memory effects, and evaluating intervention strategies. This study presents a systematic and critical review of fractional-order models applied to COVID-19, Zika, HIV/AIDS, influenza, and Ebola. A systematic search was conducted in Scopus, ScienceDirect, and Google Scholar, including studies that employed fractional-order formulations for infectious disease dynamics. Among 1,258 identified records, 279 studies met the inclusion criteria. Most studies originated from Asia (68.45%) and Africa (21.14%). Fractional compartmental models were predominant (79.21%), while hybrid frameworks integrating stochastic approaches or artificial intelligence accounted for 11.11% of studies. The Caputo and Atangana–Baleanu operators were the most frequently used, representing 46.62% and 25.40% of the reviewed studies, respectively. Only 14.98% of studies incorporated biologically interpretable fractional parameters, and dimensional consistency was explicitly considered in only 44 studies. Quarantine and vaccination were among the most frequently investigated control strategies, included in 34.10% and 27.30% of models, respectively. The findings highlight the rapid expansion and methodological diversity of fractional epidemiological modeling. Future research should focus on biological interpretation, rigorous validation, dimensional consistency, and standardized comparisons, while exploring hybrid fractional-order frameworks integrating artificial intelligence and stochastic approaches.