Fractional-order analysis of asymptomatic COVID-19 transmission dynamics with stability and control strategies

Understanding the hidden role of asymptomatic carriers remains a major challenge in controlling COVID-19 transmission. To address this, we develop a fractional-order SEVIAR model that captures memory-dependent infection dynamics using the Caputo derivative. This framework incorporates persistent behavioral and biological effects that classical integer-order models fail to represent. A rigorous mathematical analysis is conducted to establish the existence and uniqueness of solutions, along with the positivity and boundedness of all state variables. In addition, Hyers–Ulam stability is proven to further demonstrate the robustness of the model dynamics. The effective reproduction number $$\mathcal {R}_e$$ is derived using a graph-theoretic approach, and the model is calibrated with epidemiological data from South Africa to assess the impact of fractional dynamics on disease transmission. The results show that fractional orders $$\alpha < 1$$ slow epidemic growth and prolong infection persistence, highlighting the influence of memory effects on outbreak patterns. Simulations also reveal that asymptomatic individuals significantly contribute to transmission and that combined interventions involving vaccination, public health measures, and awareness campaigns yield the greatest reduction in infection peaks. Overall, this study introduces a comprehensive fractional-order modeling framework that improves understanding of asymptomatic COVID-19 transmission, demonstrates strong theoretical stability properties, and provides quantitative insights to support more effective public health strategies.