Semi-Analytical Solution of Fractional –Order Mathematical Model of COVID-19 Via Atangana Baleanu- Caputor Derivative

COVID-19, caused by the novel coronavirus SARS-CoV-2, has had a profound global impact due to its high transmission rate and evolving clinical profile. Understanding its spread and identifying effective intervention strategies remain critical for public health planning. In this study, we develop a deterministic compartmental model to explore the transmission dynamics of COVID-19, incorporating a fractional-order derivative to account for memory effects inherent in disease progression. The human population is divided into six epidemiological compartments: susceptible, exposed, infected, under treatment, deceased, and recovered individuals. To more accurately reflect the temporal and cumulative effects of infection, we applied the Atangana–Baleanu–Caputo (ABC) fractional-order derivative, which improves the model's capacity to capture long-term dependencies often overlooked in classical models. A semi-analytical solution is derived using this approach. Stability analysis reveals that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number is less than one, and unstable when othrwise. Through numerical simulations, it showed that reducing the contact rate and enhancing treatment interventions significantly lower infection prevalence and increase recovery rate. The findings highlight the effectiveness of timely treatment and behavioral control measures in curbing COVID-19 transmission. We recommend the continued enforcement of public health strategies such as reducing human-to-human contact, improving treatment accessibility, and increasing vaccine coverage. The proposed fractional-order model provides a more realistic framework for studying infectious diseases with memory-driven dynamics and can be adapted for future epidemic preparedness.