Numerical Simulation and Fractional Order Analysis of COVID-19 Model with Treatment Intervention

COVID-19 remains a significant global health challenge, especially in regions where healthcare systems are strained and treatment accessibility varies. This study develops a fractional-order mathematical model for COVID-19 transmission that incorporates treatment effects to realistically capture disease control measures. Using Caputo fractional derivatives, the model effectively accounts for memory effects and complex time-dependent dynamics that classical integer-order models may overlook. The model’s semi-analytical solution is obtained through the Adams–Bashforth–Moulton method, ensuring accurate and computationally efficient results. Analytical proofs confirm the existence, uniqueness, and boundedness of solutions, verifying the model's robustness. A thorough sensitivity analysis identifies critical parameters impacting COVID-19 spread, such as treatment rate and transmission coefficients. Simulation outcomes demonstrate that increasing treatment rate and reducing contact rate substantially decrease infection prevalence. Comparative studies reveal that the fractional-order model offers superior flexibility and precision over traditional integer-order models in representing COVID-19 dynamics. The Adams–Bashforth–Moulton method serves as an effective numerical technique for approximating model solutions, supporting its use in epidemic control strategies. The findings highlight the vital role of sustained treatment efforts combined with behavioural controls in mitigating COVID-19 transmission. This model provides a valuable framework for public health planning and can be adapted to other infectious diseases exhibiting memory-dependent transmission characteristics