Global Dynamics of a Fractional-Order COVID-19 Model for India with Modified Crowley-Martin Incidence Rate and Optimal Vaccination Control Using Real Data Analysis

This study presents a novel fractional-order SEIR model to analyze the transmission dynamics of COVID-19 in India, incorporating a modified Crowley-Martin nonlinear incidence rate to account for saturation effects in disease spread. The model utilizes the Caputo fractional derivative to capture memory and hereditary properties inherent in epidemic processes, offering a more realistic alternative to classical integer-order approaches. Key theoretical properties of the system including positivity, boundedness, and the existence and uniqueness of solutions are rigorously established. The basic reproduction number R 0 is derived, and global stability conditions for both disease-free and endemic equilibria are examined using Lyapunov functional techniques. To align the model with real-world conditions, parameter estimation is performed using actual COVID-19 case data from India through both least squares and Bayesian inference methods. An optimal control problem is formulated to assess the effectiveness of combined vaccination and treatment strategies, and is solved using Pontryagin's Minimum Principle. Numerical simulations are conducted using the Adams-Bashforth-Moulton predictor-corrector method to explore the impact of fractional-order dynamics and control interventions on epidemic progression. Results indicate that lower fractional orders delay the infection peak, and that optimal control significantly reduces the number of infections and intervention costs. This work underscores the importance of fractional modeling and data-driven control in managing large-scale epidemics, and provides actionable insights for public health policy in India and beyond.