Abstract

Mathematical models that capture time-memory and behavioral interventions within a single dynamical system can be used to investigate infectious disease dynamics. In this study, we provide a Caputo fractional-order SEIR model with preventive controls and behavioral awareness. The equilibrium and stability analysis show disease persistence and eradication, while the fractional approach captures nonlocal temporal dependence in the evolution of the model's state variables. We formulate the constrained optimization problem using Pontryagin’s maximum principle and use normalized sensitivity analysis to assess the impact of fractional-order and epidemiological parameters. We further investigate the forward-backward sweep technique using numerical convergence analysis. Using the same parameterizations and initial conditions, we perform updated numerical simulations of the susceptible, infected, and recovered states under different fractional orders and controls. Within the same fractional-order system, the trajectory technique provides an analytical comparison of memory effects and behavior modulation. By combining optimal control, sensitivity analysis, convergence analysis, and fractional differential equation modeling, the paper provides a mathematical framework for understanding the dynamic behavior of infectious diseases.