This study explores and investigates a human respiratory syncytial virus (RSV) infection using a generalized fractional-order susceptible-exposed-infected-recovered (SEIR) model. The model incorporates the recently introduced fractional derivative operator, the \(\psi\) -Caputo derivative, defined with respect to an auxiliary function, \(\psi (t)\) . The formulation allows flexible depiction of memory and genetic effects in disease dynamics, beyond integer-order models. A rigorous mathematical framework proves the existence and uniqueness of solutions to the \(\psi\) -Caputo fractional initial-value problem (IVP), proving the model’s theoretical well-posedness. We also offer an innovative and efficient numerical approach for solving the fractional model, with verified convergence and a valid error bound. Comprehensive simulations and analyses are conducted to the applicability of the model. In particular, the model represents diverse dynamic behaviors by varying the fractional order \(\alpha\) within the range (0, 1]. These results indicate that the system’s reaction is sensitive to the fractional order \(\alpha\) , with classical integer-order dynamics regained when \(\alpha \rightarrow 1\) . Furthermore, the fractional SEIR model with an optimal control framework uses treatment as a control variable to evaluate intervention options. Simulation results indicate that the fractional \(\psi\) -Caputo model, with optimal control, better decreases infectious people than standard integer-order models. These findings demonstrate the modeling and control approach’s potential to analyze, predict, and mitigate RSV infections in real-world circumstances.
