Mathematical analysis and dynamical transmission of SEIrIsR model with different infection stages by using fractional operator

This paper presents a Respiratory Syncytial Virus (RSV) epidemic model for a continuous human population of super-spreading infected individuals. The model uses a generalized fractal–fractional derivative with the Mittag-Leffler function to analyze transmission, considering different infection stages, and demonstrates the effectiveness of certain individuals as viral spreaders. Using linear growth and Lipschitz requirements, the study determines the existence, uniqueness, positiveness, and boundedness of a proposed fractional-order system in order to assess its viability. The global stability of equilibrium points is verified by the Lyapunov function, and the effects of the model’s parameters are investigated through sensitivity analysis. To comprehend the model’s behavior and create preventative measures for infected people, a numerical simulation of its activity is also carried out. By offering a more realistic depiction of virus behavior at various dimensions and population effects, the fractal–fractional model enhances comprehension and forecasts. The results highlight the importance of fractional order and its fitting function in the model by demonstrating how input parameters affect the dynamic behavior of RSV infection. Such an investigation will aid in understanding the behavior of the RSV and develop prevention measures for infected individuals.