Manipulating the Hopf and Generalized Hopf Bifurcations in an Epidemic Model via Braga's Methodology

Using Braga's control theory as a foundational approach, this paper investigates the control of Hopf and generalized Hopf bifurcations within a Susceptible-Infectious model featuring two distinct infectious stages, one being nonlethal and the other lethal. The model with control inputs is analyzed to understand the dynamics at one of its equilibrium points where such bifurcation phenomena occur. By applying Braga's control theory, we explore how control inputs can influence the system's behavior, specifically targeting the induction and modulation of limit cycles associated with Hopf bifurcations of codimension-1 and codimension-2. The research focuses on identifying how variations in control parameters affect these periodic oscillations and their characteristics. The results may guide public health interventions by elucidating how specific control functions and parameters can be optimized to stabilize disease dynamics and reduce undesirable fluctuations in epidemic models.