Bifurcations in SAIR Epidemic Model With Nonmonotonic Incidence and Saturated Treatment: Influence of Psychological Factors and Medical Resource Constraints

ABSTRACT In order to take into account the psychological influences on the spread of infectious diseases and the constraints of limited medical resources during the outbreaks, in this study, we propose an SAIR epidemic model with nonmonotonic incidence and saturated treatment. Theoretical and numerical analyses of the proposed model reveal complex dynamical behaviors. Under specific conditions, multiple endemic equilibria emerge, resulting in bistability within the model system. The local and global stability properties of these equilibria are analyzed and key bifurcations are investigated to characterize the epidemiological dynamics. Through carefully calibrated model parameters, extensive simulations of rich dynamical phenomena have been conducted to validate and complement the bifurcation analysis. In addition to multiequilibria, bistability, stability switches, and oscillatory behavior, bifurcation diagrams illustrate how key parameters affect system dynamics, particularly those related to psychological impact and saturated treatment effects. These graphical representations, including transcritical, saddle‐node, supercritical Hopf, cusp, and Bogdanov–Takens bifurcations, demonstrate the inherent complexity of the model's dynamical behaviors.