This research investigates the dynamics of an SEIVR nonlinear epidemiological model of COVID-19 which incorporates a nonlinear incidence rate, saturated treatment, and reinfection of vaccinated compartment. The model reveals a unique interplay between vaccination, treatment efficacy, and reinfection within the vaccinated class. Notably, it exhibits backward bifurcation signifying the coexistence of two bistable endemic equilibria even for the instance when the basic reproduction number is less than one. This highlights challenges in disease control, as sustained transmission can persist under specific conditions. The proposed model also displays complex dynamics such as sustained oscillations through Hopf bifurcation. Our analysis delves into the stability and amplitude of these oscillations, providing insights into potential cyclical patterns in disease dynamics. These findings have consequences for understanding the long-term dynamics of COVID-19, particularly in the context of vaccination and treatment interventions. Numerical simulations and analytical results illuminate the impact of key parameters on the model’s behavior.