Abstract: This paper investigates the dynamics of a treated SIR epidemic model incorporating partial infectivity of treated individuals and demographic inflow. Explicit expressions for the disease-free and endemic equilibria are derived, along with conditions for their existence and local stability in terms of the basic reproduction number R0. A central result is the identification of a Fold (saddle-node) bifurcation, leading to a strong Allee Effect characterized by bistability between disease extinction and persistence, depending on initial infection levels and parameter values. The analytical findings are supported by symbolic computations and a MATLAB-based numerical procedure that accurately determines the critical bifurcation threshold θc. This study highlights the nonlinear interactions between treatment efficacy, partial infectivity, and population inflow, providing theoretical insights relevant to epidemic control strategies.

Keywords: Treated SIR model, Fold bifurcation, Allee effect, Epidemic dynamics

Pages: 73-77

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