Effect of Behavioral Awareness Delay on the Dynamics of a Discrete-Time SIR Model for Mpox in Kenya: Stability and Neimark–Sacker Bifurcation Analysis

Aims/ Objectives: To investigate how delayed behavioral awareness affects the dynamics of a discrete-time SIR model for Mpox transmission, with an emphasis on local stability and the occurrence of a Neimark–Sacker bifurcation. Study Design: Theoretical mathematical modeling study with analytical stability analysis and numerical simulation. Place and Duration of Study: Multimedia University of Kenya, Faculty of Science and Technology; research conducted between August 2025 and August 2026. Methodology: A normalized discrete-time SIR model incorporating a population-level behavioral awareness index Bn representing a combination of being informed about Mpox infection risk and adopting protective behavior. A discrete delay t was introduced in the behavioral-awareness response to the infection. The disease-free and endemic equilibria were derived and their local stability was analyzed using linearization and the Jury criterion. For t > 0, the system was linearized about the endemic equilibrium and the spectral radius p examined numerically in MATLAB as t varied. Time-series simulations and phase portraits were used to characterize the resulting dynamics. Time-series simulations and phase portraits were generated to illustrate the dynamics.