This paper introduces a novel mathematical model to investigate the complex dynamics of Anthroponotic Cutaneous Leishmania (CL) transmission. The model, which includes seven compartments for both human and vector populations, incorporates a convex incidence rate to account for the increased infection rate over short periods due to dual exposures. The authors derive the threshold value \( R_0 \) using the next-generation method and explore both local and global stability conditions at the disease-free equilibrium (DFE) and the endemic equilibrium (EE) points. For the DFE, they establish stability when \( R_0 < 1 \) using center manifold theory and the Castillo-Chavez method. For the EE, they determine stability conditions when \( R_0 > 1 \) using a geometric approach and Lyapunov theory. The study also includes sensitivity analysis to identify parameters that significantly influence the model's behavior and numerical simulations to validate the theoretical findings. The results demonstrate global asymptotic stability at the DFE and EE under specific conditions, providing valuable insights for understanding and controlling CL transmission.This paper introduces a novel mathematical model to investigate the complex dynamics of Anthroponotic Cutaneous Leishmania (CL) transmission. The model, which includes seven compartments for both human and vector populations, incorporates a convex incidence rate to account for the increased infection rate over short periods due to dual exposures. The authors derive the threshold value \( R_0 \) using the next-generation method and explore both local and global stability conditions at the disease-free equilibrium (DFE) and the endemic equilibrium (EE) points. For the DFE, they establish stability when \( R_0 < 1 \) using center manifold theory and the Castillo-Chavez method. For the EE, they determine stability conditions when \( R_0 > 1 \) using a geometric approach and Lyapunov theory. The study also includes sensitivity analysis to identify parameters that significantly influence the model's behavior and numerical simulations to validate the theoretical findings. The results demonstrate global asymptotic stability at the DFE and EE under specific conditions, providing valuable insights for understanding and controlling CL transmission.