Global Dynamical Behavior of an Age-Dependent SI Epidemic Model with General Infection Function

This study investigates an age-structured SI epidemic model with a general infection function [Formula: see text]. We establish well-posedness of the model, showing that the solutions generate a unique semiflow that admits a global compact attractor. A sharp threshold dynamic governed by the basic reproduction number [Formula: see text] is established: when [Formula: see text], the disease-free equilibrium is globally asymptotically stable, ensuring disease elimination; when [Formula: see text], the system exhibits uniform persistence and the unique endemic equilibrium is globally asymptotically stable. Numerical simulations confirm the theoretical findings, demonstrating the robustness and relevance of the model.