Fractional Modeling of Zoonotic Spillover with Optimal Control in a Multi Host System with Memory Effects

We propose a fractional-order multi-host epidemic model that integrates human--pig--bird transmission with optimal control, explicitly capturing memory effects absent in existing integer-order and single-host frameworks. Unlike previous studies, the model simultaneously couples fractional dynamics, multi-host spillover pathways, and time-dependent prevention and treatment controls. Numerical investigations reveal that fractional order significantly alters transient dynamics, delays epidemic peaks, and enhances control efficiency. Contour and phase-portrait analyses further demonstrate how coordinated interventions reshape the reproduction number landscape and redirect trajectories toward disease-free states. These results provide new mechanistic insight into how memory and optimal control interact in complex zoonotic systems.