Global Asymptotic Stability of a Fractional-Order Model for Mpox Dynamics with Media Effects

A fractional-order mathematical model is derived for mpox transmission dynamics that explicitly incorporates the influence of public awareness through a new awareness-dependent transmission function. The proposed incidence function models the reduction in disease transmission as the level of awareness increases, thereby capturing the dynamic interaction between epidemic progression and behavioral response. The model further accounts for asymptomatic infection, hospitalization, recovery, and awareness evolution using Caputo fractional derivatives to incorporate memory effects. Basic mathematical properties of the model, including positivity, boundedness, and existence of solutions, are established. The basic reproduction number, R0, is derived using the next-generation matrix approach, and a sensitivity analysis is performed to identify the epidemiological parameters that most strongly influence disease transmission. Local and global stability analyses demonstrate that the disease-free equilibrium is locally and globally asymptotically stable whenever R0<1, while an endemic equilibrium exists and is globally asymptotically stable when R0>1 and a forward transcritical bifurcation occurs at R0=1. Numerical simulations validate the analytical findings and illustrate the significant role of sustained public awareness in reducing disease transmission and mitigating epidemic outbreaks. The results obtained from the proposed model suggest that combining behavioral awareness strategies with conventional public health interventions can substantially improve the long-term control of mpox.