A Fractional Optimal Control Problem for Mpox Integrating Vaccination, Treatment and Awareness Campaign

The aim of the present study is to propose a new mathematical model of compartment type for an epidemic problem using fractional order derivatives. This epidemic model takes into account vaccination, hospitalization, asymptomatic infection, and health awareness programs. Caputo fractional derivatives are used to model the temporal non-locality of epidemic phenomena in the proposed model. The qualitative analysis of the model includes the characterization of equilibrium points and their stability. The disease-free equilibrium (DFE) is shown to be locally asymptotically stable when the basic reproduction number R0<1, and unstable otherwise. Conversely, an endemic equilibrium emerges when R0>1, corresponding to the instability of the DFE. Periodic oscillation is observed for a higher rate of infection transmission. A fractional optimal control problem is formulated to minimize disease prevalence through vaccination, hospitalization, and treatment strategies, supported by sustained awareness campaigns. The results emphasize the role of vaccination, treatment and awareness campaign in controlling Mpox outbreaks, showing their success in minimizing the epidemic. In addition, a fractional optimal control model is proposed to reduce disease prevalence using preventive measures such as vaccinations and treatments coupled with awareness impacts. From these results, one can clearly understand that vaccinations and continuous public health awareness are essential in reducing Mpox cases, which help flatten epidemic trends.