The transmission dynamics of an infectious disease model in fractional derivative with vaccination under real data

The resurgence of monkeypox causes considerable healthcare risks needing efficient immunization programs. This work investigates the monkeypox disease dynamics in the UK, focusing on the impact of vaccination under real data. The key difficulty is to correctly predict the spread of the disease and evaluate the success of immunization efforts. We construct a mathematical model for monkeypox infection and extend it to the fractional case considering the Caputo derivative. The analysis ensures the positivity, boundedness, and uniqueness of the solution for the non-integer system. We conduct a local asymptotical stability analysis (LAS) at the disease-free equilibrium (DFE) D0, showing the result for R0