Analysis of Monkeypox viral infection with human to animal transmission via a fractional and Fractal-fractional operators with power law kernel.

Monkeypox (MPX) is a global public health concern. This infectious disease affects people all over the world, not just those in West and Central Africa. Various approaches have been used to study epidemiology, the source of infection, and patterns of transmission of MPX. In this article, we analyze the dynamics of MPX using a fractional mathematical model with a power law kernel. The human-to-animal transmission is considered in the model formulation. The fractional model is further reformulated via a generalized fractal-fractional differential operator in the Caputo sense. The basic mathematical including the existence and uniqueness of both fractional and fractal-fractional problems are provided using fixed points theorems. A numerical scheme for the proposed model is obtained using an efficient iterative method. Moreover, detailed simulation results are shown for different fractional orders in the first stage. Finally, a number of graphical results of fractal-fractional MPX transmission models are presented showing the combined effect of fractal and fractional orders on model dynamics. The resulting simulations conclude that the new fractal-fractional operator added more biological insight into the dynamics of illness.