Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equations

In this work, the application of the system of fractal fractional differential equations is exploited. Infectious diseases modeling of non-integer order attracts many mathematicians and biological scientists. The presentation of an advanced fractal fractional model for studying the exact dynamical behavior of infectious diseases in epidemiology is necessary. In this study, a new version of a mathematical model for whooping cough is presented. Whooping cough is a disease and can be transmitted from humans to humans through various means, i.e., touch, cough, and air droplets. In this study, we considered the whooping cough model with a new permanent compartment. Our modified model after incorporating the permanent recovered compartment explains better regarding the individuals who have developed long term immunity against whooping cough. This addition to the model enhances the model's accuracy towards real world scenarios. The considered model was analyzed by using a system of fractal fractional differential equations, and numerical simulation was established for the findings of this study. The fixed point theorem was used to determine the existence, uniqueness, and Hyers–Ulam stability of the model. Numerical results of the dynamical behavior of the model are also recorded in tables.