Abstract
In this paper, we formulate the transmission phenomena of Hand-Foot-Mouth Disease (HFMD) through non-integer derivative. We interrogate the biological meaningful results of the recommended system of HFMD. The basic reproduction number is determined through next generation method and the impact of different parameters on the reproduction number is examined with the help of partial rank correlation coefficient (PRCC) technique. In addition, we concentrated on qualitative analysis and dynamical behavior of HFMD dynamics. Banach's and Schaefer's fixed-point theorems are used to analyze the uniqueness and existence of the solution of the proposed HFMD model. The HFMD system's Ulam-Hyers stability has been confirmed to be sufficient. To highlight the impact of the parameters on the dynamics of HFMD, we performed several simulations through numerical scheme to conceptualize the transmission route of the infection. To be more specific, numerical simulations are used to visualize the effect of input parameters on the systems dynamics. We have shown the key input parameters of the system for the control of infection in the society.