This paper investigates a mathematical model of typhoid infectious disease using the piecewise Caputo fractional differential operator (CFDO). There are four distinct groups within the human population: The susceptible, the unprotected, the infectious, and the recovered. A piecewise power-law fractional differential operator is used to quantitatively represent the interactions between these groups. Furthermore, we calculate the reproductive number and equilibrium point of the suggested model. A solution to the underlying problem is found using the well-known fixed point theory. The Hyers–Ulam (H–U) idea is used to verify the system’s stability, and it produces the intended outcomes. Additionally, we create a numerical scheme for the suggested system using the conventional Runge–Kutta method of order four (RK4) in order to extract the numerical results. We have used numerous sorts of values for the order of the derivative and the isolation parameter, and have offered distinct graphical presentations of each class based on the reported statistics of typhoid disease. The effect of these parameter values on the dynamics and multi-behaviors is then thoroughly examined. Henceforth, we can verify the validity of the suggested approach and we can also compare our numerical results for different model compartments with the Euler method’s answer.
Khan et al. (Mon,) studied this question.