In this paper, we examine the pathological behavior of pneumonia transmission. The proposed model is examined using three fractional derivative operators. Caputo, Caputo-Fabrizio, and Atangana-Baleanu use an efficient numerical Euler method to approximate fractional-order systems. These three operators lead to several asymptomatic behaviors not found in integerorder derivative models. The paper aims to generalize four ODEs with four unknowns (susceptible, carrier, infected, and recovered). Hyers-Ulam stability, local and global stability are examined. If R 0 is less than one, the free equilibrium point is local, asymptotic, or otherwise global. We provide simulation results to confirm the theory. Compared to the theoretical results, the simulations were well-approximated.
Alhazmi et al. (2026) studied this question.