Poliomyelitis dynamics under the normalized caputo–fabrizio operator: analysis, stability, and numerics

We formulate and analyze a seven-compartment fractional model for poliomyelitis using the normalized Caputo-Fabrizio (NCF) derivative of order [Formula: see text]. The model keeps the biological structure susceptible S, vaccinated V, exposed E, non-paralytic infected [Formula: see text], paralytic infected P, recovered R, and post-paralytic A and transmission terms from a recent ABC-based study, but replaces the derivative by the NCF operator with an exponential kernel. We prove positivity, an invariant region, well-posedness, and Ulam-Hyers (UH) stability. A practical Adams-Bashforth (AB) type time-marching scheme tailored to the NCF integral is given. The analysis shows that the equilibrium structure and threshold quantities coincide with those of the classical system, while memory effects are encoded in the exponential kernel and the normalization [Formula: see text].