Key result
Normalized Caputo-Fabrizio fractional poliomyelitis model preserves classical equilibrium and thresholds while encoding memory effects.
The study formulates and analyzes a seven-compartment fractional model for poliomyelitis using the normalized Caputo-Fabrizio derivative, proving its stability and well-posedness.
Vaccination limits polio paralysis in fractional simulations; extends ABC models with NCF operator for refined epidemiological research.
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].
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Alamry et al. (2026) studied this question. The normalized Caputo-Fabrizio fractional model for poliomyelitis shares the equilibrium structure and threshold quantities of the classical system while encoding memory effects.
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