Numerical simulation of a normalized time-fractional SUC epidemic model.

Abstract

We develop a normalized time-fractional susceptible-unidentified infected-confirmed (SUC) epidemic model that incorporates memory effects through fractional calculus to capture non-local time interactions. Unlike integer-order models, this model reflects how past states influence present transmission. Numerical simulations show that smaller fractional orders accelerate the decline of susceptible individuals and produce faster but lower infection peaks, while larger orders yield slower, oscillatory declines and delayed peaks, indicating prolonged outbreaks. Moreover, the confirmation parameter critically shapes epidemic dynamics, as higher values reduce infection spread and lower peak levels of unidentified and confirmed cases, and this result highlights its role in controlling epidemic progression.