Mathematical and computational analysis of a Kayo-Kengne-Akgül fractional-order Lassa fever model

This study developed a Caputo-type Kayo-Kengne-Akgül (KKA) fractional model for Lassa fever transmission with memory in coupled human-rodent dynamics. The model contains five compartments: susceptible, infected, and recovered humans, together with susceptible and infected rodents. Using the inverse relation between the KKA derivative and its associated integral, the system was rewritten as an equivalent Volterra-type integral equation. The analysis proved positivity, boundedness, existence, uniqueness, and Ulam-Hyers stability. For computation, a two-step KKA Adams-Bashforth scheme was constructed to examine the effect of the fractional order, showing that smaller orders produce stronger memory and slower epidemic evolution. A deep neural network surrogate was trained on the numerical trajectories, and parameter estimation from clean and noisy synthetic data showed close agreement between the reference and recovered solutions for all compartments and selected transmission parameters.