  In the present work, we have introduced and studied two epidemic models that
are constructed with Caputo fractional derivative. We considered standard
incidence rate and varying population dynamics for SIS and SIRS mathematical
models. Model equilibria, basic reproduction numbers are determined and local
stability analysis are established for the two fractional dynamical models.
Finally, the efficient fracPECE iterative scheme for fractional order
deterministic dynamical models is applied to perform numerical simulations.
