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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.

A Caputo based SIRS and SIS fractional order models with standard incidence rate and varying population