Dynamic Analysis of a Delayed Fractional-Order SIR Model with Saturated Incidence and Treatment Functions

Abstract

In this paper, a delayed fractional-order SIR (susceptible, infected, and removed) epidemic model with saturated incidence and treatment functions is presented. Firstly, the non-negativity and boundedness of solutions of the proposed model are proved. Next, some sufficient conditions are established to ensure the local asymptotic stability of the disease-free equilibrium point [Formula: see text] and the endemic equilibrium point [Formula: see text] for any delay. Meanwhile, global asymptotic stability of the endemic equilibrium point [Formula: see text] is investigated by constructing a suitable Lyapunov function. Some sufficient conditions are established for the global asymptotic stability of this endemic equilibrium point. Finally, some numerical simulations are illustrated to verify the correctness of the theoretical results.