This paper introduces a susceptible, infected, recovered (SIR) epidemic model incorporating the logistic growth of the susceptible population and disease transmission following the non-monotonous incidence rate. It accounts for delays in treatment owing to saturation and emphasizes the significance of memory effects in epidemic dynamics by employing a system of fractional differential equations in the Caputo sense. The existence, uniqueness, non-negativity and boundedness of the solution have been established. The local asymptotic stability of disease-free and endemic equilibrium points is examined and global stability analysis for endemic equilibrium is also conducted. Sufficient conditions for global stability are derived. The analytical results are verified using numerical simulations which show that the memory effect can stabilize the periodic solutions and it takes less time to reach the stable attractor for higher memory effect.
Saha et al. (Tue,) studied this question.