Stability of a Fractional-Order Epidemic Model with Nonlinear Incidences and Treatment Rates

Abstract

In the present study, Caputo derivative-based a new fractional-order epidemic model is presented along with two explicit saturated incidences and saturated treatment rates. For this, a new fearful population compartment is incorporated into the susceptible-infected-recovered compartmental model, which emphasizes to consider two specific incidence rates: one from susceptible individuals’ compartment to infected individuals’ compartment and another from fearful individuals’ compartment to infected individuals’ compartment. The model is analyzed mathematically for disease-free equilibrium (DFE) and endemic equilibrium (EE). The stability of the model’s equilibria is investigated for local as well as global behaviors. It is investigated that DFE is locally asymptotically stable whenever the basic reproduction number $$ R_{0} $$ is less than one, and EE exists when $$ R_{0} $$ crosses one. The EE is proved to be locally stable under certain conditions. Further, global stability behavior is investigated for both equilibria using the basic reproduction number $$ R_{0} $$ . Finally, numerical results are presented in support of the analytical findings.