Dynamical behavior of a fractional order SIR model with stability analysis

Abstract

The fractional order SIR model with a Holling type II saturated incidence rate and treatment rate are explored in this manuscript in the Caputo order fractional derivative approach. The existence and uniqueness criterion, as well as non-negativity and boundedness of the solution of the new model have been established. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium point E0when R01. For R0=1at E0the model exhibits a forward bifurcation. Fractional-order Taylor’s approach is utilized to approximate the solution of the proposed model. Graphical demonstrations and numerical simulations have been presented using MATLAB.

Keywords

• SIR model
• Stability
• Forward bifurcation
• Taylor’s scheme
• Numerical study