Study of a fractional order SIR model with M-H typetreatment rate and its stability analysis

Abstract

he fractional order SIR compartmental model with a Holling type II and saturated treatment rate are explored in this manuscript with three different categoriesin the Caputo approach. A few findings for the new model’s existence and uniqueness criterion, as well as non-negativity and boundedness of the solution, have beenestablished. The stability analysis of the model shows that the system is locallyas well as globally asymptotically stable at disease-free equilibrium point E0 when R0 < 1 and at epidemic equilibrium E1 when R0 > 1. We also present an optimumcontrol scheme for an SIR model using the control parameter “Treatment rate”. Inaddition, the fractional-order Taylor’s approach is utilized to approximate the solution to the proposed model. With the help of MATLAB, we were able to conductgraphical demonstrations and numerical simulations.