Stability analysis of a fractional-order epidemics model with multiple equilibriums

摘要

In this paper, we extend the SIR model with vaccination into a fractional-order model by using a system of fractional ordinary differential equations in the sense of the Caputo derivative of order α ∈ ( 0 , 1 ] $lphain(0,1]$ . By applying fractional calculus, we give a detailed analysis of the equilibrium points of the model. In particular, we analytically obtain a certain threshold value of the basic reproduction number R 0 $R_{0}$ and describe the existence conditions of multiple equilibrium points. Moreover, it is shown that the stability region of the equilibrium points increases by choosing an appropriate value of the fractional order α. Finally, the analytical results are confirmed by some numerical simulations for real data related to pertussis disease.