Comparison of fractional order techniques for measles dynamics

A mathematical model which is non-linear in nature with non-integer order ϕ , 0 < ϕ ≤ 1 is presented for exploring the SIRV model with the rate of vaccination μ 1 and rate of treatment μ 2 to describe a measles model. Both the disease free F 0 and the endemic F ∗ points have been calculated. The stability has also been argued for using the theorem of stability of non-integer order differential equations. R 0 , the basic reproduction number exhibits an imperative role in the stability of the model. The disease free equilibrium point F 0 is an attractor when R 0 < 1 . For R 0 > 1 , F 0 is unstable, the endemic equilibrium F ∗ subsists and it is an attractor. Numerical simulations of considerable model are also supported to study the behavior of the system.