Global Stability of Switched HIV/AIDS Models with Drug Treatment Involving Caputo-Fractional Derivatives

Abstract

In this paper, we formulate and investigate new switched HIV/AIDS models with drug treatment involving Caputo-fractional derivatives. Initially, due to the fractional derivative order related to the memory and hereditary effects and supposing that the model coefficients are time-varying parameters, we develop a Caputo-fractional order HIV/AIDS models with switching parameters and study their dynamics utilizing Lyapunov–Razumikhin technique. Furthermore, the results show that the fractional derivative α ( 0 < α < 1 ) and the switching parameters are related to the critical threshold value ( R ^ or R ¯ ) which ensures disease eradication under the condition of R ^ < 1 or R ¯ < 1 . Then, a treatment compartment is introduced into the above model from the asymptomatic infected individuals until the full blown AIDS individuals. Novel sufficient conditions on the threshold value are derived to verify that the disease is eventually cleared as the critical threshold parameter is below unity. Finally, some simulations are employed to support the main results and one future research direction is presented.

The Influence of Saturated and Bilinear Incidence Functions on the Dynamical Behavior of HIV Model Using Galerkin Scheme Having a Polynomial of Order Two

“…They first established Caputo-fractional order HIV/AIDS models with switching parameters and studied their dynamics using the Lyapunov-Razumikhin approach, based on the fractional derivative order linked to memory and genetic effects, and considering that the model coefficients are time-varying parameters. Wang et al [16] proposed an SIR model with long-range temporal memory. The proposed model consists of delayed differential equations.…”