Global stability of a fractional order HIV infection model with cure of infected cells in eclipse stage

Moussa Bachraoui (1) , Khalid Hattaf (1) , Noura Yousfi (1)

1 Faculté des Sciences Ben M'sik [Casablanca]

Modeling by fractional order differential equations has more advantages to describe the dynamics of phenomena with memory which exists in many biological systems. In this paper, we propose a fractional order model for human immunodeficiency virus (HIV) infection by including a class of infected cells that are not yet producing virus, i.e., cells in the eclipse stage. We first prove the positivity and bound-edness of solutions in order to ensure the well-posedness of the proposed model. By constructing appropriate Lyapunov functionals, the global stability of the disease-free equilibrium and the chronic infection equilibrium is established. Numerical simulations are presented in order to validate our theoretical results.

Mots clés: global stability; eclipse stage; HIV infection; nonlinear incidence rate

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

Moussa Bachraoui, Khalid Hattaf, Noura Yousfi. Global stability of a fractional order HIV infection model with cure of infected cells in eclipse stage. 2018. ⟨hal-01721304v1⟩