Stability Analysis of Fractional Order Mathematical Model of Leukemia

Subject Areas : International Journal of Mathematical Modelling & Computations

Lahoucine Boujallal ¹ (Department of Mathematics, Faculty of Sciences Ain Chock, University Hassan II, Casablanca, Morocco)

Received: 2020-08-26 Accepted : 2020-10-23 Published : 2021-03-01

Keywords: Stability Analysis, Caputo fractional derivative, Leukemia, Reproduction Number, Compartment model, Lyapunov functions,

Abstract :

In this paper, we propose a fractional order model of leukemia in terms of a system of ordinary differential equations with the Caputo derivative that provides convenience for initial conditions of the differential equations. Firstly, we prove the global existence, positivity, and boundedness of solutions. The local stability properties of the equilibrium are obtained by using fractional Routh-Hurwitz stability criterion. Furthermore, a suitable Lyapunov functions are constructed to prove the global stability of equilibrium. Finally, numerical simulation of the model are presented to illustrate our theoretical results for different choices of fractional order of derivative α. Then, we can observe the impact of fractional derivative α on the evolution of the model states.