Stability Analysis of Fractional Order Mathematical Model of Leukemia

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.

Keywords:

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