Stability Analysis of Fractional Order Mathematical Model of Leukemia

International Journal of Mathematical Modelling & Computations

مقاله 2، دوره 11، 1 (WINTER) - شماره پیاپی 41، خرداد 2021، صفحه 15-27   

نوع مقاله: Full Length Article

شناسه دیجیتال (DOI): 10.30495/ijm2c.2021.684812

نویسنده

Lahoucine Boujallal^*

Department of Mathematics, Faculty of Sciences Ain Chock, University Hassan II, Casablanca, Morocco

چکیده

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.

کلیدواژه‌ها

Compartment model؛ Leukemia؛ Caputo fractional derivative؛ Stability analysis؛ Lyapunov functions؛ Reproduction number