A fractional‐order model for chronic lymphocytic leukemia and immune system interactions. (28th July 2020)

• Record Type: Journal Article
• Authors: Fadaei, Yasin; Ahmadi, Ali; Fekri, Kiavash; Masoumi, Rohollah; Radunskaya, Ami
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 1(2021)
• Page Start: 391
• Page End: 406
• Publication Date: 2020-07-28
• Subjects: bifurcation -- chronic lymphocytic leukemia -- mathematical model of fractional‐order -- stability analysis; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6743
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this study, a mathematical, fractional‐order model was developed for B cell chronic lymphocytic leukemia, with immune system, and then analyzed. Interactions between B leukemia cells, natural killer cells, cytotoxic T cells, and T‐helper cells are considered to be incorporated into a system consisting of four fractional differential equations. For estimation of the parameters, clinical data of six patients were used. By numerical solution of the system, the interactions between the leukemia cell population and the immune system cell populations for values of α ∈ (0, 1) at different times were explained. By determining points of equilibrium and stability of the system were met. Bifurcation analysis showed that use of the fractional‐order model, figure out unpredictable behaviors of the system such as saddle‐node, bistability and hysteresis phenomenon occurred in the system by changing the values of some of the parameters, it was predictable.