Mathematical analysis and optimal control applied to the treatment of leukemia

• Published in: Journal of applied mathematics & computing Vol. 64; no. 1-2; pp. 331 - 353
• Main Authors: Khatun, Mst. Shanta, Biswas, Md. Haider Ali
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-10-2020; Springer Nature B.V
• Subjects: Applied mathematics; Computational Mathematics and Numerical Analysis; Computer simulation; Leukemia; Leukocytes; Mathematical analysis; Mathematical and Computational Engineering; Mathematical models; Mathematics; Mathematics and Statistics; Mathematics of Computing; Maximum principle; Nonlinear differential equations; Nonlinear equations; Optimal control; Original Research; Public health; Theory of Computation; 92D30; Treatment; Numerical analysis; Secondary: 34A34; Leukemia; Optimal control; Mathematical model; Primary: 93A30; 49K15
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-020-01357-0

Leukemia is a worldwide public health problem. It is the result of unconstrained growth of immature white blood cells in the blood. In this paper, we propose a compartmental model of leukemia in terms of a system of ordinary nonlinear differential equations and apply optimal control technique in obtaining optimal strategies to minimize the number of infected cells in the blood. Initially, a mathematical model of leukemia is formulated. We verify the stability of the equilibria (disease-free and endemic equilibrium point) of the model based on the basic reproduction number. After words, in order to minimize the number of infected cells as well as the costs of the control, we develop the proper optimal control model by using Pontryagin’s maximum principle. Finally, numerical simulation of the proposed model and optimal control model are performed to show that the effectiveness of immune boosting drugs as well as immunotherapy to defend leukemia in the blood.