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Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2020

07.05.2020 | Original Research

Mathematical analysis and optimal control applied to the treatment of leukemia

verfasst von: Mst. Shanta Khatun, Md. Haider Ali Biswas

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2020

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Abstract

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.
Vorheriger Artikel A new full-Newton step interior-point method for -LCP based on a positive-asymptotic kernel function
Nächster Artikel Modified viscosity implicit rules for proximal split feasibility and fixed point problems

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Metadaten
Titel
Mathematical analysis and optimal control applied to the treatment of leukemia
verfasst von
Mst. Shanta Khatun
Md. Haider Ali Biswas
Publikationsdatum
07.05.2020
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2020
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-020-01357-0

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