Mathematics Faculty Articles

Mathematical models and dynamic behaviors of cancer treatment by continuous and pulsed radiotherapy

Document Type

Article

Publication Date

11-6-2022

Publication Title

Journal of Applied Mathematics and Computing

Keywords

Radiotherapy, Cure, Coexistence, Cancer eradication periodic solution, Cancer win periodic solution

ISSN

1865-2085

Volume

69

First Page

1819

Last Page

1843

Abstract

In this study, two mathematical models are introduced to describe treatment of cancer by continuous and pulsed radiotherapy. In the continuous radiotherapy model, we determine all of the equilibrium points and conduct a thorough examination of the stability of these equilibria. Criterions of the radiation dose that guarantee the cancer to be eradicated or take a positive balance with normal cells are provided. In the pulsed radiotherapy model, conditions of the existence and stability of cancer win periodic solution, cancer eradication periodic solution and coexistent periodic solution are derived. Meanwhile, numerical simulations to the effect of radiation dose on the cure and spread of the cancer are carried out. A brief conclusion is presented, as well as a few intriguing subjects for additional investigation are discussed.

Comments

This research was supported by the National Science Foundation (DMS-1853562), the National Natural Science Foundation of China (12271068), Chongqing Municipal Education Commission (KJQN201900707), Joint Training Base Construction Project for Graduate Students in Chongqing (JDLHPYJD2021016), Group Building Scientific Innovation Project for universities in Chongqing (CXQT21021) and Guangxi Natural Science Foundation (2018GXNSFBA281185).

© The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2022

ORCID ID

0000-0001-8893-8156

DOI

10.1007/s12190-022-01813-z

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