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Computational and Mathematical Methods in Medicine
Volume 2017, Article ID 2906282, 12 pages
Research Article

Periodically Pulsed Immunotherapy in a Mathematical Model of Tumor, CD4+ T Cells, and Antitumor Cytokine Interactions

1Department of Applied Mathematics, Feng Chia University, Seatwen, Taichung 40724, Taiwan
2Department of Financial and Computational Mathematics, Providence University, Shalu Dist., Taichung 43301, Taiwan

Correspondence should be addressed to Jui-Ling Yu;

Received 11 June 2017; Revised 15 September 2017; Accepted 12 October 2017; Published 9 November 2017

Academic Editor: Konstantin Blyuss

Copyright © 2017 Hsiu-Chuan Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Immunotherapy is one of the most recent approaches for controlling and curing malignant tumors. In this paper, we consider a mathematical model of periodically pulsed immunotherapy using T cells and an antitumor cytokine. Mathematical analyses are performed to determine the threshold of a successful treatment. The interindividual variability is explored by one-, two-, and three-parameter bifurcation diagrams for a nontreatment case. Numerical simulation conducted in this paper shows that (i) the tumor can be regulated by administering T cells alone in a patient with a strong immune system or who has been diagnosed at an early stage, (ii) immunotherapy with a large amount of an antitumor cytokine can boost the immune system to remit or even to suppress tumor cells completely, and (iii) through polytherapy the tumor can be kept at a smaller size with reduced dosages.