Optimal Immunotherapy Control of Aggressive Tumors Growth


Tumor cells can evade immune surveillance by secreting immuno-suppressive factors such as transforming growth factor-beta (TGF-β) and also, Interlukin-10 (IL-10). In this paper the optimal control of mathematical model for aggressive tumor growth via a new and proper approach known as AVK method has been considered. Moreover, we have implemented a special treatment so-called small interfering RNA (siRNA) to reduce presence and effect of TGF-β in tumor cells and also we have added Interlukin-2 (IL-2) into our treatment model to minimize the population of tumor cells. Further research and experimentation with these combination therapies may provide an effective solution in addressing the immuno-suppressive effects of TGF-β. Finally, we analyze the optimal control and system optimality of these equations using numerical techniques.

Share and Cite:

E. Kiani, A. Kamyad and H. Shirzad, "Optimal Immunotherapy Control of Aggressive Tumors Growth," Intelligent Control and Automation, Vol. 3 No. 2, 2012, pp. 168-175. doi: 10.4236/ica.2012.32019.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] A. K. Abbas, A. H. Lichtman and J. S. Pober, “Cellular and Molecular Immunology,” Elsevier, Amsterdam, 2007.
[2] K. E. de Visser and W. M. Kast, “Effects of TGF-β on the Immune System: Implications for Cancer Immunotherapy,” Leukemia, Vol. 13, No. 8, 1999, pp. 1188-1199. doi:10.1038/sj.leu.2401477
[3] M. A. Nash, G. Ferrandina, M. Gordinier, A. Loercher, and R. S. Freedman, “The Role of Cytokines in both the Normal and Malignant Ovary,” Endocrine-Related Cancer, Vol. 6, No. 1, pp. 93-107.
[4] D. Kirschner and J. C. Panetta, “Modeling Immunotherapy of the Tumor—Immune Interaction,” Journal of Mathematical Biology, Vol. 37, No. 3, 1998, pp. 235-252. doi:10.1007/s002850050127
[5] R. R. Sarkar and S. Banerjee, “Cancer self Remission and Tumor Stability: A Stochastic Approach,” Mathematical Biosciences, Vol. 196, No. 1, 2005, pp. 65-81. doi:10.1016/j.mbs.2005.04.001
[6] B. Joshi, X. Wang, S. Banerjee, H. Tian, A. Matzavinos and M. A. Chaplain, “On Immunotherapies and Cancer Vaccination Protocols: A Mathematical Modelling Approach,” Journal of Theoretical Biology, Vol. 259, No. 4, 2009, pp. 820-827
[7] S. M. Mousavi1, M. M. Gouya, R. Ramazani, M. Davanlou, N. Hajsadeghi and Z. Seddighi, “Cancer Incidence and Mortality in Iran,” Annals of Oncology, Vol. 20, No. 3, pp. 556-563. doi:10.1093/annonc/mdn642
[8] J. C. Arciero, T. L. Jackson and D. E. Kirschner, “A Mathematical Model of Tumor-Immune Evasion and siRNA Treatment,” Discrete and Continuous Dynamical Systems, Vol. 4, No. 1, 2004, pp. 39-58. doi:10.3934/dcdsb.2004.4.39
[9] T. Holen, M. Amarzguioui, M. T. Wiiger, E. Babaie and H. Prydz, “Positional Effects of Short Interfering RNAs Targeting the Human Coagulation Trigger Tissue Factor,” Nucleic Acids Research, Vol. 30, No. 8, 2002, pp. 17571766. doi:10.1093/nar/30.8.1757
[10] S. M. Elbashir, J. Harborth, W. Lendeckel, A. Yalcin, K. Weber and T. Tuschl, “Duplexes of 21-Nucleotide RNAs Mediate RNA Interference in Cultured Mammalian Cells,” Nature, Vol. 411, No. 6836, 2001, pp. 494-49. doi:10.1038/35078107
[11] F. Wianny and M. Zernicka-Goetz, “Specific Interference with Gene Function by Doublestranded RNA in Early Mouse Development,” Nature Cell Biology, Vol. 2, No. 2, 2000, pp. 70-75. doi:10.1038/35000016
[12] K. P. Badakhshan, A. V. Kamyad and A. Azemi, “Using AVK Method to Solve Nonlinear Problems with Uncertain Parameters,” Applied Mathematics and Computation, Vol. 189, No. 1, 2007, pp. 27-34. doi:10.1016/j.amc.2006.11.172

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.