Mathematical Biosciences and Engineering, 2015, 12(5): 1037-1053. doi: 10.3934/mbe.2015.12.1037.

Primary: 92C50, 93C10; Secondary: 93D05.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Analysis of a cancer dormancy model and control of immuno-therapy

1. Department of Mathematics, Iowa State University, Ames, IA 50011

   

The goal of this paper is to analyze a model of cancer-immune system interactions from [16], and to show how the introduction of control in this model can dramatically improve the hypothetical patient response and in effect prevent the cancer from growing. We examine all the equilibrium points of the model and classify them according to their stability properties. We identify an equilibrium point corresponding to a survivable amount of cancer cells which are exactly balanced by the immune response. This situation corresponds to cancer dormancy. By using Lyapunov stability theory we estimate the region of attraction of this equilibrium and propose two control laws which are able to stabilize the system effectively, improving the results of [16]. Ultimately, the analysis presented in this paper reveals that a slower, continuous introduction of antibodies over a short time scale, as opposed to mere inoculation, may lead to more efficient and safer treatments.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Lyapunov stability.; Modeling of immuno-therapy; application of control theory to cancer therapy

Citation: Ben Sheller, Domenico D'Alessandro. Analysis of a cancer dormancy model and control of immuno-therapy. Mathematical Biosciences and Engineering, 2015, 12(5): 1037-1053. doi: 10.3934/mbe.2015.12.1037

References

  • 1. Cancer Research, 73 (2013), 583-594.
  • 2. Physica D, 208 (2005), 220-235.
  • 3. Annu. Rev. Immunol., 22 (2004), 329-360.
  • 4. Bull. Math. Biol., 73 (2011), 2-32.
  • 5. Nature, 440 (2006), 1222-1226.
  • 6. IEEE Transactions on Automatic Control, 30 (1985), 747-755.
  • 7. Springer Verlag, Heidelberg-Berlin, 1967.
  • 8. Prentice-Hall Information and System Sciences Series. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1980.
  • 9. John Wiley and Sons, 1995.
  • 10. Cybern. syst. Anal, 23 (1988), 556-564.
  • 11. Bull. Math. Biol, 56 (1994), 295-321.
  • 12. Discrete and Continuous Dynamical Systems, Series B, 18 (2013), 1031-1051.
  • 13. Journal of Mathematical Biology, 64 (2012), 557-577.
  • 14. J. of the National Cancer Institute, 58 (1977), 1735-1741.
  • 15. Cancer Research, 48 (1988), 7067-7071.
  • 16. Leukemia and Lymphoma, 46 (2005), 313-327.
  • 17. PNAS, 100 (2003), 8372-8377.
  • 18. SIAM J. Control Optim., 48 (2010), 4377-4394.
  • 19. Prentice-Hall, Advanced Reference Series (Engineering), 1989.
  • 20. Nature Reviews Cancer, 12 (2012), 278-287.
  • 21. Biophysics, 24 (1980), 917-923.
  • 22. IPSJ Trans Math Model Appl., 47 (2006), 61-67.
  • 23. Automatica, 21 (1985), 69-80.
  • 24. Systems Biology of Tumor Dormancy, Springer, New York, 2013.
  • 25. Israel Jerusalem Academic Press, 1962.
  • 26. the Netherlands, Noordhoff, 1964.
  • 27. January 7-10, 2013.

 

This article has been cited by

  • 1. Frank C. Cackowski, Russell S. Taichman, Parallels between hematopoietic stem cell and prostate cancer disseminated tumor cell regulation, Bone, 2018, 10.1016/j.bone.2018.02.025

Reader Comments

your name: *   your email: *  

Copyright Info: 2015, Ben Sheller, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved