Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy

  • Received: 01 October 2015 Accepted: 29 June 2018 Published: 01 October 2016
  • MSC : Primary: 58F15, 58F17; Secondary: 53C35.

  • Understanding the global interaction dynamics between tumor and the immunesystem plays a key role in the advancement of cancer therapy.Bunimovich-Mendrazitsky et al. (2015) developed a mathematical model for thestudy of the immune system response to combined therapy for bladder cancerwith Bacillus Calmette-Guérin (BCG) and interleukin-2 (IL-2) . Weutilized a mathematical approach for bladder cancer treatment model forderivation of ultimate upper and lower bounds and proving dissipativityproperty in the sense of Levinson. Furthermore, tumor clearance conditionsfor BCG treatment of bladder cancer are presented. Our method is based onlocalization of compact invariant sets and may be exploited for a predictionof the cells populations dynamics involved into the model.

    Citation: K. E. Starkov, Svetlana Bunimovich-Mendrazitsky. Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy[J]. Mathematical Biosciences and Engineering, 2016, 13(5): 1059-1075. doi: 10.3934/mbe.2016030

    Related Papers:

  • Understanding the global interaction dynamics between tumor and the immunesystem plays a key role in the advancement of cancer therapy.Bunimovich-Mendrazitsky et al. (2015) developed a mathematical model for thestudy of the immune system response to combined therapy for bladder cancerwith Bacillus Calmette-Guérin (BCG) and interleukin-2 (IL-2) . Weutilized a mathematical approach for bladder cancer treatment model forderivation of ultimate upper and lower bounds and proving dissipativityproperty in the sense of Levinson. Furthermore, tumor clearance conditionsfor BCG treatment of bladder cancer are presented. Our method is based onlocalization of compact invariant sets and may be exploited for a predictionof the cells populations dynamics involved into the model.


    加载中
    [1] Bull. Math. Biol., 69 (2007), 1847-1870.
    [2] Bull. Math. Biol., 70 (2008), 2055-2076.
    [3] Math. Med. Biol., 33 (2016), 159-188.
    [4] Math. Biosci. Eng., 8 (2011), 529-547.
    [5] Teubner Wiesbaden, 2005.
    [6] J. Math. Biol., 37 (1998), 235-252.
    [7] Differ. Equ., 41 (2005), 1669-1676.
    [8] Phys. Lett. A, 353 (2006), 383-388.
    [9] Commun. Nonlinear Sci. Numer. Simul., 15 (2010), 1159-1165.
    [10] J. Urol., 116 (1976), 180-183.
    [11] IMA J. Appl. Math., 15 (1998), 165-185.
    [12] Phys. Lett. A, 375 (2011), 3184-3187.
    [13] Internat. J. Bifur. Chaos Appl. Sci. Engrg., 19 (2009), 1037-1042.
    [14] Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 2565-2570.
    [15] Nonlinear Anal. Real World Appl., 14 (2013), 1425-1433.
    [16] Internat. J. Bifur. Chaos Appl. Sci. Engrg., 23 (2013), 1350020, 9pp.
    [17] Math. Methods Appl. Sci, 37 (2014), 2854-2863.
    [18] Bull. Math. Biol., 63 (2001), 731-768.
  • Reader Comments
  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2709) PDF downloads(535) Cited by(13)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog