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MODELING THE INTERACTION BETWEEN AVASCULAR CANCEROUS CELLS AND ACQUIRED IMMUNE RESPONSE

B. DUBEY

Mathematics Group, Birla Institute of Technology and Science (BITS), Pilani 333 031, India

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UMA S. DUBEY

Biological Science Group, Birla Institute of Technology and Science (BITS), Pilani 333 031, India

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, and

SANDIP BANERJEE

Mathematics Group, Birla Institute of Technology and Science (BITS), Pilani 333 031, India

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https://doi.org/10.1142/S0218339008002605Cited by:7 (Source: Crossref)

Abstract

This paper deals with the interaction between dispersed cancer cells and the major populations of the immune system, namely, the T helper cells, T Cytotoxic cells, B cells, and antibodies produced. The system is described by a set of five ordinary differential equations. Both local and global stability of the system has been investigated. It has been observed that under appropriate conditions this interaction is capable of controlling the growth of these cancer cells. The analytical findings are supported by numerical and computational analytical methods.

Keywords:

References

WHO, Cancer, World Health Organization, 2006, Retrieved on 2007-06-25, http://www.who.org/ . Google Scholar
J. Adam and N. Bellomo , A Survey of Models for Tumor–Immune System Dynamics ( Birkhäauser , Boston, MA , 1996 ) . Crossref, Google Scholar
L. Preziosi, Math. Comput. Model. 23(6), 135 (1996), DOI: 10.1016/0895-7177(96)00023-4. Crossref, Web of Science, Google Scholar
V. Kuznetsov and M. Taylor, Bull. Math. Biol. 56(2), 295 (1994). Crossref, Web of Science, Google Scholar
D. Kirschner and J. Panetta, J. Math. Biol. 37, 235 (1998), DOI: 10.1007/s002850050127. Crossref, Web of Science, Google Scholar
M. Kolev, Math. Comput. Model. 37, 1143 (2003), DOI: 10.1016/S0895-7177(03)80018-3. Crossref, Web of Science, Google Scholar
J. C. Arciero, T. L. Jackson and D. E. Kirschner, Disc. Cont. Dyn. Syst. Ser. B 4(1), 39 (2004). Web of Science, Google Scholar
A. Matzavinos and M. A. J. Chaplain, C. R. Biol. 327, 995 (2004), DOI: 10.1016/j.crvi.2004.07.016. Crossref, Web of Science, Google Scholar
R. Sarkar and S. Banerjee, Math. Biosci. 196, 65 (2005), DOI: 10.1016/j.mbs.2005.04.001. Crossref, Web of Science, Google Scholar
U. S. Dubey and B. Dubey, J. Biol. Syst. 15(4), 473 (2007), DOI: 10.1142/S0218339007002301. Link, Web of Science, Google Scholar
T. Roose, S. J. Chapman and K. P. Maini, SIAM Rev. 49(2), 179 (2007), DOI: 10.1137/S0036144504446291. Crossref, Web of Science, Google Scholar
N. Bellomo, L. Preziosi and G. Forni, J. Biol. Syst. 4(4), 479 (1996), DOI: 10.1142/S0218339096000326. Link, Google Scholar
E. J. Darleneet al., Clin. Exp. Metastasis 20(8), 733 (2003). Web of Science, Google Scholar
R. Hoffman, Lancet Oncol. 3(9), 546 (2002), DOI: 10.1016/S1470-2045(02)00848-3. Crossref, Web of Science, Google Scholar
R. A. Goldsbyet al., Immunology (Freeman & Co., 2003) pp. 499–522. Google Scholar
H. Siuet al., J. Immunol. 137, 1376 (1986). Crossref, Web of Science, Google Scholar
J. LaSalle and S. Lefschetz , Stability by Liapunov's Direct Method with Applications ( Academic Press , New York, London , 1961 ) . Google Scholar