Abstract
In this paper, the stationary probability distribution (SPD) function and the mean first passage time (MFPT) are investigated in a tumor growth model driven by non-Gaussian noise which is introduced to mimic random fluctuations in the levels of the immune system. Results demonstrate the different transitions induced by the strength of non-Gaussian noise under different immune coefficients and the dual roles of non-Gaussian noise in promoting host protection against cancer and in facilitating tumor escape from immune destruction. Additionally, it can be discovered that increases in noise strength, the degree of departure from Gaussian noise, and the immune coefficient can accelerate the extinction of tumor cells. Numerical simulations are performed, and their results present good agreement with the theoretical results.
Similar content being viewed by others
References
H.D. Abarbanel, M.I. Rabinovich, Curr. Opin. Neurobiol. 11, 423 (2001)
V. Toronov, T. Myllylä, V. Kiviniemi, V. Tuchin, Eur. Phys. J. Special Topics 222, 2607 (2013)
R.J. Nee, D. Butler, Phys. Ther. Sport 7, 36 (2006)
E. Batlle, H. Clevers, Nat. Med. 23, 1124 (2017)
V. Panzetta, M. De Menna, I. Musella, M. Pugliese, M. Quarto, P.A. Netti, S. Fusco, Cytoskeleton 74, 40 (2017)
Y. Jiang, H. Gang, M. Ben-Kun, Phys. Rev. B 39, 4572 (1989)
S. Kar, S.K. Banik, D.S. Ray, Phys. Rev. E 65, 061909 (2002)
M. Molski, J. Konarski, Phys. Rev. E 68, 021916 (2003)
D.A. Kessler, H. Levine, J. Stat. Phys. 158, 783 (2014)
R. Lefever, W. Horsthemke, Bull. Math. Biol. 41, 469 (1979)
G.P. Dunn, L.J. Old, R.D. Schreiber, Immunity 21, 137 (2004)
R. Lefever, R. Garay, Local description of immune tumor rejection (North-Holland Biomedical Press: Elsevier, 1978)
W.-R. Zhong, Y.-Z. Shao, Z.-H. He, Phys. Rev. E 73, 060902 (2006)
T. Bose, S. Trimper, Phys. Rev. E, 79, 051903 (2009)
L.-C. Du, D.-C. Mei, Phys. Lett. A, 374, 3275 (2010)
V. Dakos, S.R. Carpenter, W.A. Brock, A.M. Ellison, V. Guttal, A.R. Ives, S. Kefi, V. Livina, D.A. Seekell, E.H. van Nes, M. Scheffer, PLoS One 7, e41010 (2012)
V. Dakos, F. Soler-Toscano, Ecol. Complex. 32, 144 (2017)
I.A. van de Leemput, V. Dakos, M. Scheffer, E.H. van Nes, Ecosystems 21, 141 (2017)
K. Wiesenfeld, D. Pierson, E. Pantazelou, C. Dames, F. Moss, Phys. Rev. Lett. 72, 2125 (1994)
D. Nozaki, D.J. Mar, P. Grigg, J.J. Collins, Phys. Rev. Lett. 82, 2402 (1999)
X. Dong, C. Zeng, F. Yang, L. Guan, Q. Xie, W. Duan, Physica A 492, 851 (2018)
J. Duarte, M. Vermelho, M. Lyra, Physica A 387, 1446 (2008)
K. Kanazawa, T.G. Sano, T. Sagawa, H. Hayakawa, Phys. Rev. Lett. 114, 090601 (2015)
P. Majee, G. Goswami, B.C. Bag, Chem. Phys. Lett. 416, 256 (2005)
D. Valenti, C. Guarcello, B. Spagnolo, Phys. Rev. B 89, 214510 (2014)
J.D. Murray, in Mathematical Biology I: An Introduction, Interdisciplinary Applied Mathematics (Springer, New York, NY, USA, 2002), Vol. 17
H. Fröhlich, Phys. Lett. A 51, 21 (1975)
K.A. Hossmann, D. Hermann, Bioelectromagnetics 24, 49 (2003)
I. Yakymenko, O. Tsybulin, E. Sidorik, D. Henshel, O. Kyrylenko, S. Kyrylenko, Electromagn. Biol. Med. 35, 186 (2016)
A. d’Onofrio, Phys. Rev. E 81, 021923 (2010)
A.S. Perelson, G. Weisbuch, Rev. Mod. Phys. 69, 1219 (1997)
P.C. Nowell, Tumor progression: a brief historical perspective, in Seminars in cancer biology (Elsevier, 2002), pp. 261–266
J. Schmielau, O.J. Finn, Cancer Res. 61, 4756 (2001)
D.I. Gabrilovich, A.A. Hurwitz, in Tumor-induced immune suppression (Springer, 2008), Vol. 93, pp. 499–513
L. Borland, Phys. Lett. A 245, 67 (1998)
M. Fuentes, R. Toral, H.S. Wio, Physica A 295, 114 (2001)
M. Fuentes, H.S. Wio, R. Toral, Physica A 303, 91 (2002)
H.S. Wio, R. Toral, Physica D 193, 161 (2004)
C. Li, W. Da-Jin, K. Sheng-Zhi, Phys. Rev. E 52, 3228 (1995)
R.L. Honeycutt, Phys. Rev. A 45, 604 (1992)
W.R. Zhong, Y.Z. Shao, Z.H. He, Phys. Rev. E 74, 011916 (2006)
K. Lindenberg, B.J. West, J. Stat. Phys. 42, 201 (1986)
J. Masoliver, B.J. West, K. Lindenberg, Phys. Rev. A 35, 3086 (1987)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Du, L., Guo, Q. & Sun, Z. Influence of non-Gaussian noise on a tumor growth system under immune surveillance. Eur. Phys. J. Spec. Top. 227, 895–905 (2018). https://doi.org/10.1140/epjst/e2018-700136-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2018-700136-8