Immunomodulatory role of black tea in the mitigation of cancer induced by inorganic arsenic

Abstract

We present a model analysis of the tumor and normal cell growth under the influence of a carcinogenic agent, an immunomodulator (IM) and variable influx of immune cells including relevant interactions. The tumor growth is facilitated by carcinogens such as inorganic arsenic, while the IM considered here is black tea (Camellia sinesnsis). The model with variable influx of immune cells is observed to have considerable advantage over the constant influx model, and while the tumor cell population is greatly mitigated, normal cell population remains above healthy levels. The evolutions of normal and tumor cells are computed from the proposed model and their local stabilities are investigated analytically. Numerical simulations are performed to study the long-term dynamics and an estimation of the effects of various factors is made. This helps in developing a balanced strategy for tumor mitigation without the use of chemotherapeutic drugs that usually have strong side effects.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Notes

  1. 1.

    We let \(N(t) (\equiv N)\) denote the number of normal cells at time t, \(T(t) (\equiv T)\) denote the number of tumor cells at time t, \(I(t) (\equiv I)\) denote the number of immune cells at time t, and \(s(t)(\equiv s)\) denote the variable influx of immune cells. \(A(t) (\equiv A)\) and \(D(t) (\equiv D)\) are the Arsenic and BT, respectively.

References

  1. 1.

    F. Bray, J. Ferlay, I. Soerjomataram, R.L. Siegel, L.A. Torre, A. Jemal, Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA Cancer J. Clin. 68(6), 394–424 (2018)

    Article  Google Scholar 

  2. 2.

    D. Sinha, S. Roy, M. Roy, Antioxidant potential of tea reduces arsenite induced oxidative stress in Swiss albino mice. Food Chem. Toxicol. 48(4), 1032–1039 (2010)

    Article  Google Scholar 

  3. 3.

    D. Sarkar, D. Rupali, Biogeochemistry of Arsenic in Contaminated Soils of Superfund Sites (United States Environmental Protection Agency, Washington, DC, 2007)

    Google Scholar 

  4. 4.

    J. Carelton, Final Report: Biogeochemistry of Arsenic in Contaminated Soils of Superfund Sites (United States Environmental Protection Agency, Washington, DC, 2007)

    Google Scholar 

  5. 5.

    D.N. Guha Mazumder, Diagnosis and treatment of chronic arsenic poisoning. United Nations synthesis report on arsenic in drinking water (2000)

  6. 6.

    H.M. Srivastava, U. Dey, A. Ghosh, J.P. Tripathi, S. Abbas, A. Taraphder, M. Roy, Growth of tumor due to arsenic and its mitigation by black tea in Swiss albino mice. Alex. Eng. J. 59(3), 1345–1357 (2020)

  7. 7.

    M.R. Haque, S.H. Ansari, Immunostimulatory effect of standardised alcoholic extract of green tea (Camellia sinensis l.) against cyclophosphamide-induced immunosuppression in murine model. Int. J. Green Pharm. (IJGP) 8(1), 52–57 (2014)

  8. 8.

    A. Gomes, P. Datta, A. Sarkar, S.C. Dasgupta, A. Gomes, Black tea (Camellia sinensis) extract as an immunomodulator against immunocompetent and immunodeficient experimental rodents. Orient. Pharm. Exp. Med. 14(1), 37–45 (2014)

    Article  Google Scholar 

  9. 9.

    C. Chattopadhyay, N. Chakrabarti, M. Chatterjee, S. Mukherjee, K. Sarkar, A.R. Chaudhuri, Black tea (Camellia sinensis) decoction shows immunomodulatory properties on an experimental animal model and in human peripheral mononuclear cells. Pharmacogn. Res. 4(1), 15 (2012)

    Article  Google Scholar 

  10. 10.

    L.G. De Pillis, A. Radunskaya, A mathematical tumor model with immune resistance and drug therapy: an optimal control approach. Comput. Math. Methods Med. 3(2), 79–100 (2001)

    MATH  Google Scholar 

  11. 11.

    L.G. De Pillis, A. Radunskaya, The dynamics of an optimally controlled tumor model: a case study. Math. Comput. Modell. 37(11), 1221–1244 (2003)

    MATH  Article  Google Scholar 

  12. 12.

    J.C. Panetta, A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competitive environment. Bull. Math. Biol. 58(3), 425–447 (1996)

    MATH  Article  Google Scholar 

  13. 13.

    S. Michelson, J.T. Leith, Host response in tumor growth and progression. Invasion Metastasis 16(4–5), 235–246 (1996)

    Google Scholar 

  14. 14.

    V.A. Kuznetsov, I.A. Makalkin, M.A. Taylor, A.S. Perelson, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol. 56(2), 295–321 (1994)

    MATH  Article  Google Scholar 

  15. 15.

    C. Castillo-Chavez, Z. Feng, W. Huang, On the computation of \(R_0\) and its role on global stability, in Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, edited book, vol. 1 (2002), p. 229

  16. 16.

    P. Van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1–2), 29–48 (2002)

    MathSciNet  MATH  Article  Google Scholar 

  17. 17.

    A. Ghafari, N. Naserifar, Mathematical modeling and lyapunov-based drug administration in cancer chemotherapy. Iran. J. Electr. Electron. Eng. 5(3), 151–158 (2009)

    Google Scholar 

  18. 18.

    X. Yang, L. Chen, J. Chen, Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models. Comput. Math. Appl. 32(4), 109–116 (1996)

    MathSciNet  MATH  Article  Google Scholar 

  19. 19.

    Y. Song, S. Yuan, Bifurcation analysis in a predator–prey system with time delay. Nonlinear Anal. Real World Appl. 7(2), 265–284 (2006)

    MathSciNet  MATH  Article  Google Scholar 

Download references

Acknowledgements

The authors are thankful to the reviewers for their constructive comments, which helped in improving the manuscript.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Syed Abbas.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kiran, R., Tyagi, S., Abbas, S. et al. Immunomodulatory role of black tea in the mitigation of cancer induced by inorganic arsenic. Eur. Phys. J. Plus 135, 735 (2020). https://doi.org/10.1140/epjp/s13360-020-00766-1

Download citation