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