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Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

Author

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  • Sardanyés, Josep
  • Rodrigues, Carla
  • Januário, Cristina
  • Martins, Nuno
  • Gil-Gómez, Gabriel
  • Duarte, Jorge

Abstract

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems – the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.

Suggested Citation

  • Sardanyés, Josep & Rodrigues, Carla & Januário, Cristina & Martins, Nuno & Gil-Gómez, Gabriel & Duarte, Jorge, 2015. "Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 484-495.
    • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:484-495
    DOI: 10.1016/j.amc.2014.12.005
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    1. Khaled Ali & Dalya R. Soond & Roberto Piñeiro & Thorsten Hagemann & Wayne Pearce & Ee Lyn Lim & Hicham Bouabe & Cheryl L. Scudamore & Timothy Hancox & Heather Maecker & Lori Friedman & Martin Turner &, 2014. "Inactivation of PI(3)K p110δ breaks regulatory T-cell-mediated immune tolerance to cancer," Nature, Nature, vol. 510(7505), pages 407-411, June.
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    Cited by:

    1. Naik, Parvaiz Ahmad & Zu, Jian & Ghoreishi, Mohammad, 2020. "Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Al-Qudah, Alaa & Odibat, Zaid & Shawagfeh, Nabil, 2022. "A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 505-522.
    3. Xiangcheng You & Shiyuan Li & Lei Kang & Li Cheng, 2023. "A Study of the Non-Linear Seepage Problem in Porous Media via the Homotopy Analysis Method," Energies, MDPI, vol. 16(5), pages 1-13, February.
    4. Li, Wei & Zhang, Ying & Huang, Dongmei & Rajic, Vesna, 2022. "Study on stationary probability density of a stochastic tumor-immune model with simulation by ANN algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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