效应免疫细胞的激活促进肿瘤的随机消退：一种同伦分析方法
Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach
摘要：
在这篇文章中，我们提供了一个癌症非线性模型的同伦解，该模型描述了肿瘤细胞与健康细胞和效应免疫细胞相互作用的动力学。我们应用半解析技术解决强非线性系统-步同伦分析方法（SHAM）。该算法，基于修改的标准同伦分析方法（HAM），允许获得一个参数家庭的显式系列解决方案。通过使用同伦解，我们首先研究了确定性动力学中效应免疫细胞激活的动力学效应，表明增加的激活使系统通过倍周期分岔方案进入混沌动力学。然后，通过将人口统计随机性添加到同伦解中，我们表明，与确定性动力学不同，免疫细胞的激活增加有助于癌症清除，包括肿瘤细胞的灭绝和健康细胞的持久性。我们的研究结果强调了在癌症进展的早期阶段激活效应免疫细胞的疗法的重要性。
英文摘要：
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.
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