膀胱癌治疗模型中卡介苗感染延迟免疫反应的随机扰动稳定性分析
Stability Analysis of Delayed Immune Response BCG Infection in Bladder Cancer Treatment Model by Stochastic Perturbations.
作者信息
Shaikhet Leonid, Bunimovich-Mendrazitsky Svetlana
机构信息
Department of Mathematics, Ariel University, Ariel 40700, Israel.
出版信息
Comput Math Methods Med. 2018 Jul 9;2018:9653873. doi: 10.1155/2018/9653873. eCollection 2018.
Abstract
We present a revised mathematical model of the immune response to Bacillus Calmette-Guérin (BCG) treatment of bladder cancer, optimized according to biological and clinical data accumulated during the last decade. The improved model accounts for cytotoxic T lymphocyte differentiation as an integral element of the delayed immune response, as well as the logistic growth terms for cancer cell proliferation. Three equilibria are demonstrated for the proposed model, which is assumed to be influenced by white noise stochastic perturbations that are directly proportional to the system state deviation from an equilibrium. Stability conditions for all equilibria are analyzed using the Kolmanovskii-Shaikhet general method of Lyapunov functionals construction.
摘要
我们提出了一种经修订的针对卡介苗（BCG）治疗膀胱癌的免疫反应数学模型，该模型根据过去十年积累的生物学和临床数据进行了优化。改进后的模型将细胞毒性T淋巴细胞分化视为延迟免疫反应的一个组成部分，同时考虑了癌细胞增殖的逻辑斯蒂增长项。针对所提出的模型证明了三个平衡点，该模型假定受与系统状态偏离平衡点成正比的白噪声随机扰动影响。使用科尔马诺夫斯基 - 沙伊赫特构建李雅普诺夫泛函的一般方法分析了所有平衡点的稳定性条件。
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