肿瘤免疫相互作用模型的数学分析：一个运动边界问题。

Mathematical analysis of a tumour-immune interaction model: A moving boundary problem.

机构信息

Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X 20, Hatfield, Pretoria 0028, South Africa.

Department of Mathematical Sciences, Stellenbosch University, Private Bag X1 Matieland, 7602, South Africa.

出版信息

Math Biosci. 2019 Feb;308:8-19. doi: 10.1016/j.mbs.2018.12.009. Epub 2018 Dec 8.

DOI:10.1016/j.mbs.2018.12.009

PMID:30537482

Abstract

A spatio-temporal mathematical model, in the form of a moving boundary problem, to explain cancer dormancy is developed. Analysis of the model is carried out for both temporal and spatio-temporal cases. Stability analysis and numerical simulations of the temporal model replicate experimental observations of immune-induced tumour dormancy. Travelling wave solutions of the spatio-temporal model are determined using the hyperbolic tangent method and minimum wave speeds of invasion are calculated. Travelling wave analysis depicts that cell invasion dynamics are mainly driven by their motion and growth rates. A stability analysis of the spatio-temporal model shows a possibility of dynamical stabilization of the tumour-free steady state. Simulation results reveal that the tumour swells to a dormant level.

摘要

我们建立了一个时空数学模型（以运动边界问题的形式）来解释癌症休眠。对该模型的时空情况分别进行了分析。对时变模型的稳定性分析和数值模拟再现了免疫诱导肿瘤休眠的实验观察结果。利用双曲正切法确定了时空模型的行波解，并计算了入侵的最小波速。行波分析表明，细胞的入侵动力学主要受其运动和生长速度的驱动。对时空模型的稳定性分析表明，肿瘤无定态的动态稳定是可能的。模拟结果表明，肿瘤会膨胀到休眠水平。