A stochastic model for cancer metastasis: branching stochastic process with settlement.

IF 0.8 4区 数学 Q4 BIOLOGY
Christoph Frei, Thomas Hillen, Adam Rhodes
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引用次数: 5

Abstract

We introduce a new stochastic model for metastatic growth, which takes the form of a branching stochastic process with settlement. The moving particles are interpreted as clusters of cancer cells, while stationary particles correspond to micro-tumours and metastases. The analysis of expected particle location, their locational variance, the furthest particle distribution and the extinction probability leads to a common type of differential equation, namely, a non-local integro-differential equation with distributed delay. We prove global existence and uniqueness results for this type of equation. The solutions' asymptotic behaviour for long time is characterized by an explicit index, a metastatic reproduction number $R_0$: metastases spread for $R_{0}>1$ and become extinct for $R_{0}<1$. Using metastatic data from mouse experiments, we show the suitability of our framework to model metastatic cancer.

肿瘤转移的随机模型:带有沉降的分支随机过程。
我们引入了一个新的转移生长随机模型,该模型采用带有沉降的分支随机过程的形式。移动的粒子被解释为癌细胞簇,而静止的粒子对应于微肿瘤和转移。通过对期望粒子位置、它们的位置方差、最远粒子分布和消光概率的分析,得到一类常见的微分方程,即具有分布延迟的非局部积分微分方程。证明了这类方程的整体存在唯一性结果。解的长期渐近性表现为一个明确的指数,即转移繁殖数$R_0$:当$R_{0}>1$时,转移扩散,而当$R_{0}时,转移消失。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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