A Stochastic Model for Cancer Metastasis: Branching Stochastic Process with Settlement
| Autor: | Thomas Hillen, Christoph Frei, Adam Rhodes |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Extinction probability
Stochastic modelling Differential equation Quantitative Biology::Tissues and Organs Type (model theory) Models Biological General Biochemistry Genetics and Molecular Biology Quantitative Biology::Cell Behavior Mice 03 medical and health sciences 0302 clinical medicine Cell Movement Animals Humans Applied mathematics Computer Simulation Neoplasm Invasiveness Uniqueness Neoplasm Metastasis General Environmental Science 030304 developmental biology Branching process Mathematics Pharmacology Stochastic Processes 0303 health sciences Models Statistical Extinction General Immunology and Microbiology Settlement (structural) Stochastic process Applied Mathematics General Neuroscience Computational Biology General Medicine Mathematical Concepts Neoplastic Cells Circulating 3. Good health Distribution (mathematics) Modeling and Simulation 030220 oncology & carcinogenesis Algorithms |
| DOI: | 10.1101/294157 |
| Popis: | 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-tumors 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 behavior for long time is characterized by an explicit index, a metastatic reproduction number R0: metastases spread for R0 > 1 and become extinct for R0 < 1. Using metastatic data from mouse experiments, we show the suitability of our framework to model metastatic cancer. |
| Databáze: | OpenAIRE |
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