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bioRxiv · 10.1101/294157

A Stochastic Model for Cancer Metastasis: Branching Stochastic Process with Settlement

Frei, C.·Hillen, T.·Rhodes, A.
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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-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.

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Frei, C., Hillen, T., Rhodes, A.. 2018-04-03. A Stochastic Model for Cancer Metastasis: Branching Stochastic Process with Settlement. https://doi.org/10.1101/294157

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