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Title: Numerical schemes and algorithms for branching processes models in cancer Authors:  Maroussia Slavtchova-Bojkova - Sofia University (Bulgaria) [presenting]
Kaloyan Vitanov - Sofia University (Bulgaria)
Abstract: A special class of reducible multi-type branching processes in continuous time is proposed as a powerful tool for studying the mutations in cancer cell populations. This model turns out to be useful for studying the dynamics of the number of different types of cells, which due to a small reproduction ratio are fated to become extinct. However, mutations occurring during the reproduction process, may lead to the appearance of a new type of cells that may escape extinction. We were deriving the limit distributions of the numbers of mutations of the escape type up to time t and in the whole process. A cell of the mutation type, which leads possibly to the beginning of a lineage, that will never become extinct is called successful mutant. These asymptotic results are used for developing numerical schemes and algorithms implemented in Python via the NumPy package for approximate calculation of the corresponding quantities. In conclusion, our conjecture is that this methodology can be advantageous in revealing the role of the lifespan distribution of the cancer cells in the context of cancer disease evolution and other complex cell population systems, in general.