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Limits of Applicability for the Deterministic Approximation of the Two‐Step Clonal Expansion Model
Author(s) -
Heidenreich Wolfgang F.,
Hoogenveen Rudolf
Publication year - 2001
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/0272-4332.211093
Subject(s) - constant (computer programming) , simplicity , hazard , mathematics , exact solutions in general relativity , division (mathematics) , computer science , mathematical analysis , physics , chemistry , arithmetic , organic chemistry , quantum mechanics , programming language
Motivated by a hypothesis published recently, the limits of applicability of the deterministic approximation of the two‐step clonal expansion model are investigated. The approximate hazard increases unlimited, while the exact hazard is approaching a constant value. The approximate solution becomes inapplicable for hazards in the order of that constant rate. When the initiation rate is much larger than the cell division rate, the survival rate is small when the approximation becomes inapplicable. The simplicity of the exact solutions suggests using them in all situations.