Some classes of stochastic differential equations as an alternative modeling approach to biomedical problems. (English) Zbl 1311.37039
Kloeden, Peter E. (ed.) et al., Nonautonomous dynamical systems in the life sciences. Cham: Springer (ISBN 978-3-319-03079-1/pbk; 978-3-319-03080-7/ebook). Lecture Notes in Mathematics 2102. Mathematical Biosciences Subseries, 269-307 (2013).
Stochastic differential equations (SDEs) provide an appropriate framework for the modelling of biomedical problems, allowing a detailed presentation about kinetics of biochemical tools and their influence on the illness current and taking into account the “noise” effects. In this work the potential of some classes of SDEs in modelling several problems from biology and medicine is presented. Three applications of modelling with SDEs and SDE-like processes are considered: they are related to intracellular signaling pathway, to radio-oncological treatments and to cell dispersal. For the last of them the modelling via SDEs or simply via stochastic processes offers an alternative to the partial integro-differential approach enabling to numerically handle complex, more realistic (even multiscale) situations which cannot be treated in the PDE framework.
For the entire collection see [Zbl 1282.37004].
For the entire collection see [Zbl 1282.37004].
Reviewer: Irina V. Konopleva (Ul’yanovsk)
MSC:
| 37H10 | Generation, random and stochastic difference and differential equations |
| 92C40 | Biochemistry, molecular biology |
| 92C50 | Medical applications (general) |
Keywords:
cell dispersal; intracellular signaling pathways; nonparametric estimation; stochastic differential equations; stochastic processes; tumor control probabilityReferences:
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