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Título

Dynamics and bifurcations in a simple quasispecies model of tumorigenesis

AutorCastillo, Vanessa; Lázaro, J. Tomás; Sardanyés, Josep
Palabras claveApplied mathematics
Bifurcations
Cancer
Complex systems
Quasispecies dynamics
Fecha de publicaciónmar-2017
EditorSpringer
CitaciónComputational and Applied Mathematics 36(1): 415–431 (2017)
ResumenCancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behavior, at least qualitatively, also allowing us to make predictions. Here, we analyze a simplified quasispecies mathematical model given by differential equations describing the time behavior of tumor cell populations with different levels of genomic instability. We find the equilibrium points, also characterizing their stability and bifurcations focusing on replication and mutation rates. We identify a transcritical bifurcation at increasing mutation rates of the tumor cells. Such a bifurcation involves a scenario with dominance of healthy cells and impairment of tumor populations. Finally, we characterize the transient times for this scenario, showing that a slight increase beyond the critical mutation rate may be enough to have a fast response towards the desired state (i.e., low tumor populations) by applying directed mutagenic therapies.
Versión del editorhttp://dx.doi.org/10.1007/s40314-015-0234-3
URIhttp://hdl.handle.net/10261/151336
DOI10.1007/s40314-015-0234-3
ISSN0101-8205
E-ISSN1807-0302
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