2024-03-19T01:40:48Zhttp://digital.csic.es/dspace-oai/requestoai:digital.csic.es:10261/1513362017-07-05T12:17:13Zcom_10261_9676com_10261_8col_10261_9677
00925njm 22002777a 4500
dc
Castillo, Vanessa
author
Lázaro, J. Tomás
author
Sardanyés, Josep
author
2017-03
Cancer 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.
Computational and Applied Mathematics 36(1): 415–431 (2017)
0101-8205
http://hdl.handle.net/10261/151336
10.1007/s40314-015-0234-3
1807-0302
http://dx.doi.org/10.13039/501100000780
http://dx.doi.org/10.13039/501100004837
http://dx.doi.org/10.13039/501100002809
http://dx.doi.org/10.13039/501100006373
Applied mathematics
Bifurcations
Cancer
Complex systems
Quasispecies dynamics
Dynamics and bifurcations in a simple quasispecies model of tumorigenesis