Examinando por Autor "Duarte, Jorge"

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    The role of noise in the tumor dynamics under chemotherapy treatment
    (Springer, 2021) Bashkirtseva, Irina; Ryashko, Lev; Duarte, Jorge; Seoane, Jesús M.; Sanjuán, Miguel A. F.
    Dynamical systems modeling tumor growth have been investigated to analyze the dynamics between tumor and healthy cells. Recent theoretical studies indicate that these interactions may lead to different dynamical outcomes under the effect of particular cancer therapies. In the present paper, we derive a system of nonlinear differential equations, in order to investigate solid tumors in vivo, taking into account the impact of chemotherapy on both tumor and healthy cells. We start by studying our model only in terms of deterministic dynamics under the variation of a drug concentration parameter. Later, with the introduction of noise, a stochastic model is used to analyze the impact of the unavoidable random fluctuations. As a result, new insights into noise-induced transitions are provided and illustrated in detail using techniques from dynamical systems and from the theory of stochastic processes.