Avoiding healthy cells extinction in a cancer model

López, Álvaro G.; Sabuco, Juan; Seoane, Jesús M.; Duarte, Jorge; Januário, Cristina; Sanjuán, Miguel A. F.

doi:10.1016/j.jtbi.2014.01.040

Cited by 25 publications

(20 citation statements)

References 36 publications

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“…The partial control method has been successfully applied in several situations [6,[9][10][11][12], where the control was applied on the variables of the system, and also where the control was applied on some parameter of the system [15]. The method was originally defined on maps, however it also applies well in the case of flows [12], taking a suitable discretization of the dynamics.…”

Section: Mapsmentioning

confidence: 99%

Partial control of delay-coordinate maps

2018

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Delay-coordinate maps have been widely used recently to study nonlinear dynamical systems, where there is only access to the time series of one of their variables. Here, we show how the partial control method can be applied in this kind of framework in order to prevent undesirable situations for the system or even to reduce the variability of the observable time series associated with it. The main advantage of this control method, is that it allows to control delay-coordinate maps even if the control applied is smaller than the external disturbances present in the system. To illustrate how it works, we have applied it to three well-known models in Nonlinear Dynamics with different delays such as the two-dimensional cubic map, the standard map and the three-dimensional hyperchaotic Hénon map. For the first time we show here how hyperchaotic systems can be partially controlled.

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Section: Mapsmentioning

confidence: 99%

Partial control of delay-coordinate maps

2018

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“…In biology, it has been suggested that the disappearance of chaos may be the signal of a pathological behaviour (Yang et al, 1995). In addition, there are systems where the transient dynamics evolves to an undesirable state like in Capeáns et al (2014), where after a chaotic transient behaviour, one of the species gets extinct, or in the cancer model described in López et al (2014), where the dynamics evolves towards an undesirable tumour growth.…”

Section: Introductionmentioning

confidence: 99%

“…This set is called the safe set. The partial control method has been successfully applied to several paradigmatic systems like the Hénon map or the Duffing oscillator (Sabuco et al, 2012a), as well as other models in the context of ecology or cancer dynamics (Capeáns et al, 2014;López et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

Escaping from a chaotic saddle in the presence of noise

CapeÁ¡ns

Sabuco

SanjuÁ¡n

2017

IJNDC

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Abstract:There are certain situations in noisy nonlinear dynamical systems, for which it is required a fast transition between a chaotic and a periodic state.Here, we present a novel procedure to achieve this goal in the context of the partial control method of chaotic systems. The partial control method is a recently developed control procedure, that allows to keep the dynamics of a system showing transient chaos, close to its chaotic saddle. In this kind of systems, and in absence of an external control, trajectories remain chaotic for a while in a certain region of phase space before eventually escaping towards an external attractor. The aim of the control algorithm proposed here, is to maintain the chaotic orbits as much time as we want close to the chaotic saddle before forcing an immediate escape. To do that, we use the safe sets defined in the partial control method in a completely different way. By only using this set, we show how possible is to handle the stabilisation and destabilisation of the chaotic dynamics of the partially controlled system.

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“…Motivated by the characterization of chaos provided by Itik and Banks, a collection of questions pertaining to chaotic tumor behavior in terms of symbolic dynamics and predictability as well as to the control of healthy cells behavior corresponding to physiological relevant parameter regions, have been recently addressed in Refs. [29] and [30], respectively. In fact, chaos in tumor dynamics and its property of sensitivity to initial conditions have been suggested to have numerous analogies to clinical evidences [31,32].…”

Section: Introductionmentioning

confidence: 99%

“…This key parameter is especially interesting because modulates the response of the immune system against tumor cells and, as we will show, the dynamics is especially sensitive to r 3 . Despite its importance, the dependence of the dynamics of the model under investigation on r 3 remains poorly explored (see [30] for the analysis of a narrow range of r 3 values within the framework of chaotic crises and chaos control). Moreover, the impact of this parameter on possible extinction scenarios of tumor cells due to demographic fluctuations has, as far as we know, not being investigated.…”

Section: Introductionmentioning

confidence: 99%

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

Sardanyés

Rodrigues

Januário

et al. 2015

Applied Mathematics and Computation

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In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems -the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.

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Avoiding healthy cells extinction in a cancer model

Cited by 25 publications

References 36 publications

Partial control of delay-coordinate maps

Partial control of delay-coordinate maps

Escaping from a chaotic saddle in the presence of noise

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

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