Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response

Fiasconaro, Alessandro; Spagnolo, Bernardo; Ochab-Marcinek, Anna; Gudowska–Nowak, Ewa

doi:10.1103/physreve.74.041904

Cited by 120 publications

(85 citation statements)

References 44 publications

(89 reference statements)

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“…[17][18][19][20][21][22]26]. The occurrence of the RA together with other stochastic effects such as noise-enhanced stability [12,20,[27][28][29] and stochastic resonance [30] have been also investigated [11][12][13][14]19,20]. The RA effect is characterized by the strong correlation between the mean time of the potential fluctuations and the crossing time over the barrier, and it is totally different from the dynamic resonance requiring the matching between the driving frequency and the natural * afiascon@unizar.es † http://gip.dft.unipa.it frequency of the system [31].…”

Section: Introductionmentioning

confidence: 99%

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Resonant activation in piecewise linear asymmetric potentials

Fiasconaro

Spagnolo

2011

Phys. Rev. E

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This work analyzes numerically the role played by the asymmetry of a piecewise linear potential, in the presence of both a Gaussian white noise and a dichotomous noise, on the resonant activation phenomenon. The features of the asymmetry of the potential barrier arise by investigating the stochastic transitions far behind the potential maximum, from the initial well to the bottom of the adjacent potential well. Because of the asymmetry of the potential profile together with the random external force uniform in space, we find, for the different asymmetries: (1) an inversion of the curves of the mean first passage time in the resonant region of the correlation time τ of the dichotomous noise, for low thermal noise intensities; (2) a maximum of the mean velocity of the Brownian particle as a function of τ ; and (3) an inversion of the curves of the mean velocity and a very weak current reversal in the miniratchet system obtained with the asymmetrical potential profiles investigated. An inversion of the mean first passage time curves is also observed by varying the amplitude of the dichotomous noise, behavior confirmed by recent experiments.

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Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][23][24][25] and experimentally revealed in Refs. [17][18][19][20][21][22]26].…”

Section: Introductionmentioning

confidence: 99%

Resonant activation in piecewise linear asymmetric potentials

Fiasconaro

Spagnolo

2011

Phys. Rev. E

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“…Meanwhile, if we consider the external environmental fluctuations (e.g., temperature, the dosage of the medicine in chemotherapy, the intensity of the ray in radiotherapy), the immune rate β can be rewritten as β + ( ) + A cos ω , where A and ω are the amplitude and frequency of the periodic signal, respectively. Likewise, a fluctuation of tumor cell population is inevitable, which behaves in the form of additive noise [15]. As a result, we get…”

Section: The Snrmentioning

confidence: 86%

“…to explain periodic recurrences of the earth's ice has attracted much attention [15][16][17][18][19][20]. There are several mathematical functions for describing tumor growth, such as the logistic model [21], Eden model [22] and Gompertzian growth model [23].…”

Section: Introductionmentioning

confidence: 99%

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

et al. 2014

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Abstract:The phenomenon of stochastic resonance (SR) in a tumor growth model under the presence of immune surveillance is investigated. Time delay and cross-correlation between multiplicative and additive noises are considered in the system. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced multiplicatively. Our results show that: (i) the time delay can accelerate the transition from the state of stable tumor to that of extinction, however the correlation between two noises can accelerate the transition from the state of extinction to that of stable tumor; (ii) the time delay and correlation between two noises can lead to a transition between SR and double SR in the curve of SNR as a function of additive noise intensity, however for the curve of SNR as a function of multiplicative noise intensity, the time delay can cause the SR phenomenon to disappear, and the cross-correlation between two noises can lead to a transition from SR to stochastic reverse-resonance. Finally, we compare the SR phenomenon for the multiplicative periodic signal with that for additive periodic signal in the tumor growth model with immune surveillance. PACS

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“…Therefore it is crucial to find the optimal range of parameters in which the positive role of resonant activation phenomenon, with respect to the cancer extinction, prevails over the negative role of NES, which enhances the stability of the tumoral state. These are just the main results of the paper [13], that is both NES and RA phenomena are revealed in a biological system with a metastable state, with a co-occurrence region of these effects (see Fig. 8).…”

Section: Cancer Growth Dynamicsmentioning

confidence: 97%

Enhancement of stability in systems with metastable states

Spagnolo¹,

Augello²,

Fiasconaro³

et al. 2007

AIP Conference Proceedings

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Abstract.The investigation of noise-induced phenomena in far from equilibrium systems is one of the approach used to understand the behaviour of physical and biological complex systems. Metastability is a generic feature of many nonlinear systems, and the problem of the lifetime of metastable states involves fundamental aspects of nonequilibrium statistical mechanics. The enhancement of the lifetime of metastable states through the noise enhanced stability effect and the role played by the resonant activation phenomenon will be discussed in models of interdisciplinary physics: (i) Ising model (ii) Josephson junction; (iii) stochastic FitzHugh-Nagumo model; (iv) a population dynamics model, and (v) a market model with stochastic volatility.

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Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response

Cited by 120 publications

References 44 publications

Resonant activation in piecewise linear asymmetric potentials

Resonant activation in piecewise linear asymmetric potentials

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

Enhancement of stability in systems with metastable states

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