Pure Multiplicative Noises Induced Population Extinction in an Anti-tumor Model under Immune Surveillance

Wang, Can-Jun; Li, Di; Dong-Cheng, Mei

doi:10.1088/0253-6102/52/3/16

Cited by 13 publications

(2 citation statements)

References 53 publications

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“…However, to the leading order in the correlation time, an approximate approach to the Markovian Fokker-Planck equation can be found [3,4]. The study of complex biological and physical systems driven by colored noise have been given much attention in the recent decades [5][6][7][8][9]. Moreover, Transitions in a logistic growth model induced by noise coupling and noise color shows some interesting behavior [10].…”

Section: Introductionmentioning

confidence: 99%

Effect of tumor microenvironmental factors on the steady state of tumor growth with non-zero correlation time

Idris¹,

Bakar²

2016

ams

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The effect of non-immunogenic tumor microenvironmental factors on the steady state tumor growth dynamics modeled by multiplicative colored noise is investigated. Using the Novikov theorem and Fox approach, an approximate Fokker-Planck equation for the non-Markovian stochastic model is obtained and analytic expression for the steady state distribution P st (x) is derived. We find that the strength of the tumor response to the microenvironmental factors effect θ reduces the value of the steady state distribution P st (x) of tumor growth at weak correlation time τ which is an inhibitive effect, and at strong correlation time the inhibitive effect is suppressed and instead the value of the steady state distribution is increased which corresponds to growth enhancement. The result indicated that the growth effect exerted by the non-immunogenic tumor microenvironmental factors on tumor growth depend on the correlation time strength τ of the tumor response.

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Section: Introductionmentioning

confidence: 99%

Effect of tumor microenvironmental factors on the steady state of tumor growth with non-zero correlation time

Idris¹,

Bakar²

2016

ams

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“…Logistic growth model is one of the classical examples of self-organization in many natural and artificial systems [5], which was introduced by Verhulst for saturated proliferation at a single-species [6], and has been extended to include spatial dynamics by Fisher [7] and by Kolmogoroff et al [8]. Much attention has been paid to the statistical properties of the logistic growth model with noises.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Resonance in a Time-Delayed Logistic Growth Model Driven by Periodic Signal and White Noise

Zhou

Fang

2011

AMM

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stochastic resonance; time-delayed Logistic growth model; signal-to-noise ratio Abstract. The stochastic resonance in a time-delayed Logistic growth model subject to correlated multiplicative and additive white noise as well as to multiplicative periodic signal is investigated. Using small time delay approximation, we get the expression of the signal-to-noise ratio (SNR). It is found that the SNR is a non-monotonic function of the system parameters, of the intensities of the multiplicative and additive noise, as well as of the correlation strength between the two noises. The effects of the delay time in the random force is in opposition to that of the delay time in the deterministic force.

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Effect of Tumor Microenvironmental Factors on the Stability of Tumor Growth Dynamics with Nonzero Correlation Time

Idris

Bakar

2016

Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015)

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The effect of tumor microenvironmental factors on tumor growth dynamics modeled by multiplicative colored noise is investigated. Using the Novikov theorem and Fox approach, an approximate Fokker-Planck equation for the non-Markovian stochastic equation is obtained and an analytic expression for the steady-state probability distribution Pst(x) is derived. We found that the strength of the microenvironmental factors θ have a negative effect on the stability of tumor growth at weak correlation time τ and at strong correlation time, the effect of θ is opposed and instead a positive growth stability is noticed for the tumor growth dynamics which in other words corresponds to growth effect. The result indicated that the growth effect exerted by the non-immunogenic components of tumor microenvironmental depend on the strength of the correlation time τ.

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Pure Multiplicative Noises Induced Population Extinction in an Anti-tumor Model under Immune Surveillance

Cited by 13 publications

References 53 publications

Effect of tumor microenvironmental factors on the steady state of tumor growth with non-zero correlation time

Effect of tumor microenvironmental factors on the steady state of tumor growth with non-zero correlation time

Stochastic Resonance in a Time-Delayed Logistic Growth Model Driven by Periodic Signal and White Noise

Effect of Tumor Microenvironmental Factors on the Stability of Tumor Growth Dynamics with Nonzero Correlation Time

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