Stochastic dynamics and survival analysis of a cell population model with random perturbations

  • Received: 22 March 2017 Accepted: 06 April 2018 Published: 01 October 2018
  • MSC : Primary: 37H10, 60J70; Secondary: 60H10

  • We consider a model based on the logistic equation and linear kinetics to study the effect of toxicants with various initial concentrations on a cell population. To account for parameter uncertainties, in our model the coefficients of the linear and the quadratic terms of the logistic equation are affected by noise. We show that the stochastic model has a unique positive solution and we find conditions for extinction and persistence of the cell population. In case of persistence we find the stationary distribution. The analytical results are confirmed by Monte Carlo simulations.

    Citation: Cristina Anton, Alan Yong. Stochastic dynamics and survival analysis of a cell population model with random perturbations[J]. Mathematical Biosciences and Engineering, 2018, 15(5): 1077-1098. doi: 10.3934/mbe.2018048

    Related Papers:

  • We consider a model based on the logistic equation and linear kinetics to study the effect of toxicants with various initial concentrations on a cell population. To account for parameter uncertainties, in our model the coefficients of the linear and the quadratic terms of the logistic equation are affected by noise. We show that the stochastic model has a unique positive solution and we find conditions for extinction and persistence of the cell population. In case of persistence we find the stationary distribution. The analytical results are confirmed by Monte Carlo simulations.


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