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

. Department of Mathematics and Statistics, Grant MacEwan University, Edmonton, AB T5J 4S2, Canada

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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Keywords Stochastic logistic equation; stationary distribution; ergodic property; extinction; stochastic permanence

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


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