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

Cristina Anton; Alan Yong; Cristina Anton; Alan Yong

doi:10.3934/mbe.2018048

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 5: 1077-1098. doi: 10.3934/mbe.2018048

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

Cristina Anton ^,,
Alan Yong

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

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.
- 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[J]. Mathematical Biosciences and Engineering, 2018, 15(5): 1077-1098. doi: 10.3934/mbe.2018048

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Abstract

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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