Stochastic dynamics and survival analysis of a cell population model with random perturbations
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 a...
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| Format: | Article |
| Language: | English |
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AIMS Press
2018-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018048 |
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| author | Cristina Anton Alan Yong |
| author_facet | Cristina Anton Alan Yong |
| author_sort | Cristina Anton |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-83b7451e2ff1492aabe866b4bc31f95b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-83b7451e2ff1492aabe866b4bc31f95b2025-01-24T02:41:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-09-011551077109810.3934/mbe.2018048Stochastic dynamics and survival analysis of a cell population model with random perturbationsCristina Anton0Alan Yong1Department of Mathematics and Statistics, Grant MacEwan University, Edmonton, AB T5J 4S2, CanadaDepartment of Mathematics and Statistics, Grant MacEwan University, Edmonton, AB T5J 4S2, CanadaWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2018048stochastic logistic equationstationary distributionergodic propertyextinctionstochastic permanence |
| spellingShingle | Cristina Anton Alan Yong Stochastic dynamics and survival analysis of a cell population model with random perturbations Mathematical Biosciences and Engineering stochastic logistic equation stationary distribution ergodic property extinction stochastic permanence |
| title | Stochastic dynamics and survival analysis of a cell population model with random perturbations |
| title_full | Stochastic dynamics and survival analysis of a cell population model with random perturbations |
| title_fullStr | Stochastic dynamics and survival analysis of a cell population model with random perturbations |
| title_full_unstemmed | Stochastic dynamics and survival analysis of a cell population model with random perturbations |
| title_short | Stochastic dynamics and survival analysis of a cell population model with random perturbations |
| title_sort | stochastic dynamics and survival analysis of a cell population model with random perturbations |
| topic | stochastic logistic equation stationary distribution ergodic property extinction stochastic permanence |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018048 |
| work_keys_str_mv | AT cristinaanton stochasticdynamicsandsurvivalanalysisofacellpopulationmodelwithrandomperturbations AT alanyong stochasticdynamicsandsurvivalanalysisofacellpopulationmodelwithrandomperturbations |