Open AccessStochastic dynamics and survival analysis of a cell population model with random perturbations
Author(s) -
Cristina Antón,
A. Yong
Publication year - 2018
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2018048
Subject(s) - logistic function , statistical physics , population , mathematics , monte carlo method , stationary distribution , population model , dynamics (music) , stochastic modelling , extinction (optical mineralogy) , quadratic equation , persistence (discontinuity) , stochastic dynamics , stochastic process , statistics , physics , demography , engineering , geometry , geotechnical engineering , sociology , markov chain , acoustics , optics
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.